Design recommendations against progressive collapse in steel and steel-concrete buildings

2021 2021 DESIGN RECOMMENDATIONS AGAINST PROGRESSIVE COLLAPSE IN STEEL AND STEEL-CONCRETE BUILDINGS steelconstruct.com/eu-projects/failnomore/ linkedin.com/company/failnomore/ researchgate.net/project/FAILNOMORE… D3-1: Design recommendations against progressive collapse in steel and steel-concrete buildings December 2021 List of contributors: University of Liège Jean Francois DEMONCEAU, Tudor GOLEA and Jean Pierre JASPART Imperial College London Ahmed ELGHAZOULI and Zeyad KHALIL University of Coimbra Aldina SANTIAGO, Ana Francisca SANTOS and Luís SIMÕES DA SILVA University of Stuttgart Ulrike KUHLMANN and Georgios SKARMOUTSOS University of Trento Nadia BALDASSINO, Riccardo ZANDONINI, Martina BERNARDI and Marco ZORDAN Politehnica University Timisoara Florea DINU, Ioan MARGINEAN, Dominiq JAKAB and Dan DUBINA Feldmann + Weynand GmbH Freddy WERTZ and Klaus WEYNAND ArcelorMittal Belval & Differdange S.A. Renata OBIALA, Miguel CANDEIAS, Marion CHARLIER and Omer ANWAAR This project has received funding from the Research Fund for Coal and Steel under grant agreement No 899371 D3-1%% Mitigation of the risk of progressive collapse in steel and composite building frames under exceptional events FAILNOMORE!* FAILNOMORE D3-1: Design recommendations against progressive collapse in steel and steel-concrete buildings 1st Edition, December 2021 Published by: ECCS – European Convention for Constructional Steelwork [email protected] www.steelconstruct.com All rights reserved. No parts of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, re-cording or otherwise, without the prior permission of the copyright owner ECCS assumes no liability regarding the use for any application of the material and information contained in this publication. Copyright © 2021 ECCS – European Convention for Constructional Steelwork ISBN: 978-92-9147-172-0 Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 3 TABLE OF CONTENTS Table of contents Acknowledgement .................................................................................................................................. 7 Definitions ............................................................................................................................................... 9 Introduction .......................................................................................................................................... 11 Part 1 – Design for Robustness ............................................................................................................ 13 1 Normative context ........................................................................................................................ 13 1.1 Overview ............................................................................................................................... 13 1.2 Robustness requirements in Eurocodes ................................................................................ 13 1.2.1 Basic principles .............................................................................................................. 13 1.2.2 Design situations ........................................................................................................... 13 1.2.3 Consequence classes ..................................................................................................... 14 1.3 Robustness strategies ........................................................................................................... 14 1.3.1 General .......................................................................................................................... 14 1.3.2 Strategies based on identified accidental actions ......................................................... 14 1.3.3 Strategies based on limiting the extent of localised failure .......................................... 15 1.4 Current normative developments ......................................................................................... 15 1.5 Concluding remarks ............................................................................................................... 17 2 Design for robustness ................................................................................................................... 19 2.1 Design strategies ................................................................................................................... 19 2.1.1 Introduction .................................................................................................................. 19 2.1.2 General design philosophies ......................................................................................... 19 2.1.3 Design for well-identified accidental actions ................................................................ 19 2.1.4 Design for unidentifiable accidental actions ................................................................. 20 2.2 Importance of structural joints in the design for robustness ................................................ 22 2.2.1 Classical design at SLS and ULS ...................................................................................... 22 2.2.2 Design of joints under exceptional events .................................................................... 23 2.2.3 Minimum ductility requirements for structural joints .................................................. 24 3 Consequence classes ..................................................................................................................... 31 4 Identified threats .......................................................................................................................... 33 4.1 Introduction .......................................................................................................................... 33 4.2 Impact ................................................................................................................................... 33 4.2.1 Prevent/eliminate hazard .............................................................................................. 33 4.2.2 Explicit design ................................................................................................................ 34 4.3 Explosion ............................................................................................................................... 36 4.3.1 Prevent/eliminate hazard .............................................................................................. 37 4.3.2 External explosion – Explicit design .............................................................................. 38 4 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings TABLE OF CONTENTS 4.3.3 Internal gas explosion - Explicit design .......................................................................... 44 4.4 Fire as exceptional event ...................................................................................................... 46 4.4.1 Prevent/eliminate hazard .............................................................................................. 46 4.4.2 Design strategy .............................................................................................................. 47 4.5 Earthquake as exceptional event .......................................................................................... 49 4.5.1 Prevent/eliminate hazard .............................................................................................. 50 4.5.2 Prescriptive approach ................................................................................................... 50 4.5.3 Design strategies ........................................................................................................... 51 5 Unidentified threats ...................................................................................................................... 53 5.1 Selection of appropriate design strategies ............................................................................ 53 5.2 Identification of local damages ............................................................................................. 53 5.3 Alternative load path methods ............................................................................................. 55 5.3.1 Prescriptive methods .................................................................................................... 59 5.3.2 Analytical methods ........................................................................................................ 65 5.3.3 Simplified numerical approaches .................................................................................. 74 5.3.4 Full numerical approach ................................................................................................ 80 5.3.5 Prediction of the dynamic response from the static one .............................................. 83 5.4 Key element method ............................................................................................................. 84 5.5 Segmentation method .......................................................................................................... 85 5.5.1 Weak segment borders ................................................................................................. 86 5.5.2 Strong segment borders ................................................................................................ 86 6 Risk assessment ............................................................................................................................ 87 7 Conclusions ................................................................................................................................... 89 Part 2 – Worked examples ................................................................................................................... 91 8 Introduction .................................................................................................................................. 91 8.1 General .................................................................................................................................. 91 8.2 Geometry and structural systems proposed for investigation .............................................. 93 8.3 Actions, combination of actions ............................................................................................ 94 8.4 Design requirements and output .......................................................................................... 94 8.5 Joints ................................................................................................................................... 101 8.5.1 SS/NS ........................................................................................................................... 101 8.5.2 CS/NS ........................................................................................................................... 102 8.5.3 SS/S and CS/S .............................................................................................................. 102 8.6 Comments on the final selection of the worked example structures ................................. 103 8.6.1 Seismic vs. non-seismic ............................................................................................... 103 8.6.2 Steel vs. composite ...................................................................................................... 105 8.7 Identified exceptional events .............................................................................................. 106 Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 5 TABLE OF CONTENTS 8.7.1 Impact ......................................................................................................................... 106 8.7.2 Blast analysis ............................................................................................................... 119 8.7.3 Localised fire analysis .................................................................................................. 141 8.7.4 Seismic analysis ........................................................................................................... 143 8.8 Unidentified exceptional events ......................................................................................... 148 8.8.1 Prescriptive approach (tying method) ......................................................................... 148 8.8.2 Key element method ................................................................................................... 161 8.8.3 Segmentation method ................................................................................................ 165 8.8.4 Alternate load path method ........................................................................................ 166 8.9 Conclusions for worked examples ....................................................................................... 202 Part 3 – Annexes ................................................................................................................................. 205 A.1 Design resistance of joints under combined bending moments and axial forces ................... 205 A.1.1 Resistance criteria with due account of group effects ........................................................ 205 A.1.2 Definition of the failure criterion for the whole connection ............................................... 206 A.2 Detailing requirements to allow sufficient rotation capacity of simple joints ........................ 208 A.2.1 Joints with a header plate ................................................................................................... 208 A.2.2 Joints with a fin plate .......................................................................................................... 209 A.3 Specific ductility recommendations for partial-strength steel and composite bolted joints with endplates ............................................................................................................................................ 211 A.3.1 Application of the simplified method (Rölle, 2013) ............................................................ 213 A.4 Evaluation of the plastic rotational capacity of joints at ULS .................................................. 215 A.4.1 General principles and method ........................................................................................... 215 A.4.2 Simplified method of Keller for the deformation capacity of composite joints .................. 216 A.5 Resistance of joints under tension .......................................................................................... 220 A.5.1 Simple joints under tension ................................................................................................ 220 A.5.1.1 General data for connections with header plate, fin plate or web cleats ........................... 220 A.5.1.2 Particular notations for header plate connections ............................................................. 221 A.5.1.3 Particular notations for fin plate connections ..................................................................... 222 A.5.1.4 Particular notations for cleat web connections .................................................................. 222 A.5.1.5 Tying resistance of header plate connections ..................................................................... 224 A.5.1.6 Tying resistance of fin plate connections ............................................................................ 225 A.5.1.7 Tying resistance of connections with web cleats ................................................................ 226 A.5.2 Partial-strength joints and column splices under tension ................................................... 226 A.5.3 Simplified method for the characterisation of steel or composite joints with bolted endplates under axial force ................................................................................................................................. 226 A.6 Tabular tools for response estimation of SDOF systems ......................................................... 227 A.6.1 Transformation factors for beams and one-way slabs ........................................................ 227 6 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings TABLE OF CONTENTS A.6.2 Maximum deflection and maximum response time of elasto-plastic SDOF systems ......... 229 A.7 Simplified analytical method for 3D structures with simple joints ......................................... 231 A.8 Advanced analytical approach ................................................................................................ 232 Part 4 – References ............................................................................................................................. 237 Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 7 ACKNOWLEDGEMENT Acknowledgement The present document has been prepared in the framework of a European project with a financial grant from the Research Fund for Coal and Steel of the European Community (FAILNOMORE project - Grant N° 899371) which is greatly thanked. 14 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 1. NORMATIVE CONTEXT 1.2.3 Consequence classes The design strategies for accidental design situations to meet the robustness requirements are based on the consequence class of the structure. The proposed classification in Annex A of EN 1991-1-7 categorises buildings into four consequence classes (CC) considering the building type, occupancy, and size. In EN 1990 and EN 1991-1-7, Cl 3.4, only three consequence classes are identified. However, in Annex A of EN 1991-1-7, Table A.1, Consequence Class 2 is subdivided into CC2a (medium consequences-lower risk group) and CC2b (medium consequences-upper risk group), with the other classes being CC1 (low consequences of failure) and CC3 (high consequences). More details regarding the consequence class of buildings as adopted herein can be found in Section 3. 1.3 Robustness strategies 1.3.1 General As stipulated in EN 1991-1-7, the strategy adopted for hazard mitigation and the design of structures for accidental actions would depend on whether the accidental actions are identified or unidentified as summarised in Figure 1. Figure 1. Robustness strategies for accidental design situations in (EN 1991-1-7, 2006) 1.3.2 Strategies based on identified accidental actions EN 1991-1-7, 3.2 states that when accidental actions are identified and taken into account, the following factors should be also considered: (i) the measures taken for preventing or reducing the severity of an accidental action; (ii) the probability of occurrence of the identified accidental action; (iii) the consequences of failure due to the identified accidental action; (iv) public perception; (v) the level of acceptable risk. It also states that under such actions, localised failure may be acceptable provided it will not endanger the stability of the whole structure, and that the overall load-bearing capacity of the structure is maintained and allows necessary emergency measures to be taken. Additionally, it emphasises that measures should be taken to mitigate the risk of accidental actions and these measures should include, as appropriate, one or more of the following strategies: (i) preventing the action from occurring or reducing the probability and/or magnitude of the action to an acceptable level through the structural design process; (ii) protecting the structure against the effects of an accidental action by reducing the effects of the action on the structure; (iii) ensuring that the Accidental design situation Strategies based on identified accidental actions (e.g. explosions and impact) Strategies based on limiting the extent of localised failure Design the structure to have sufficient minimum robustness Preventing or reducing the action (e.g. protective measures) Design the structure to sustain the action Enhanced redundancy (e.g. alternative load paths) Key element designed to sustain notional accidental action Ad Prescriptive rules (e.g. integrity and ductility) Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 15 1.4 CURRENT NORMATIVE DEVELOPMENTS structure has sufficient robustness by adopting one or more of the following approaches: a) designing certain components of the structure, upon which stability depends, as key elements to increase the likelihood of the structure survival following an accidental event; b) designing structural members, and selecting materials, to have sufficient ductility capable of absorbing significant strain energy without rupture; c) incorporating sufficient redundancy in the structure to facilitate the transfer of actions to alternative load paths following an accidental event. The notional values for identified accidental actions (e.g., in the case of impact or internal explosion) are proposed in EN 1991-1-7. These values may be changed in the National Annex for individual countries or for a specific project and agreed in the design by the relevant authority and the client. 1.3.3 Strategies based on limiting the extent of localised failure Strategies based on limiting the extent of localised failure cover a wide range of possible events and are mostly related to unidentified accidental actions. The adoption of strategies for limiting the extent of localised failure may provide adequate robustness against other accidental actions apart from those covered by EN 1991-1-7 (e.g., external explosions and terrorist attacks) or any other actions resulting from unspecified causes. For most building structures, potential accidental actions are mostly unidentified, hence designing structures for such situations would involve robustness strategies largely based on limiting the extent of failure using one of the following approaches, as stated in EN 1991-17, Cl 3.3: (i) designing key elements, on which the stability of the structure depends, to sustain the effects of a representation of accidental action; (ii) in the event of localised failure, such as failure of a single primary member, the stability of the structure or a significant part of it is not endangered; (iii) applying prescriptive design and detailing rules that provide acceptable robustness for the structure. Such strategies include prescriptive tying force methods, alternative load paths methods and key element design methods. They aim to provide an acceptable level of robustness to sustain localised failure without a disproportionate level of collapse. Annex A of EN 1991-1-7 further details the application of such strategies to the different building categories. More stringent requirements are recommended going from CC1 to CC3, reflecting the increased level of risk due to structural collapse. Both EN 1993 and EN 1994 provide recommendations which may be either directly or indirectly relevant to the design and detailing for robustness, including information related to the ductility and rotation capacity of beams and partial-strength joints, amongst others. Various robustness requirements also exist in other international guidelines. These include, but are not limited to: the Unified Facilities Criteria (UFC): Design of Buildings to Resist Progressive Collapse (UFC 4-023-03, developed by USA Department of Defense (DoD, 2016), the USA General Services Administration (GSA, 2016) Alternate Path Analysis and design guidelines, recommendations included within ASCE 7-16 (ASCE, 2017b) and the International Building Code (IBC) (ICC, 2018), in addition to the stipulations in the UK Building Regulations 2010 Approved Document A (ODPM, 2013) as well as the Chinese Code for Anti-Collapse Design of Building Structures (CECS 392) (CECS, 2014). As mentioned before, these provisions are referred to where necessary in other parts of this document, and are described in more detail in the background document (Demonceau et al., 2021). 1.4 Current normative developments The current draft revision of EN 1990 (prEN 1990, 2019) for the forthcoming second generation of Eurocodes introduces Section 4.4 and Informative Annex E, which are exclusively dedicated to structural robustness. Section 4.4 states that: “A structure should be designed to have an adequate 16 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 1. NORMATIVE CONTEXT level of robustness so that, during its design service life it will not be damaged by adverse and unforeseen events, such as the failure or collapse of a structural member or part of a structure, to an extent disproportionate to the original cause”. It also notes that for most structures, design in accordance with the Eurocodes provides an adequate level of robustness without the need for any additional design measures to enhance structural robustness; if such measures are needed, it should be specified by the relevant authority or agreed for a specific project by the relevant parties. On the other hand, Annex E of the draft EN 1990 gives informative guidance for enhancing the robustness of buildings and bridges. It provides strategies based on limiting the extent of damage, while the explicit design of structures for identified accidental action is covered within the scope of EN 1991. The proposed robustness strategies follow the typical methods discussed above, with the addition of a “Segmentation Strategy”. To this end, Table E.1 in Annex E gives recommendations for indicative design methods for enhancing robustness for consequence classes CC1, CC2 and CC3. It is also worth noting that the new EN 1990 adds two more consequence classes, CC0 and CC4. CC4 is considered to have extreme risk of loss of human life or personal injury and a considerable economic, social or environmental risk. The provisions in the Eurocodes do not entirely cover design rules needed for structures classified as CC4. For these structures, additional provisions to those given in the Eurocodes may be needed. On the other side, CC0 has the lowest risk, where either the Eurocodes or alternative provisions may be used and where elements other than structural may be classified as CC0. Therefore, the provisions in Eurocodes mainly cover design rules for structures classified as CC1 to CC3. Figure 2. Design strategies for identified accidental actions and for general enhanced robustness according to (prEN 1990, 2019) In addition to the proposed revisions in EN 1990 (prEN 1990, 2019), there are developments within EN 1993 and EN 1998 which may be of direct and indirect relevance to the satisfaction of the robustness requirements. These include guidance on the rotation capacity assessments in beams and joints in EN 1993, as well as the provision of load-deformation relationships for steel and composite steel-concrete components for nonlinear static (pushover) analysis in EN 1998. These provisions are referred to where Design for accidental actions (EN 1991) Explicit design of the structure (e.g. against explosion, impact) Design for enhanced robustness (EN 1990) Strategies based on limiting the extent of damage Design structure to resist the action (*) Prevent or reduce the action e.g. protective measures, control of events Alternative load paths either providing adequate deformation capacity and ductility or applying prescriptive design rules Key members i.e. designing selected members to resist notional action(s) Segmentation i.e. separation into parts (*) Structural design against identified accidental actions can incorporate specifically designed members, which fail partially or fully, provided their failure does not lead to further structural collapse as agreed with authorities. Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 17 1.5 CONCLUDING REMARKS necessary in other parts of this document, and are described and critically assessed in more detail in the background document (Demonceau et al., 2021). 1.5 Concluding remarks The present chapter has highlighted the requirements and available strategies for robustness design as currently stipulated and proposed in the Eurocodes. Although design for robustness is normatively approached through the general principles available in EN 1990 and EN 1991-1-7, no consistent set of rules is available. Key parameters for the performance of design for robustness, such as those required from the system and available from local ductility, require further treatments, guidance, and clarifications in normative design. More generally, despite the presence of a substantial body of research dealing with robustness in various structural forms, at both the overall and local level, there is a need to transfer this knowledge into simplified methods and tools to the engineering practice. This document therefore aims at distilling information available from recent research studies on steel and composite framed structures in the form of design provisions ranging from detailed to simplified, for the benefit of different levels of practical design, which are supported and illustrated by a number of realistic design case studies. Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 19 2.1 DESIGN STRATEGIES 2 Design for robustness 2.1 Design strategies 2.1.1 Introduction In order to comply with the requirements set by the current design standards (Section 1), the design for structural robustness is proposed herein as a step-by-step procedure relying on the consequences class of the building, the nature of accidental action to be considered and the structural layout of the building. This procedure is readily organised in a general flowchart that reflects the design process to be followed as shown in Figure 3. This flowchart can be seen as the backbone of the present design manual and will be comprehensively presented in this section. More insightful details on the approaches and procedures to be applied throughout the design process will be then addressed in the following chapters. 2.1.2 General design philosophies EN 1991-1-7 (2006) prescribes the avoidance or limitation of potential damages in accidental scenarios by preventing or reducing the accidental action, by protecting the structure against the effects of the accidental action (through adequate protective systems), or by designing the structure to withstand the accidental action or its effects. These measures lead consequently either to a low probability of hazard occurrence or to a robust structure that resists the accidental action by limiting the propagation of the initial damage. Following closely the guidelines of EN 1991-1-7, the naturally suggested starting point in the design for robustness is the identification of consequences class of the building under consideration (Box A.1 in Figure 3). The consequences class of the building allows the practitioner to assess the design approach to be adopted in view of achieving an adequate level of robustness. For instance, the design for robustness of a low consequences of failure class (CC1) doesn’t imply any specific considerations as long as the design is carried out in full compliance with the rules given in the suite of Eurocodes (EN 1990 to EN 1999). On the other hand, for buildings with higher consequences of failure, such as those identified as CC2 and CC3, the design for robustness implies specific approaches which could range from simple prescriptive rules to advanced risk analyses and complex analytical or numerical methods. More details about the definition of the consequences classes are provided in Section 3. Once the consequences class is established, the potential threats and the relevant accidental loading scenarios shall be identified by the designer in close collaboration with the client and the relevant authorities. Consequently, the identification of potential threats enables the practitioner to plead either for an explicit design for a specific identifiable accidental action (Boxes B in Figure 3) and/or for a design strategy that limits the extent of initial damage arose as a consequence of any unidentifiable accidental event (Boxes C in Figure 3). For buildings with high consequences of failure (CC3), a systematic risk assessment is generally required to identify the accidental scenarios that are most likely to occur during the life span of the structure (see Chapter 6). 2.1.3 Design for well-identified accidental actions Generally, the design for a well-identified accidental event implies the use of preventive and protective measures that would mitigate the risk of hazard occurrence or would reduce the latter’s destructive effects (Box B.2 in Figure 3). Such measures can range from conceptual solutions (selecting structural forms with low hazard sensitivity) to measures for the reduction of the effects of an accidental action (e.g., safety barriers or protective bollards). 20 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 2. DESIGN FOR ROBUSTNESS Where the measures taken to prevent the exceptional events lead to a complete avoidance of the full range of possible threats, it is reasonable to consider that the design complies fully with the robustness requirements. Conversely, as long as these protective measures only reduce the magnitude (or probability of occurrence) of the accidental action, or simply cannot be implemented, local damages are imminent and an assessment of possible local damages through an explicit design is required (Box B.3 to Box B.6 in Figure 3). If the predicted local damages are unacceptable and could trigger a disproportionate collapse of the structure, a redesign of the structure has to be carried out so that local damages are counteracted (Box B.2 in Figure 3). Where such damages are acceptable, their extent should be prevented through appropriate design strategies as proposed for unidentifiable accidental actions (see Section 2.1.4). Generally, for the explicit design under identified accidental actions, specific design strategies relying on analytical and/or numerical methods are used. The level of sophistication of the methods is strongly linked to the consequences class of the structure under consideration. The strategies and the methods currently available are presented in detail in Chapter 4. Within this chapter, four specific accidental actions will be contemplated: impact (Section 4.2), explosion (Section 4.3), fire as exceptional event (Section 4.4 ) and earthquake as exceptional event (Section 4.5). 2.1.4 Design for unidentifiable accidental actions Unidentified threats refer to accidental actions not specifically considered by standards or indicated by the client or other stakeholders or to any other actions resulting from unspecifiable causes. Due to uncertainties regarding the nature, the magnitude, and the application point (region) of an unidentifiable accidental action, the required structural performance is usually impossible to be estimated. In this case, the design for robustness requires pragmatic solutions covering a wide range of potential accidental scenarios. Currently, the design strategies deemed to achieve an adequate level of structural robustness mainly seek to limit the extent of a localised damage (Box C.2 in Figure 3), whatever is the initiating cause. These design strategies are addressed in Chapter 5. For buildings in the lower consequences classes (CC2a – see Chapter 3), EN 1991-1-7 suggests providing the structure with an efficient horizontal tying system using a prescriptive method named the “tying method” (Box C.3.a2 1n Figure 3). This method allows ensuring a minimum level of continuity between the different structural members by means of horizontal ties and thus the development of catenary actions in the damaged structure in view of activating alternative load paths. Nevertheless, due to the impossibility to estimate the level of robustness achieved through the tying method, the efficiency of the latter remains questionable, and it is seen rather as a necessary but not sufficient measure. Also, the development of catenary actions requires a sufficient ductility in key structural locations, but this point is not specifically addressed in the code which confirms the previous statement. Within Section 5.3.1, proposals will be made to overcome these identified weaknesses. For buildings in the upper consequences classes (CC2b – see Chapter 3), different alternatives are proposed. The first one is the use of the tying method as proposed for CC2a but adding the request for an efficient vertical tying system (see Section 5.3.1). The second one is the consideration of the complete removal of supporting elements (Box C.3.a2 in Figure 3). This situation simulates the case where a supporting element is lost completely further to an accidental event and allows to assess whether the structure is able to activate an alternative load path to survive to the loss of the supporting element. The current normative context defines this approach as the “notional removal of supporting elements” and, as EN 1991-1-7 prescribes, it should be applied for all supporting elements (columns, beams supporting columns, or any nominal section Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 21 2.1 DESIGN STRATEGIES of load-bearing walls) considered to be removed one at a time in each storey of the building. Even though such a method could prove to be tedious and time-consuming as it requires the use of advanced analysis tools, it provides the possibility to verify whether the building remains stable and whether the observed damages remain acceptable. From Section 5.3.2 to Section 5.3.4, analytical and numerical tools presenting different levels of sophistications will be proposed to apply this approach. * Appropriate design approaches for higher and lower consequences classes can be required **When redesign/retrofit, more advanced methods may be used where appropriate ***Strategies for designing for robustness are not mutually exclusive and may be used singly or in combination Figure 3. Flowchart reflecting the design for robustness process Where the loss of a supporting member generates a disproportionate collapse or the extent of the local damage exceeds a specific agreed or prescribed limit, the removed element should be labelled as a “key member” and the design should turn towards methods of local enhancement of resistance capacity of the element defined as the key element method (Box C.3.b in Figure 3). Moreover, the key 22 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 2. DESIGN FOR ROBUSTNESS member should be designed so that it resists a notional accidental action, and its failure should be prevented by any means. This method is detailed in Section 5.4. An alternative to these methods is the use of segmentation (Box C.3.c in Figure 3). Segmentation is a design strategy that can offer a possibility to prevent or limit an initial damage by isolating the failing part of a structure from the remaining structure by what can be referred to as segment borders. Segmentation strategies can generally be based on either weak segment borders or strong segment borders. More details are provided in Section 5.5. For buildings in CC3, the design approaches to be adopted are similar to the ones proposed for CC2b but could require the use of refined methods such as dynamic analyses (Section 5.3.5) and should be accompanied by a risk analysis (Chapter 6) as previously mentioned. 2.2 Importance of structural joints in the design for robustness 2.2.1 Classical design at SLS and ULS Structural joints are key elements which highly influence the global response of a steel building. As stated in EN 1993-1-8, joints may be classified in terms of rotational stiffness, resistance, and ductility. Three levels of rotational stiffness are considered: nominally pinned, semi-rigid and fully rigid. Stiffness classification boundaries are provided in EN 1993-1-8 but for their application to pinned joints, reference is made to (Jaspart et al., 2009). In reality, deformations occur also under axial or shear forces, but these ones remain quite limited, and they are usually assumed not to significantly influence the response of the structure. In terms of bending resistance, EN 1993-1-8 and (Jaspart et al., 2009) refer to three classes, namely nominally hinged, partial-strength, and full-strength joints, for which classification criteria are also presented. The concept of partial/full-strength joints may be easily extended to any other loading situation (axial force, combination of moment and axial forces…). As far as ductility is concerned, three categories exist also, but they are unfortunately not explicitly identified in EN 1993-1-8: brittle joints, ductile joints for plastic verification and ductile joints for plastic analysis. Similar to member cross-sections, one could speak about classes of joints. The use of rigid full-strength joints does not usually represent the most economical option, because of their high fabrication costs, but this allows to neglect the effect of the joints on the distribution of internal forces and on the design resistance of the system, yielding being only likely to develop in the member cross-section, at least if an elastic analysis is carried out together with an elastic or plastic verification of the cross-section resistance. As soon as a plastic structural analysis is carried out, thus requiring plastic rotation capacity for the development of the plastic mechanism, the risk of developing a plastic hinge in the joint adjacent to the cross-section, due to material overstrength in the member should be avoided, especially if the ductile response of the full-strength joint has not been checked. In EN 1993-1-8, the consideration of an initial “over-resistance” of the joints is then required, as compared to the nominal resistance of the cross-section. Here one could speak about “over-strength joints”. The component model available in (EN 1993-1-8, 2005) constitutes the main analytical method for the calculation of the mechanical properties, (i) stiffness, (ii) resistance and (iii) rotation capacity of the joints. It finds application both for the elastic and plastic design of any steel or steel-concrete composite (EN 1994-1-1, 2004) joint configuration. Details for the implementation procedure and supplementary information to (EN 1993-1-8, 2005) and (EN 1994-1-1, 2004) are available in (Jaspart and Weynand, 2016a) and (Demonceau et al., 2021). In order to extend its application field, (Demonceau, 2008) Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 23 2.2 IMPORTANCE OF STRUCTURAL JOINTS IN THE DESIGN FOR ROBUSTNESS characterised a not yet available component for steel-concrete composite joints, the “composite slab in compression”, and made proposals for the effective slab area and the component’s contribution to steelconcrete composite joints under sagging moments, see Chapter VIII.4.2 of (Demonceau et al., 2021). Another interesting reference is the following one in which a review of the design rules for components available in the codes and in the technical literature is presented (Jaspart et al., 2005). Finally, for components met in tubular joints, reference is made to (Weynand et al., 2015). The calculation of the stiffness and resistance design properties of joints is basically possible, whatever is the loading (moment M only, axial force N only and combination of moment M and axial force N, in addition to shear forces), through the use of the component method approach. In the above-mentioned normative documents, however, precise application rules are not provided for joints subjected to bending moments and axial forces, except for column bases. When a joint is also subjected to axial force NEd, a rough approach is just proposed in which, first, the influence of the MN interaction is disregarded as long as NEd is smaller than 5% of the axial design plastic resistance of the connected beam cross-section (Npl,Rd). In (Demonceau et al., 2019), it has been shown that the Eurocode M-N interaction predicts sometimes rather precisely, but often very safely the joint resistance, while the 5% rule leads generally to a significant overestimation of the joint resistance. Besides that, Eurocode 3 Part 1-8 is not defining the way on how to evaluate the axial joint resistance NRd. In the same publication, an improved design analytical assembly procedure is also presented for steel and steel-concrete composite joints. It has been validated through comparisons to results obtained from experimental tests performed on composite beam-to-column joints in various loading situations, including fire and progressive collapse. This advanced procedure, fully compatible with the design principles followed by the Eurocodes, is described in Annex A.1. 2.2.2 Design of joints under exceptional events Under exceptional events, classical SLS/ULS design criteria in terms of material yielding and deformation may widely be exceeded. As the final objective is to limit the local damages of the structure or the extension of these local damages to the rest of the structure, advantages from these large deformations and from the ultimate resistance of the material in the robustness assessment can be envisaged. In other words, the aim is to demonstrate that the structure can pass from an initial stable undamaged configuration, before the event, to another stable damaged configuration possibly at the cost of extremely large deformations and use of ultimate material resistance. For joints, very large extensional or rotational deformations may be involved, with a level of loading nearly equal to the joint ultimate resistance. For joints not able to exhibit such large deformations, brittle failure may prematurely occur, which adversely affects the possibility to mitigate the risk of progressive collapse. As a conclusion, ductility and large deformation capacity are seen as important properties to be provided to the structural joints. Moreover, exceptional events often induce internal forces in the joints which significantly differ from those considered as SLS/ULS. These forces vary according to the nature of the event. In addition, the possible loss of an element further to the event may drastically modify the distribution of internal forces in the undamaged part of the structure. As a conclusion, ideally, brittle failure modes should be avoided all along the complex and unforeseen loading sequence of the joint during the event. Regardless the nature of the event or of the adopted design strategy, the preliminary design of all structural joints for ductility in ULS conditions appears as a prerequisite, even if this is not strictly requested. It simply Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 31 3. CONSEQUENCE CLASSES 3 Consequence classes Building structures are classified into consequences classes based on the consequences of structural failure in terms of loss of human lives or personal injury and of economic, social, or environmental losses. Such classification is considered to be a simplification of a complex risk-based system related to building type, height, occupancy, societal perception, type of load, structural type, nature of materials, amongst others. In EN 1990 and EN 1991-1-7, Cl 3.4, three consequence classes are identified. However in Annex A of EN 1991-1-7, Table A.1, Consequence Class 2 is subdivided into CC2a (medium consequences-lower risk group) and CC2b (medium consequences-upper risk group), with the other classes being CC1 (low consequences of failure) and CC3 (high consequences), as summarised in Table 4. It is worth mentioning that Annex A is considered to be informative rather than normative, where the guidance provided does not need to be followed. However, it is the decision of individual countries whether to recommend the application of Annex A or not. More practical guidance related to building classification for robustness can also be found elsewhere (Way, 2011). On the other hand, the current draft revision of EN 1990 (prEN 1990, 2019) adds two more consequence classes, CC0 and CC4. CC4 is considered to have extreme risk of loss of human life or personal injury and a considerable economic, social or environmental risk. The provisions in the Eurocodes do not entirely cover design rules needed for structures classified as CC4. For these structures, additional provisions to those given in the Eurocodes may be needed. On the other side, CC0 has the lowest risk, where either the Eurocodes or alternative provisions may be used and where elements other than structural may be classified as CC0. Therefore, the provisions in Eurocodes mainly cover design rules for structures classified as CC1 to CC3. Additionally, the draft revision of EN 1990 allows consequence classes CC1 to CC3 to be divided into upper and lower sub-classes in other Eurocodes. There are some cases when practicing engineers may encounter difficulties if building structures may not directly follow the descriptions provided in Table 4. In such cases, engineering judgement is required, and it is the responsibility of the engineer to ensure that the safety of the structure is not compromised. Some of the common cases are listed in the following (see (Way, 2011) for more details): • Including mezzanine floors in counting the number of storeys for building classification will depend on the size and use of such floor. For an approximate guide, SCI P391 (Way, 2011) recommends the mezzanine floor to be counted if it is greater than 20% of the building footprint, which can be increased if the floor is not accessed on a daily basis. • Habitable areas of roof floors should be counted in the number of storeys regardless of the roof’s slope. • Buildings with different numbers of storeys that fall into different consequence classes should be classified relating to the most onerous class. • Mixed use buildings that fall into different consequence classes should be classified depending on the most onerous class. • Basement storeys are defined such that the external ground level should be at least 1.2 m above the top surface of the basement floor for a minimum of 50% of the building’s plan. In determining the number of storeys, basement storeys may be excluded, provided such basement storeys fulfil the requirements of "Consequence Class 2b Upper Risk Group". In case of Consequence Class 3, basement floors shall follow the requirements of such class. • The ground floor storey can be excluded from the total number of storeys for building classification if all of its structural elements including the connections are designed as key elements. In the case of using the ground storey as parking, it can be excluded from the storey count if all of the following apply: 32 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 3. CONSEQUENCE CLASSES o Parking is exclusively for users of the building. o The ground floor storey must not be accessible to or contain a right of way for the general public. o All the structural elements of the ground floor storey, and their connections, are designed as key elements. • For buildings that undergo conversions, alterations or extensions resulting in a change of consequence class, the building should then be classified to the most onerous class. Table 4. Categorisation of Consequence Classes in current EN 1990 and EN 1991-1-7 - Annex A Consequence Class (CC) Description Type and Occupancy Examples 1 Low consequence for loss of human life, and economic, social or environmental consequences small or negligible Single occupancy houses ≤ 4 storeys Agricultural buildings where people do not normally enter (e.g., storage buildings), greenhouses Buildings into which people rarely go, provided at distance 1.5 times height away from others 2a (Lower Risk Group) Medium consequence for loss of human life, economic, social or environmental consequences considerable 5 storey single occupancy houses Hotels, residential, offices ≤ 4 storeys Industrial ≤ 3 storeys Retailing premises ≤ 3 storeys and < than 1000 m2 floor area in each storey Single storey educational buildings Buildings ≤ 2 storeys admitting public with floor areas ≤ 2000 m2 at each storey 2b (Upper Risk Group) Hotels, residential, offices > 4 storeys but ≤ 15 storeys Educational buildings > single storey but ≤ 15 storeys Retailing premises > 3 storeys but ≤ 15 storeys Hospitals ≤3 storeys Offices greater than 4 storeys but not exceeding 15 storeys. Buildings admitting public with floor areas > 2000 m2 but ≤ 5000 m2 at each storey Car parking ≤ 6 storeys 3 High consequence for loss of human life, or economic, social or environmental consequences very great Buildings defined above as Class 2a and 2b that exceed limits on area and storeys Buildings to which members of the public are admitted in significant numbers (e.g., concert halls, grandstands, …etc.) Stadia accommodating more than 5000 spectators Buildings with hazardous substances/processes Note: Table is not exhaustive and can be adjusted. Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 33 4.2 IMPACT 4 Identified threats 4.1 Introduction The design for robustness of building structures can be done considering either the direct effects of an extreme action, or a specific extent of damage from an unknown / unforeseen event. Obviously, the methods from the first category require the identification of the threat and the definition of the action. Typical examples are fire, explosion, blast, or impact. For some actions, the level of threat can be reduced or even eliminated with non-structural or other measures, e.g., active fire protection - sprinklers, vent openings for gas explosions, protecting the structure against the impact using traffic bollards, or increased stand-off for blast. Also, in some cases, localised damage may be allowed to develop, but not to an extent disproportionate to the original cause. Some accidental actions are treated in detail in the Eurocodes: • Earthquake: the design of structures subjected to earthquake is covered by a specific Eurocode, EN 1998; • Fire: the design of structures subjected to fire is covered in Part 1-2 of the different “material related” Eurocodes. However, under some circumstances, the actions can exceed the conditions considered in the codes, for example under cascading loading scenarios, e.g., earthquake after earthquake, fire after earthquake, or fire after blast. The effects of the identified actions on a structure should be done considering appropriate methods of analysis, which depends on the safety category, or consequences class (EN 1991-1-7): • Consequences class 1: no specific consideration of accidental actions; • Consequences class 2: depending on the specific circumstances of the structure in question: a simplified analysis by static equivalent load models for identified accidental loads and/or by applying prescriptive design/detailing rules; • Consequences class 3: extensive study of accident scenarios using dynamic analyses and nonlinear analyses if appropriate. The next section covers the design for the following identified accidental actions: • Impact loads due to road traffic (Section 4.2); • External explosion (Section 4.3.2); • Internal explosion due to natural gas (Section 4.3.3); • Fire (Section 4.4); • Earthquake (Section 4.5). 4.2 Impact 4.2.1 Prevent/eliminate hazard The hazard coming from impact is typically associated with an incident involving vehicles. The consequences of the vehicle impact depend strongly on the weight, and speed, and direction (in relation with the building) of the vehicle. The preventive measures are part of the building safety focused on slowing the vehicle down and reducing access to the building. This can be achieved by appropriate design of access roads, which do not allow for large cars to directly approach the building, and which limit the vehicle speed. There are also various equipment starting from simple speed 34 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 4. IDENTIFIED THREATS bumpers on the road, through automatic blockers and security barriers as illustrated in Figure 6 to Figure 9. Figure 6. Speed bumpers on the hill road Figure 7. Speed bumpers in the car park Figure 8. Automatic road blocker and barrier Figure 9. Hydraulic road security blockers 4.2.2 Explicit design Impact actions are covered in Chapter 4 of EN 1991-1-7 (EN 1991-1-7, 2006). This code covers several different situations in which an impact action may occur. Independently of the situation, the impact always involves an interaction between a colliding object (source of impact) and the impacted object (e.g., a column of a building). Depending on the consequences class of the structure, the following simplifications are allowed (see Figure 10): • For structures in low and/or medium consequences class (up to CC2 - see Section 3), a static analysis such as the equivalent static approach of EN 1991-1-7 is sufficient as described in Section 4.2.2.1. • For structures in high consequence class (CC3 - see Section 3), a dynamic analysis is required. This analysis can be a simplified (EN 1991-1-7) or full dynamic analysis – see Sections 4.2.2.2 and 4.2.2.3 respectively. When using the equivalent static approach of EN 1991-1-7, the impacted object is always considered rigid, i.e., the colliding object absorbs all the impact energy (hard impact), what is conservative. However, when dynamic analyses are used, hard impact or soft impact are both allowed. In the soft impact, the capacity of the impact object in dissipating the impact load is taken into account. Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 35 4.2 IMPACT Figure 10. Representation of an impact action (EN 1991-1-7, 2006) 4.2.2.1 Equivalent static approach In this approach, the impact load is replaced by an equivalent static force F accounting for the effects of the load on the structure. For all the types of impact dealt with in Section 4 of EN 1991-1-7, values of static equivalent forces for different types of vehicles (cars, lorries, trains, ships…) are reported with explanations on how to apply them to the structures. The most common situation in buildings is the impact of a vehicle with one of the supporting columns. The application of this approach for this case is shown in Figure 11, the position (height h and area a) of the force in the column depends on the type of vehicle (car or lorry), while the magnitude of the force F is dependent of the type of road where the vehicle is travelling (i.e., the maximum velocity that it can achieve). The impacted member (and the surrounding structure) should be checked when subjected to the equivalent static force F and to the other permanent and variable loads, considering an accidental load combination. For this member, the ULS should be checked, without any limitations in terms of deformation. Figure 11. Collision force on supporting substructures near traffic lanes for bridges and supporting structures for buildings (Eurocode 1 2006) 4.2.2.2 Simplified dynamic approach This approach can be found in Annex C of EN1991-1-7 and it can be generally described by the model provided in Figure 12. The assessment of the impact force F depends on the type of impact (soft or hard impact): • For hard or soft impact in which the colliding object or impacted object, respectively, deform linearly, Eq. (2) can be used, where k is the stiffness of the colliding object (hard impact) or the impacted object (soft impact); vr is the impact velocity and m is the mass of the colliding object. (2) r Fvkm=× 36 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 4. IDENTIFIED THREATS • For soft impact, when the impact energy is absorbed through plastic deformations, it is required that the structure ductility is enough to absorb the total kinetic energy ½mvr2 of the colliding object. Assuming a rigid plastic response of the structure, this requirement is satisfied if the condition given by Eq. (3) is respected, where F0 is the plastic strength of the structure and y0 its deformation capacity. (3) Figure 12. Impact model (EN 1991-1-7, 2006) For the specific case of impact of a vehicle with a supporting member of a structure, EN 1991-1-7 suggests some values for the parameters that influence the impact force such as the mass, velocity, plastic strength F0, deceleration of the vehicle, etc., depending on the type of vehicle and the type of road. In the informative annex of EN 1991-1-7, this particular case is explained in more detail. 4.2.2.3 Full dynamic approach In a full dynamic analysis, the designer can decide between an analysis where the impact is explicitly modelled or an alternative load paths analysis (or column loss analysis) where the action is not explicitly modelled but its consequence, i.e., a column loss, is simulated. In practical terms, this second approach is more appealing because it can provide a good estimation of the structure robustness, without the complexity required to model impact actions. Several options are considered within the alternate load path analysis, differing from their complexity (linear/ non-linear, static/dynamic, etc…); the design guidelines to apply them are described in Section 5 of this manual, thus, these rules are not described here. However, some parameters are here highlighted as important for a good estimation of the robustness capacity of a structure subjected to an impact action through an alternative load path analysis, such as: • Dynamic effects can be taken into account by evaluating the time removal of the column or bearing element loss. For example, the GSA suggestions (GSA, 2003) can be followed. • Effect of the strain rates imposed by the action on constitutive laws of materials composing the structure can be easily assessed through DIF parameter. For impact loads inducing strain rate usually between 10-1 to 10, the DIF coefficient to be applied on the elastic strength of the steel material varies from 1,1 to 1,3. For the bolt mechanical properties, a DIF coefficient of 1,1 can be reasonable assumed. There are also many models available in the literature to account more accurately for this, such as the Johnson-Cook model (Johnson and Cook, 1983). 4.3 Explosion An explosion is an extremely rapid release of energy in the form of pressure wave, heat, sound, and light (Hall, 2017). The output of an explosion may also include the impact with primary fragments and/or secondary fragments. Even though all these can affect buildings and occupants in different 2 00 1 2r mv Fy×× £ Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 37 4.3 EXPLOSION ways, this chapter is mainly limited to the response of structures to the pressure load. No guidance is given to account for thermal or flying debris impact, even if the effects can be significant in some cases. Explosive materials can be solids, gases, vapours, or dust. Depending on the nature of the explosive material and the local conditions, the explosion may develop as a deflagration or expand rapidly and generate shock waves (detonation). More information can be found in (Demonceau et al., 2021). Generally, buildings are not designed for loading conditions generated by explosions, excepting the facilities designed to resists such actions (e.g., blast resistant buildings) or buildings where gas is burned or regulated. Thus, when buildings are subjected to such extreme loads, they may sustain extensive damages (Ellingwood et al., 2007; Somes, 1973; Burnett, 1975a; EN 1991-1-7, 2006). The possibility that primary structural components may fail shall be recognized and measures shall be taken to mitigate this risk, for example by preventing the progressive collapse after a column loss (CSA, 2012). In the following, details about the main characteristics of explosions and possible design approaches are given. Also, measures to reduce or prevent the explosion threat are given. 4.3.1 Prevent/eliminate hazard 4.3.1.1 External explosion There are several available methods to reduce or eliminate the external explosion threats without any intervention to the structural systems. The blast pressure reduces significantly with increase of the distance, therefore maximizing stand-off distance will decrease the effects of a blast (Figure 13a). In case of public spaces, where it is not possible to create / control a certain stand-off distance, bollards, trees, street furniture can be used as obstacles, as illustrated in Figure 13b. For higher risk area, a blast resistant wall can be built, which is a barricade that protects the structure from an explosion. The main aim of the wall is to keep the energy imparted by the explosion from reaching the structure, which is now protected from permanent damage and can continue the operation after the blast. The selection of the building shape and materials can also mitigate the effect of an explosion. Nonstructural elements attached to the building exterior have to be avoided to limit flying debris and improve emergency egress by ensuring that exits remain passable. If used, they should be designed using lightweight materials with connections designed to resist the capacity of the element. Windows are the most vulnerable part of building causing severe injuries. Depending on the risk level, appropriate type of glazing should be used as well as reduced area of windows on the exposed facades. It has been identified that structural shapes and dimensions have considerable influence on the design blast load. A square edge section results in higher peak reflected over pressure when compared with long rectangular edge section subjected to blast loads. In case of a circular shaped structure, the highest peak reflected over pressure is observed at a point on the edge, which is nearest to the explosion. This pressure diminishes in magnitude towards both the sides of the center. Further, in modern buildings, it is observed that a parabolic or cubic shaped facade performs better than an upright faced facade. Thus, by analysing the shape of the building, the design can be adjusted to use the shape that results in minimum design blast load and simultaneously provides usable area. 38 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 4. IDENTIFIED THREATS a) b) Figure 13. Mitigation of explosion effects: a) concept of stand-off distance; b) streetscape security elements (FEMA 426) 4.3.1.2 Internal gas explosion Lessons learned from previous accidents show that prevention of gas explosions by reducing the probability of the accidental releases and ignition only, is not sufficient. If effectively implemented, a good engineering practice may help reducing the consequences (Bjerketvedt et al., 1997a): • Take into consideration the gas explosion hazard from the beginning of the project. It is in the early phase of the development project that major decisions such as location of different areas, separation of areas and overall layout (that will influence the vent arrangement and the process itself) are made. • Buildings subjected to possible internal explosions should have a strong frame structure supporting roof and intermediate floors. The "walls" should be open, if possible. If a solid wall is needed, use low weight wall panels to facilitate early explosion venting. • Vent areas are important not only in terms of the size, but also in terms of location. Thus, when there is sufficient venting close to the ignition point (see also a) for the importance of the conceptual design), the flame speed will be low, and the turbulence generated behind the obstacles will be limited. • As a general principle, the gas explosion venting should be directed into open areas with a minimum of obstructions. • Partial obstruction of a vent opening can result in strong pressure increases. 4.3.2 External explosion – Explicit design 4.3.2.1 Definition of the structural blast loads An explosion scenario is defined first, including the expected charge weight W, type of explosion, and distance to the building R. The evolution of the pressure vs time associated to a front wave can be idealised through the curve presented in Figure 14. Unless better information is available, the blast load parameters can be determined using the diagrams presented in Figure 15, which involves the computation of the scaled distance, Z, which depends on the explosive mass W (in kg of TNT), and the actual distance from the centre of the spherical explosion R (in m). Except for the pressures and velocity, all the other values in Figure 15 are scaled by a factor W1/3 so as to take into account the actual size of the charge. The idealised pressure-time diagram for the front wall can be constructed using the following relationships: Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 39 4.3 EXPLOSION 𝑡(=4𝑆 (1+𝑅)𝐶) 7 (4) 𝑡$* =2𝑖+ 𝑃+, (5) 𝑡)* =2𝑖) 𝑃) (6) where: - tc is the clearing time; - S is the smallest of the surface’s height H or half width W/2; - Cr is the sound velocity in the reflected medium; - R is the ratio S/G, where G is the largest of the surface’s height H or the half width W/2; - tof is the fictitious time (tof < to, where t0 is the actual duration of the positive phase) of the incident wave; - is is the impulse value of the positive phase of the blast wave; - Pso is the peak incident pressure; - trf is the fictitious duration of the reflected wave; - ir is the total reflected impulse; - Pr is the peak reflected pressure. The peak dynamic pressure qo is calculated from Figure 16. This parameter is required to compute the value of Pso +CDqo (see Figure 14) which is determined by using CD=1 for the drag coefficient for the front face of the structure. Note: For the positive phase of the reflected pressure, two curves Pr-t are constructed and compared: one corresponding to infinite surface conditions, and another derived using the assumption that the finite surface geometry influences the value of the reflected pressure. The curve to be used for loading the structure is the one that produces the smallest impulse value (JRC). The loads computed for front face of the structure are applied in the structural design of the building using the load combination rules given in EN 1990 for the accidental design situations. Depending on the complexity of the building and class of consequences, different types of analysis may be required (e.g., equivalent SDOF, dynamic non-linear analysis) as reported in the next sections. Figure 14. Front wall pressure 46 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 4. IDENTIFIED THREATS • η is the explosive yield (or efficiency) factor; • Wg is the mass of vapour in cloud of gas (equal to the mass of the air and flammable gas mixture); • EC is the heat of the combustion of the flammable material; • ETNT is the detonation energy of TNT. For typical hydrocarbons (e.g., methane, propane, butane), the energy equivalence ( .! ."#" ) can be taken as 10. For a natural gas explosion, if the explosive yield (or efficiency) factor is considered as equal to 20 % (η=0.2), the equivalent mass of TNT can be estimated (assuming atmospheric pressure initially) with the following formula (Bjerketvedt et al., 1997b; Harris and Wickens, 1989): 𝑊898 ≅0.16𝑉7[𝑘𝑔] 7 (16) where: • V [m3] is the smaller of either the total volume of the congested region or the volume of the gas cloud. When the equivalent mass of TNT is known, then the wavefront parameters (pressure, impulse, duration) can be determined using the methods presented in Section 4.3.2. The limitations of the TNT equivalent method are: • This method can be applied with satisfactory results to strong gas cloud explosions. For explosion pressures below 1 bar, the TNT equivalent method will overestimate the pressure. • The deviation is small for describing the far field effects, while it is large for describing the near field effects. • The TNT equivalent method can be useful as a rough approximation if one uses a yield factor of 20% and appropriate value for V (or the corresponding mass of hydrocarbon). 4.4 Fire as exceptional event Fire actions should always be considered when designing steel and composite structures, using the prescriptive approach or a performance-based approach prescribed by the Eurocode. These design approaches are presented in Parts 1-2 of EN 1993 and EN 1994 and it is detailed in the FAILNOMORE background document (Demonceau et al., 2021). A fire action as exceptional event should be seen as fire events not directly covered by the building regulation, in terms of intensity or location, due to their low probability of occurrence, but which could be associated with significant consequences. This is the situation which is addressed in the present section. 4.4.1 Prevent/eliminate hazard Fire in buildings can be a result of different events such as blast and earthquake or it can be ignited directly (careless use of matches, cigarettes and pipes, faulty wiring or electrical equipment, careless use of cooking equipment, etc). The first step to avoid the ignition of a fire is avoiding any self-igniting materials in the building (storage of chemicals, petrol). Building regulations are specifying rules regarding the storage of such materials in buildings – often storage around columns is prohibited as a general rule. The other aspects regulated by law are materials used for facades and the distance between buildings to reduce the risk of fire spread Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 47 4.4 FIRE AS EXCEPTIONAL EVENT between buildings and along the building. Among other systems preventing fire spread (passive and active) and mitigate the effect of hazard are: • Fire extinguishers – activated manually, when fire appears; • Sprinklers – automatic systems activated, when smoke or high temperature arises; • Fire walls – vertical isolation preventing fire spread; • Vent insulators – insolation of any openings between compartments; • Compartmentation – separation of building into quarters, between which the fire cannot be spread. Very important is a quick detection of fire and early warning and evacuation systems enabling fast evacuation of occupants and quick activation of fire man and systems to stop the fire. For this issue, the use of the following equipment can be contemplated: • Smoke detectors; • Thermal detectors; • Alarm systems; • Exit road marking. Figure 20. Sprinkler, vent insulators, fire door Figure 21. Fire wall and compartmentation Figure 22. Fire extinguishers and early warning systems. 4.4.2 Design strategy An example of fire as exceptional event is a fire localised around a column (when in normal situation fire load should not be located here) due to exceptional thermal loading. This action can be taken into account using a model defined in Annex C of EN 1991-1-2 (see next subsection) and/or by advanced 48 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 4. IDENTIFIED THREATS fire models such as Zone models or CFD models. The model of Annex C is presented in Section 4.4.2.1 while recommendations for advanced fire modelling are reported in Section 4.4.2.2. However, based on recent research results, it can be highlighted that the increase of temperature due to an unexpected localised fire situation is unlikely to lead to the collapse of some of the bearing elements and consequently the loss of stability of the structure, when the structure was designed for fire following the rules of the Eurocode and the National requirements. Table 7 shows four fire scenarios and load that have been considered for localised fire next to a column. The resulted distribution of temperature along the columns is illustrated in Figure 23. As it can be seen, only at the bottom of the column (up to 1 m) significant steel temperatures is reached that could cause some local buckling or plastic failure. Table 7. Different localised fire scenarios for office buildings and commercial areas (Demonceau et al., 2021) Scenario Diameter of the fire basis Rate of heat release density Fire load density Fire growth rate A 2 m 250 kW/m2 (office building) 511 MJ/m2 (office building) 300 sec (office building) B 1 m 500 kW/m2 (office building) 511 MJ/m2 (office building) 300 sec (office building) C 2 m 250 kW/m2 (commercial area) 730 MJ/m2 (commercial area) 150 sec (commercial area) D 1 m 500 kW/m2 (commercial area) 730 MJ/m2 (commercial area) 150 sec (commercial area) Figure 23. Increase of temperature along the height of the column for different localised fire scenarios (Demonceau et al., 2021) A different and more severe situation in terms of robustness with fire defined as an exceptional load is when a sequence of exceptional event scenarios is considered, such as fire after an earthquake or after an impact or explosion. In those situations, the structure is already damaged after the first event, thus, the normal fire design is not valid anymore, since this design always considers that the structure is undamaged. Therefore, the fire event should be considered as an exceptional load. For these cases, column loss scenarios (see Section 5) could be considered for the design for robustness as a safe sided approach. Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 49 4.5 EARTHQUAKE AS EXCEPTIONAL EVENT 4.4.2.1 Localised fire models In the model of Eurocode, a localised fire (or pre-flashover fire) is a fire where a flashover is unlikely to occur. Depending on the size of the fire and of the compartment, a localised fire can or not impinge on the ceiling of the compartment. In this model, the temperature in the flame and plume and the surrounding gases are not uniform. This model is described in Annex C of EN 1991-1-2 (EN 1991-1-2, 2002). A localised fire impinges the ceiling of the compartment when the length of the flame (Lf), estimated through Eq. (17), is equal to or higher than the distance between the fire source and the ceiling (H). (17) with D, the diameter of the fire and Q, the rate of heat release (Annex E of EN 1991-1-2) . The temperature of the flame along the symmetrical vertical flame axis when Lf < H can be obtained by Eq. (18) (18) with Qc, the convective part of the rate of heat release (=0.8Q); Z, the height of the flame along its axis; Z0, the virtual origin of the fire (Eq.(19)) (19) For cases when the flame impinges the ceiling, the net heat flux received by the fire exposed per unit of surface at the level of the ceiling is given by Eq. (20). (20) with , the heat flux received by the fire exposed per unit of surface at the level of the ceiling; αc, the heat transfer coefficient by convection; θm, the temperature at the surface of the element; Φ, the configuration factor; εm, the surface emissivity of the member (0.7 – carbon steel; 0.8 stainless steel); εf, the fire emissivity; σ, is the Stephan Boltzmann constant (5.67 x 10-8 W/m2K4). 4.4.2.2 Advanced fire models To use advanced fire models, it is always required to use specific software. • Zone models – see Annex D of EN 1991-1-2 for basic equations of conservation of mass and energy. Examples of software that can be used are the CFAST from NIST or the OZONE developed in the University of Liege • CFD model (Computational fluid dynamic model) – see Annex D of EN 1991-1-2 for suggestions. An example of software that can be used for CFD analysis is the FDS from NIST 4.5 Earthquake as exceptional event Seismic risk results from the interaction of seismic hazard and structural vulnerability. Therefore, an earthquake can be considered exceptional when: - Structure is not designed for a seismic action at all, e.g., it is designed for gravity and wind loads only (e.g., when the building site is not considered as seismic at the time of construction) or is designed for lower seismic demands – the hazard is therefore exceptional. - Structure is seismically vulnerable (pre-existing damages, system not designed following modern code design requirements). 0.4 0.0148 1.02 f LQD=- 2/3 5/3 () 0 20 0.25 ( ) 900 zc Qzz q - =+ - £ 2/5 01.02 0.00524ZD Q=-+ 44 (20) [(273)(20273)] net c m m f m hh aq eesq =- - -F +-+ !! h ! 50 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 4. IDENTIFIED THREATS 4.5.1 Prevent/eliminate hazard An earthquake is a sudden release of strain energy accumulated in the Earth’s crust. Earthquakes are caused mostly by the rupture of geologic faults. Other causes include volcanic activity, landslides (all with natural causes), but also human activities (mine blasts, nuclear tests, oil/gas drilling). Due to its nature, it is not possible to prevent or eliminate the seismic hazard. Therefore, the reduction and prevention of consequences (e.g., structural / non-structural damages) are strictly associated with the building structure and the integrated systems, which help the building to adequately respond to the seismic action, see next sections. 4.5.2 Prescriptive approach Even not directly evaluating the performance of the structure in case of a seismic event, prescriptive requirements can improve the seismic response with minimum engineering effort and structural interventions. This approach is especially beneficial for non-seismic areas where seismic actions may occur but with a very low probability of occurrence, at least sufficiently low to not consider it in the design process. Indeed, this approach favours systems, materials, and detailing with performances demonstrated in past seismic events. Selection of the structural configuration and knowledge about the building’s period, torsion, damping, ductility, strength, stiffness, can help one determine the most appropriate design strategy to employ: - Building configuration: this term defines a building’s size and shape, and structural and nonstructural elements. Building configuration determines the way seismic forces are distributed within the structure, their relative magnitude, and other design concerns. Regular configuration buildings generally have: o Low Height to Base Ratios o Equal Floor Heights o Symmetrical Plans o Uniform Sections and Elevations o Maximum Torsional Resistance o Short Spans and Redundancy o Direct Load Paths o Design of secondary/non-structural elements to avoid debris. - Torsional effects: they develop due to the asymmetric distribution of inertial masses and/or rigidities. Symmetrical arrangements will result in balanced stiffness and reduced torsional effects. Regularity in plan and in elevation is also recommended. - Vibration control: buildings in general are poor resonators to dynamic shocks and dissipate vibration by absorbing it. The following systems can be employed to improve the response: o Base isolation can be used to detach (isolate) the building from the ground in such a way that seismic energy that is transferred to the superstructure is greatly reduced. Most suitable candidates for base-isolation are low to medium-rise buildings constructed on stiff soils; high-rise buildings or buildings constructed on soft soils are not suitable for base isolation. o Passive damping systems. The most common application is a tuned mass damper (TMD) device, which consists of a mass, a spring, and a damper that is attached to a structure. The seismic energy is dissipated by the damper inertia force acting on the structure. o Active damping systems. Active tuned mass dampers cancel out speed-dependent vibrations by counteracting the excitation forces of a disrupted main system. Each TMD consists of an actuator, a control system, and a power electronic unit. All the Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 51 4.5 EARTHQUAKE AS EXCEPTIONAL EVENT components of the TMD are mutually balanced so that the TMD force acts in precisely the opposite direction of the excitation force. o Semi-active control systems, which take advantage of the best features of both passive and active control systems. The term “semi-active” is used to indicate that the operation of these systems requires a very small amount of external power. The control forces are developed through appropriate adjustment of damping or stiffness characteristics. - Strength and Stiffness: Strength is a property of a material to resist the applied forces within a safe limit. Stiffness of a material is a degree of resistance to deflection. Selection of strength and stiffness properties should be done considering the balance between deformability and force resistant capacity. - Ductility: Ductility is the characteristic of a material (such as steel) or element to dissipate part of the energy by plastic deformations. Ductile elements typically fail only after the development of considerable plastic deformations. Non-ductile elements, such as poorly reinforced concrete members, fail by brittle fracture, with no plastic deformations. The ductility demands can refer both to elements and to their joints. o For elements, the main requirements target the slenderness and the prevention of instability (e.g., lateral-torsional buckling of beams in flexure) before reaching their plastic strength. At the level of the section, ductile or semi-ductile cross-sections (class 1, class 2) are favoured. o For joints, symmetrical configurations are recommended, as they can provide a more stable hysteretic response throughout subsequent cycles. Also, components that fail in a brittle mode (e.g., welds, bolts) need to be provided with overstrength. To ensure a ductile behaviour of the joints, the recommendations from Section 2.2 can be followed. 4.5.3 Design strategies In the aftermath of an earthquake, the primary concern is the structural condition and whether it is safe from collapse under gravity loads, earthquake aftershocks, and other hazards (FEMA P-2090, 2021). If the structure lacks the robustness, there is a risk of further damages or progressive collapse under an aftershock or other hazards, even the structure initially resists the ground motion. To avoid such a disastrous scenario, the building’s residual capacity needs to be assessed. The residual capacity after an earthquake can be defined as: - load-carrying capacity of the lateral load-resisting system – the minimum spectral acceleration that corresponds to local or global collapse during an aftershock. - load-carrying capacity of the gravity load-resisting system – the minimum level of gravity loads that corresponds to local or global collapse after a damaging earthquake. In the following, a procedure for the evaluation of the seismic robustness is presented. i) Step 1: Design/evaluation for persistent / seismic design situations The structure is first designed to meet the code-based requirements (see Figure 24.a) (for new structures, only). The seismic response can be calculated using a Nonlinear Static analysis (N2 method, EN 1998) following the recommendations from EN 1993-1-14 (2020) regarding the behaviour laws to be used for the materials and the modelling of the structural elements. The general load-deformation relation of a structural component can be characterized using prEN 1998-1-2:2019.3, Annex L (Figure 24.b). Thus, the component model shall be defined by: - an effective elastic stiffness, Ke considering both flexural and shear deformations. 52 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 4. IDENTIFIED THREATS - the yield point, which is defined by the effective yield strength, Qy ∗ , and the corresponding yield deformation, δy ∗ . - the post-yield range, in which the structural component exhibits hardening prior to reaching its maximum strength, Qmax ∗ (i.e., peak response). - the pre-peak plastic deformation, δp∗ defines the plastic deformation up to the peak response of the structural component. - the post-peak response is represented by the post-peak plastic deformation, δpc ∗ of the component. The global seismic performance can be presented in the form of a base shear force – top displacement Fb – dtop curve, see Figure 24.c. Performance levels (PL) are defined by the corresponding maximum top displacement, e.g., PL1 (limited damage), PL2 (moderate damage) and PL3 (large damage). Depending on the level of hazard, a certain damage level is expected. ii) Step 2: Evaluation of the residual capacity after an earthquake After the evaluation of the local and global ductility demands (Step 1), modifications of flexural hinges are introduced for the damaged elements (i.e., elements with plastic deformations), resulting in a modified nonlinear model (see Figure 24.d). The residual strength of a column shall be conservatively assumed as zero if the peak response is attained during the seismic motion. P-∆ effects must be accounted for (especially when residual lateral deformations after the earthquake are significant). The resistance of the frame structure against a seismic aftershock can be evaluated using a nonlinear analysis (e.g., pushover analysis). The analysis is done on the damaged model. The resistance of the frame structure against progressive collapse under gravity loads can be evaluated using a pushdown (vertical) static analysis using the methods proposed in Section 5.3. a) b) c) d) Figure 24. The steps of the seismic robustness assessment for framed structures (adapted from Polese et al., 2012): a) view with the building model; b) general definition of load-deformation relationship for steel and steel-composite structural components; c) seismic capacity curve obtained in the nonlinear static analysis for the undamaged (initial) structure; d) modelling parameters for the damaged plastic hinges Fb dtop PL1 PL2 PL3 dyr Ker Qyr dpr Stiffness Strength Ductility Initial (intact) Ke Qy dp Damaged Ker Qyr dpr Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 53 5.2 IDENTIFICATION OF LOCAL DAMAGES 5 Unidentified threats 5.1 Selection of appropriate design strategies Unidentified threats refer to accidental actions not specifically considered by standards or indicated by the client or other stakeholders or to any other actions resulting from unspecifiable causes. Due to uncertainties regarding the nature, the magnitude and the application point (region) of an unidentifiable accidental action, the required structural performance is usually impossible to estimate. Currently, the design strategies deemed to achieve an adequate level of structural robustness mainly seek to limit the extent of a localised damage, whatever is the initiating cause. The identification of the localised damage to consider is addressed in Section 5.2 while the design strategies to check the adequate level of robustness are described in Section 5.3 (alternative load path methods), 5.4 (key element method) and 5.6 (segmentation method). 5.2 Identification of local damages Generally, the main objective of robustness design is to ensure that any local damage resulting from unforeseen extreme events does not cause disproportionate collapse. In this regard, any local damage scenario has to be threat-independent. Accordingly, this requires the identification of local damages to be considered in the design process. If reference is made to the present draft of (EN 1991-1-7, 2006), the local damage to be considered for building structures included in the upper group of Consequences Classes (CC 2b and CC3) is the notional removal of each supporting column, or each beam supporting a column, or of any section of load-bearing wall (one at a time in each storey of the building). The concept of “Notional column removal” stated in (EN 1991-1-7, 2006) represents the removal of the entire column on the clear height between the connections at the level of the floors. Elements are removed without affecting end joints / connections. Notional removal of a column may not always be conservative, due to the infinite possibilities of loading scenarios and load-structure interaction, but for an accomplishable assessment of the structural system capacity to transfer loads through alternative paths, notional removal is seen as an efficient and practical analysis scenario. In the Eurocodes, it is not stated if this notional column removal has to be assumed as instantaneous or as “quasi-static”. The consideration of a “quasi-static” removal allows (i) the use of more simple tools as no dynamic effects need to be accounted for and (ii) to have a good indication on the ability of a structure to activate alternative load paths. However, the consideration of an instantaneous of local part of the structure maximises inertial effects; in particular, sudden column loss was shown to offer an upper bound on the subsequent response of building structures in comparison with column damage due to a blast event (Gudmundsson and Izzuddin, 2010). In addition, damaged elements may have residual capacity, which is not conservatively taken into consideration implicitly, except in case of applying residual strength method. As stated previously, the removal of each supporting element, one at a time, should be contemplated according to (EN 1991-1-7, 2006), what could require a significant amount of design work. However, possibilities of reducing the number of local damage scenarios to be considered in the design process exist, in particular in regular building structures for which design scenarios can be identified considering possible structural symmetry, similarity of boundary conditions and other engineering reasoning principles. In UFC 04-023-03 (DoD, 2016), it is required to consider at least the following column loss for a storey plan as a minimum of scenarios (see Figure 25): 54 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 5. UNIDENTIFIED THREATS • external columns and internal columns near the middle of the short side and the middle of the long side; • the corner of the building; • columns at locations where the plan geometry of the structure changes significantly, such as abrupt decrease in bay size or re-entrant corners; • columns with adjacent columns lightly loaded or adjacent bays with different tributary sizes; • locations where members frame in at different orientations or elevations; • locations where the structure has any vertical load discontinuity (i.e., transfer conditions) (GSA, 2016). For locations in terms of the storey itself, the following should be considered: • First storey above ground; • Storey directly below the roof; • Storey at mid-height; • Storey above the location of a column splice or change in column size. Figure 25. External and internal column removal scenarios (DoD, 2016) For the considered local damage scenario, the extent of damage it would create should be limited. The Annex A of the current version of EN 1991-1-7 (EN 1991-1-7, 2006) and Annex E of the proposed draft of the imminent second generation EN 1990 (prEN 1990:2019, 2019) specifies this limit as 15 % of the floor area or 100 m2, whichever is smaller in each of the two adjacent storeys to the one where the column was removed. However, in principle, the acceptable limit of damage can be defined by the client or relevant authorities based on performance objectives related to the importance of the structure and the consequences of such damage on life safety, protection of valuable contents or minimisation of operational downtime of the structure. If for the respective scenario the damage limit cannot be respected, it means that this scenario (local damage) cannot be allowed to occur, and so the supporting element which was assumed to be lost has to be prevented from failure and designed as a key element. Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 55 5.3 ALTERNATIVE LOAD PATH METHODS Figure 26. Acceptable limit of damage in case of removal of a column in a framed structure. The limit ‘A’ is 15 % of the floor area, or 100 m2, whichever is smaller, in each of two adjacent storeys. ‘B’ is the column notionally removed. A) Plan and b) Section (EN 1991-1-7, 2006) 5.3 Alternative load path methods A building structure losing a column can be divided in two main parts, as illustrated in Figure 27: • the directly affected part (DAP) which represents the part of the building directly affected by the column loss, i.e., the beams, the columns, and the beam-to-column joints which are just above the failing column; • the indirectly affected part (IAP) which includes the rest of the structure; this one is affected by the loads developing within the directly affected part; but obviously, these forces are themselves influenced by the own response of the indirectly affected part. If a cut is realised in the structure at the top of the failing column (see Figure 27), different internal forces in the vertical direction are identified: (i) the shear forces V1 and V2 at the beam extremities close to the failing column, (ii) the axial force Nup in the column just above the failing column and (iii) the axial force Nlo in the failing column. . Figure 27. Schematic representation of a frame during a column loss In Figure 28, a curve representing the evolution of the vertical displacement D A according to the normal load Nlo in the failing column during the exceptional event (see Figure 27) is illustrated. V1 V2 Nup Nlo A 62 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 5. UNIDENTIFIED THREATS 5.3.1.1.2 Specificities of composite floors In case of composite floors, i.e., floors made of steel profiles with the upper flange connected to the slab, the method presented here above can be safely used neglecting the composite character of the floor. However, in the case of a column loss scenario, such a structural solution allows the development of membrane action in the composite beams and in the connected slab, so leading to the activation of an alternative load path. The efficiency of this solution has been demonstrated through experimental tests performed in Europe (Kuhlmann et al., 2017; Zandonini et al., 2014). To ensure the efficiency of the composite solution, the use of steel beam grids with the upper flange of the beams in the two main directions connected to the slab is recommended to guarantee a good collaboration between the steel members and the slab in both directions but also to allow for a proper anchorage of the slab on the lateral beams when membrane forces develop. Through recent studies (Demonceau et al., 2013; Kuhlmann et al., 2017), it has been demonstrated that (i) membrane forces mainly developed in the slab of composite floors while limited tensile forces develop in the composite beams and (ii) the activation of these membrane forces requires much less deformation capacity at the level of the structural beams. Accordingly, the activation of alternative load path in composite floors will require (i) composite beams with a minimum level of ductility at their extremities to allow for the development of a plastic mechanism and (ii) a collaborative slab with appropriate constructive details, in particular in terms of reinforcement. As previously mentioned, the composite beams will be mainly subjected to bending moments, the tensile forces developing in the beams being limited. Accordingly, the ductility at the level of the composite beam extremities is required under bending moments only. Four situations can be met in practice according to the nature of the joints at the extremities of the composite beams: - Over-strength joints are used and so the ductility is required at the level of the composite beams. As the objective is to develop a plastic mechanism with a minimum level of deformation capacity, the use of Class 1 cross-sections under sagging and hogging moments is recommended. - Partial-strength joints are used and so the ductility is required at the level of the joints. In such situation, reference is made to Section 2.2 where design recommendations are provided to ensure a minimum level of ductility to partial-strength joints. - Simple joints are used and so a minimum level of rotation capacity is required at the level of the simple joints. In such a situation reference is again made to Section 2.2 where design recommendations are provided to ensure a minimum level of rotation capacity to simple joints. - Full-strength joints are used and so ductility is required at the level of the joints and of the beams. Regarding the collaborative slab, different solutions can be contemplated: reinforced concrete slab fully cast on site, reinforced concrete slab using precast concrete elements or composite slabs. No specific design recommendations or constructive details are provided in the present draft Eurocode 4 (EN 1994-1-2, 2005) to guarantee the possibility of activating membrane forces within the slab while minimum requirements are given in Eurocode 2 (EN 1992-1-1, 2005), more precisely in Section 9.10.2, to provide a floor with a tying system. So, for composite floor, it is suggested here to follow the minimum requirements of Eurocode 2. The application of this recommendation can be seen as the application of a prescriptive tying method specific to composite floor. Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 63 5.3 ALTERNATIVE LOAD PATH METHODS For collaborative reinforced concrete slab cast on site, the above-mentioned requirements from Eurocode 2 can be directly applied. For collaborative slab using precast concrete elements, specific rules, coming in addition to the above-mentioned requirements of Eurocode 2, are proposed in (CEN/TC250/SC4, 2020) to ensure a proper anchoring of the slab to their supports (see Figure 35). Figure 35. Tying action in the floor plate using precast slabs (after N 2040, 2020) For collaborative composite slabs, no specific recommendations are available yet. Through tests recently performed at the Politehnica University Timisoara (Dinu et al., 2015), it has been demonstrated that a debonding between the composite slabs and the steel deck may occur when significant deformations develop which could limit the possibility of developing significant membrane forces in the composite slab. This requires further investigations to propose appropriate constructive details to avoid this debonding and so to effectively activate the slab in case of column loss scenario. 5.3.1.1.3 New method proposed by PT 2 of CEN TC250 Working Group 6 In (CEN/TC250/WG6, 2020), a new method developed by B. Izzuddin and presented as an alternative to the prescriptive tying method presently recommended in EN 1991-1-7 is proposed. This method allows for a better prediction of the tensile loads to be supported by the tying members in case of column loss scenario, accounting for variable levels of ductility, the floor typology and possible dynamic effects. The general formulation for the computation of the minimum tensile force to be supported is as follows: 𝑇≥η.𝜌.l𝑖* 𝛼no.𝑃 (23) where: • T is the tensile load to be supported by the considered tying member; • h is an amplification coefficient to account for possible dynamic effects; • r is a reduction factor to account for different effects such as strain hardening of interaction between tensile load and bending; • if is a tying force intensity factor depending of the system under consideration; • 𝛼 n => ,.5 is a coefficient to account for the chord rotation capacity a (in rad) for different structural typologies; • 𝑃7 is an equivalent load to account for the loads applied to the considered floor. 64 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 5. UNIDENTIFIED THREATS This formulation is presented as a “universal” one which can be used whatever the used materials and structural typology are. It requires an appropriate characterisation of the constitutive coefficients. In (CEN/TC250/WG6, 2020), different values of if and P are proposed for double-span beams, two-way floor tying and one-way floor tying subjected to different loading conditions. For the computation of a , it is clearly stated that the rotation capacity to be computed is not the one corresponding to the rotation ductility, i.e., the rotation during which the structural member is able to sustain its plastic resistance, but the one corresponding to the failure of the structural member. However, up to now, no easy-to-apply methods are available to predict such rotation capacity, in particular for steel and composite structures. Nevertheless, in case of partial-strength joints, the values of the rotation ductility predicted using the recommendation of Section 2.2.3 can be safely used for a . It is also stated that the proposed formulation is valid if a minimum level of rotation capacity a min is available. Criteria for the definition of a min values are proposed in (CEN/TC250/WG6, 2020). For the dynamic amplification h , it is mentioned that, in absence of information, the most realistic value is to consider h = 2. This can be seen as a safe estimation of this coefficient. Formulations to compute more refined values for this coefficient are also proposed in (CEN/TC250/WG6, 2020). In addition, this method is founded on assumptions regarding the behaviour of the surrounding structure and it is recommended to check the latter under tying forces and to check if it exhibits a sufficient stiffness under the action of the tying loads as the proposed formulation is based on the assumption that the horizontal stiffness at the extremities of the tying members is high. In (CEN/TC250/WG6, 2020), criteria to check if this stiffness is sufficient are provided. For structures in which it is possible to activate diaphragm effects, it can be assumed that these criteria are satisfied. As can be observed through this brief description, this method requires the characterisation of different parameters and, in particular, the analysis of the surrounding structure. It is the reason why this method can be seen as a hybrid method combining prescriptive criteria and analytical approaches. 5.3.1.2 Vertical tying Vertical tying can allow the redistribution of loads through the development of alternative load paths as illustrated in Figure 36. Vertical tying is mainly governed by the tensile capacity of the column splices. Therefore, the splices must be able to resist the tensile forces that can arise due to the loss of column support, in order to hang the above floors and redistribute the load to the rest of the undamaged structure. In Eurocode 1 Part 1-7 (EN 1991-1-7, 2006), requirements for vertical ties are given: • all the columns in the structure should be tied continuously from the foundation to the roof; • the tie should be able to resist a tensile force corresponding to the largest design vertical permanent and variable reaction applied in normal design conditions to the column from any one storey. Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 65 5.3 ALTERNATIVE LOAD PATH METHODS Figure 36. Alternative load paths developed through vertical tying The check of column splices subjected to tensile loads is not explicitly covered in the Eurocodes. Rules are proposed in Annex A.1 for the characterisation of joints under tensile loads. 5.3.2 Analytical methods In the present section, different analytical approaches will be proposed with different level of sophistication, from the simplest ones to the most advanced ones. The simplest approaches are founded on assumptions which allows a safe estimation of the structural response exposed to a column loss scenario in comparison to the most advanced ones, which allows for a more accurate prediction. This section will first focus on the possible contribution from the slab. Then, simplified analytical methods will be proposed for different structural typologies. Finally, a more advanced analytical method will be briefly addressed. But before tackling these subjects, an important preliminary remark must be made. In Sections 5.3.2.2 (simplified analytical methods for structures with pinned joints), 5.3.2.3 (simplified analytical methods for structures with partial-strength joints) and 5.3.2.4 (simplified analytical methods for structures with over-strength joints), the presence of concrete slabs acting as efficient diaphragms is assumed at each storey level. As a result, the indirectly affected part may be assumed as infinitely stiff in the horizontal direction, what induces an equal distribution of membrane forces in the storeys located above the lost column. In structures where this condition is not satisfied, the membrane forces will distribute amongst these storeys according to their relative lateral stiffnesses. In such a situation, more advanced models are required and reference can be made to Section 5.3.2.5 (advanced analytical approach) or to Sections 5.3.3 and 5.3.4 (numerical approaches). Specific failure modes related to this variation of stiffness in the height of the indirectly affected part may then occur, which will have to be checked; they have been illustrated in Figure 32: - the development of a global plastic mechanism in the indirectly affected part under the action of the membrane forces transferred by the DAP to the IAP of the structure; 66 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 5. UNIDENTIFIED THREATS - the buckling in compression of the upper beams of the DAP as a result of a possible progressive development, in the whole structure, of an arching effect induced by the sway deformability of the left part of the IAP of the structure. Finally, it must be noted that the verification of the buckling resistance of the IAP columns adjacent to the lost column (see Figure 32) will have to be achieved in all cases, whatever the stiffness of the IAP. This check will be performed by assuming an individual overloading of these columns, further to the event, equal to one-half of 𝑁@$,4B+;:- in 2D structures, and one fourth of 𝑁@$,4B+;:- in 3D structures. 5.3.2.1 Contribution from the slab As mentioned in Section 5.1, the slabs can play a key role in the way on how the structure will behave further to the loss of a column. This event leads, for the slabs located above the lost column, to the loss of one of their vertical supports and therefore to a significant increase of their free span and to the development of large deflections. The behaviour of reinforced concrete slabs undergoing large deflections is investigated since many years and models with different degrees of complexity have been proposed in the literature. Most of these ones are based on the preliminary application of the well-known first-order yield line theory proposed by Johansen (Hognestad, 1953). This theory requires first to select a failure plastic mechanism in the slab, and then, by applying the principle of virtual works, to compute the plastic load resistance as an upper bound solution. When the plastic load is reached, it is assumed that the cracks and the curvature of the slab are concentrated along yield lines (see examples in Figure 37). The blocks surrounded by these yield lines are assumed to remain elastic and planar, and rotate rigidly around the yield lines. The yield line pattern is affected by several parameters, such as the plastic moment capacities of the slab cross-sections, the support conditions, and the geometry of the slab. The models initially proposed for reinforced concrete slabs can be easily and safely extended to composite slabs by only considering the contribution of the reinforced concrete slabs located above the ribs, i.e., by neglecting the contributions from the steel sheet and the concrete inside the ribs. This procedure applies when the slabs are connected or not to the steel beams, but the presence of a connected slab may influence the yield-line pattern. In Figure 37, the left pattern may apply to both situations while the right one represents a possible yield line pattern only in the absence of connected beams. By applying this theory to the slabs located above the lost column, a plastic resistant surface load may be derived which has to be compared to the applied surface load (for an accidental combination). If this plastic load is bigger than the applied one at each storey above the lost column, the slabs are able themselves to sustain the applied accidental loads and, therefore, the structure can be assumed as robust. If it is not the case, plastic mechanisms will form in the slabs and other structural contributions will have to be activated to survive the column loss scenario. In this case, one first possibility is to activate membrane effects. If an internal column is lost, the method developed by Bailey (Bailey, 2001) can be used. In his work, Bailey investigated the loadbearing capacity of orthotropic laterally unrestrained slabs with only one layer of reinforcement, by referring to an equilibrium method and accounting for the membrane forces. By applying this method, the load carrying capacity of the slab can be evaluated. In the framework of the RobustImpact RFCS project (Kuhlmann et al., 2017), the effectiveness of the combined Johansen/Bailey method has been tested on different column loss scenarios. The results were compared with the outcomes of FE numerical model with a good agreement. As an alternative, numerical tools can also be used to predict Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 67 5.3 ALTERNATIVE LOAD PATH METHODS the response of the concrete slabs, but it falls out of the scope of the present section dedicated to analytical approach. Reference can be made to Section 5.3.4 for this alternative. When an external column is lost, the contribution coming from the development of plastic mechanism in a slab can be accounted for by considering the yielding lines illustrated in Figure 38. However, the possibility to activate membrane forces is very limited and can therefore be neglected. Possibilities to activate other structural “robustness” contributions than the “yield mechanism” and “membrane effects” ones in the slab strongly depends on the configuration of the floor and more globally of the structure. These possibilities will be addressed in the following subsections for different structural typologies. Figure 37. Examples of failure mechanisms for an internal column loss (Lemaire 2010) Figure 38. Examples of failure mechanisms for an external column loss 5.3.2.2 Simplified analytical methods for structures with simple joints If the slabs are not able to sustain the loads associated to the column loss scenario (see Section 5.3.2.1), it remains to check the possible contribution from the supporting steel structure (see Section 5.3). As simple joints act at the ends of the beams, no “plastic mechanism” robustness contribution may be expected, and the possibility to develop beam arching effects is also quite questionable. But on the other hand, large displacements may occur in the structural system leading to potential high membrane forces However, the contribution resulting from the activation of these membrane forces cannot be cumulated with the contribution from the slab. Indeed, as above-mentioned, the activation of the membrane forces in the beams is only possible for large displacements which are not compatible with the deformation capacity of the slab. Accordingly, the final objective here is so to see if an equilibrium between the so-activated membrane forces in the beams only and the load associated to the column loss can be found as explained here after. 68 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 5. UNIDENTIFIED THREATS The development of the membrane forces strongly depends on the stiffness KH,t of the indirectly affected part (see Section 5.3). If this stiffness is very small, negligible membrane forces will develop in the directly affected part and so the structure will be considered as “not robust”. On the other hand, if this stiffness is significant, large membrane forces will develop and a new state of equilibrium may be found in the deformed shape. If the slab has been initially designed to work as a diaphragm, it may be assumed to be rigid in its plane. As a consequence, the value of the KH,t stiffness of the indirectly affected part introduced in Section 5.3 may be taken as infinite, the extremities of the directly affected part being totally fixed in the horizontal direction. Indeed, when these beam extremities intent to move horizontally, the structure comes into direct contact with the slabs at the different storeys; these contacts prevent these extremities from moving by activating the slab in compression in its plan. Based on this assumption, the response of the structure further to a column loss may be easily predicted using the static and kinematic theorems, i.e., using the equations of equilibrium and expressing the compatibility of displacement. An example is given for the 2D frames with simple joints illustrated in Figure 39 in which the concrete slabs acting as diaphragms are placed at each floor level. For this frame, the membrane forces Tbeam developing in the beams of the directly affected part may be predicted referring to the sub-system illustrated in Figure 39. Because of the presence of the slabs at each storey (infinite value of KH,t), the same tension force develops in all the beams (assumed to be the same at each floor level) of the directly affected part. Accordingly, each double-beam will resist in the same way to the force 𝑁@$,4B+;:- , the axial load which is initially present in the column before the event and which can be evaluated under the accidental load combination (EN 1990, 2002). Consequently, the behaviour of the frame can finally be studied using the sub-system of Figure 39 submitted to a force 𝑁@$,4B+;:-/𝑛+3 , nst being the number of storeys activated in the directly affected part. Figure 39. Simplified analytical approach – from a 2D frame to a sub-system model For the so-defined sub-system, the following equations can be written based on equilibrium and geometrical considerations: 𝑁@$,4B+;:- 𝑛+3 =2.𝑇"B10.sin𝜃 (24) 𝐿=𝐿,/cos𝜃 (25) where L is the length of the individual beams in the deformed system and L0 is their initial length. In the elastic range, the elongation of the beams is related to the tension force they sustain: Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 69 5.3 ALTERNATIVE LOAD PATH METHODS Δ𝐿=𝐿−𝐿,=𝑇"B10.𝐿, 𝐸.𝐴 (26) where E is the Young modulus of the beam material and A is the beam cross-section area. Replacing 𝐿 by 𝐿,/cos𝜃 in this equation, a system of two equations with two unknowns, 𝑇"B10 and 𝜃 , is obtained: 𝑁@$,4B+;:- 𝑛+3 =2.𝑇"B10.sin𝜃 (27) 𝑇"B10 =1−cos𝜃 cos𝜃.𝐸.𝐴 (28) By solving this system of equation, it is possible to predict (i) the tensile load 𝑇"B10 to be supported by the beams and the joints at the extremities, and (ii) the rotation capacity demand 𝜃 for the simple joints. As previously mentioned, it is assumed that the beams of the directly affected part are remaining in the elastic range; accordingly, it is required to check if these beams subjected to bending moments (coming from the gravity load) and to the tensile load Tbeam remains elastic. For the check of the simple joints both in terms of resistance (under Tbeam) and rotation capacity ( 𝜃 ), reference can be made to Sections A.5.1 and A.2 respectively. This model can be easily extended to 3D structures as reflected in Section A.7. 5.3.2.3 Simplified analytical methods for structures with partial-strength joints If partial-strength joints are used at the extremities of the beams, the column loss scenario will result first to the development of a plastic mechanism in the directly affected part (see Section 5.1) with plastic hinges forming at the level of the partial-strength joints. The plastic load associated to the formation of a plastic mechanism in a beam with partial-strength joint (Figure 40) is obtained through the following equation (assuming the joints at the beam extremities are the same): 𝑁=@,; =2.𝑀C4,; 6+2.𝑀C4,; D 𝐿 (29) where 𝑀C4,; 6 is the design plastic resistance of the partial-strength joint at the extremities of beam i under hogging moment while 𝑀C4,; D is the one under sagging moment. This formula can be used for the beams of each storey above the lost column and the sum of the soobtained Npl,i values corresponds to the plastic load Npl required to form a plastic mechanism in the directly affected part: 𝑁=@ =v𝑁=@,; ; (30) If the so-obtained value of Npl is greater than Nlo,design (see Section 5.3.2.2), then the beams of the directly affected part can sustain the column loss and the structure can be assumed as robust. Figure 40. Beam plastic mechanism developing in a beam with partial-strength joints 70 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 5. UNIDENTIFIED THREATS If not, the contribution from the beams (Equation (30)) can be cumulated with the contribution resulting from the development of a yield plastic mechanism in the slabs (see Section 5.3.2.1). This one has here to be evaluated by applying a transverse concentrated load on the slab at the level of the lost column. For this specific loading condition, a concentrated load Npl,slab,i associated to the formation of a plastic mechanism in the slab at each storey i may be computed using the Johansen theory (see Section 5.3.2.1). Finally, the plastic load Npl,slab corresponding to the formation of a plastic mechanism in all the slabs of the directly affected part writes: 𝑁=@,+@1" =v𝑁=@,+@1",; ; (31) If Npl + Npl,slab is greater than Nlo,design (see Section 5.3.2.2), then the beams and the slabs of the directly affected part can sustain the column loss and the structure can be assumed as robust. If not, it is required to look for other possible contributions. The activation of the latter strongly depends on the nature of the failure mode at the level of the partial-strength joints as explained here below. If the failure mode is associated to components in tension, in bending or in shear, this means that the components in compression (column web in compression or beam flange and web in compression) have not reached their plastic resistance yet. In such conditions, an arching effect can be mobilised in the beams of the directly affected part, as schematically illustrated in Figure 41, as soon as the plastic mechanism is formed. This arching effect (i) prevents the apparition of significant vertical displacements within the directly affected part and (ii) allows for the mobilisation of extra resisting forces in the system. This arching effect vanishes when the resistance of the row in compression at one of the extremities of the rod representing the arch members (Frd,c – see Figure 41 in which it is assumed that the joints at the extremities of the beams are the same) is reached. Figure 41. Schematic view of the arching effect within a beam of the directly affected part To predict the extra forces which can be mobilised through this arc effect, the following procedure can be applied in which it is assumed that the stiffness of the indirectly affected part KH,c is infinite (see Figure 41). The proposed procedure can be adapted to other situations but will require more refined analytical models described in Section 5.3.2.5. The first step consists in evaluating the vertical displacement D pl,i of the beams at each storey level i, when the beam mechanism has formed. The corresponding value, obtained by means of a second order analysis, is equal to: ∆=@,;=𝑁=@,;.(2.𝐿,)E 192.𝐸.𝐼#,; +𝐿,.𝑇𝑎𝑛(𝑀C4,; 𝑆F,;-;,; 𝜂) (32) Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 71 5.3 ALTERNATIVE LOAD PATH METHODS where E is the young modulus of the steel, Iy,i is the moment of inertia of the beams, MRd,I is the bending resistance of the joint at the beam extremities, Sj,ini,i is the initial stiffness of the joint, all three values at level i. h is the stiffness modification coefficient as defined in Table 5.2 of (EN 1993-1-8 2005). This equation is valid for steel beams with joints exhibiting the same stiffness and resistance under sagging and hogging moment at each extremity, but it can be adapted to other configurations. When the plastic mechanism forms in the beams at level i, the horizontal springs from Figure 41, representing the components in compression, are already subjected to a force Ft (corresponding to the sum of the tensile loads in the rows in tension, for sake of horizontal equilibrium within the joints). Accordingly, these springs exhibit a shortening equal to: 𝛿(,B@ =𝐹3 𝑘B**,(.𝐸 (33) where keff,c is the effective stiffness coefficient of the row in compression computed according to Section 6.3.3.1 of (EN 1993-1-8 2005). The position of the arch rod when the plastic mechanism forms in the beam is illustrated in orange in Figure 42. The length of the arch rod LD at that moment is equal to: 𝐿G=|}𝐿,+2𝛿(,B@~5+}ℎ(−Δ=@,;~5 (34) The resistance of the arching effect is reached when the resistance of the joint row in compression FRd,c is reached, which corresponds to a deformation at the level of the joint row in compression equal to: 𝛿(,=@ =𝐹C4,( 𝑘B**,(.𝐸 (35) and to an inclination of the arch rod q (see Figure 42) equal to: 𝜃)=𝐴𝑐𝑜𝑠 • 𝐿,+2.𝛿(,=@ +𝛿H 𝐿G ‚ =𝐴𝑐𝑜𝑠 • 𝐿,+2.𝛿(,=@ 𝐿G ‚ (36) where 𝛿H=I$%,!6I' H(,! is the horizontal displacement of the indirectly affected part; it is here equal to 0 as KH,c is assumed to be infinite. In this equation, it is reasonably assumed that the length of the arch rod LD remains constant. It has to be highlighted that the horizontal spring reflecting the behaviour of the indirectly affected part is only activated when the plastic mechanism is formed, i.e., when the arching effect develops. Indeed, prior to the development of the plastic mechanism, no horizontal forces are reported to this part as the beams are working in bending only. Knowing this value of q r, the contribution coming from the arching effect NArch,i is finally obtained by expressing the horizontal equilibrium of the system: 𝑁J)(K,; =2.𝑇𝑎𝑛(𝜃)).}𝐹C4,( −𝐹3~ (37) Obviously, if the resistance of the joint at extremities of the beams is associated to a component in compression, Ft is equal to FRd,c (for sake of equilibrium) and so, no arching effect can be mobilised at level i (Narch,i = 0). 78 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 5. UNIDENTIFIED THREATS as illustrated in Section 5.3.2.5. Such approach would be more practical in common design practices than nonlinear finite element models allowing the easy shift from the prescriptive rules and the associated limitations to a more accurate approach in assessing structural robustness. This approach has been evoked in Section 5.3.2.5 and details are provided in Annex A.8. 5.3.3.5.2 Simplified assembly of the nonlinear static response for a single floor Simplified modelling can be utilised to determine the nonlinear static response of a single floor system though the assembly of the responses of individual beams in a grillage approximation ignoring the membrane effects of the slab. As shown in Figure 47, for a dominant deformation mode, the overall system response of the single floor system ( 𝑃 , 𝑢+ ) can be assembled from that of the individual beams ( 𝑃; , 𝑢+,; ) as: 𝑃=1 𝛼v𝛼;𝛽;𝑃; ; (41) where 𝛽; is a compatibility factor relating the individual beam displacement to the floor reference displacement ( 𝑢+,; =𝛽;𝑢+ ), as illustrated in Figure 47, 𝛼; is a non-dimensional work-related factor that depends on the assumed load distribution on the beam and may depend on the incremental deformation mode at the current level of loading (i.e., 0.5 for uniformly distributed load and 1 for point load), and 𝛼7 is also work-related factor that depends on the gravity load distribution on the beam (i.e. 0.25 for uniformly distributed load). Figure 47. Grillage approximation of a single floor system 5.3.3.5.3 Simplified assembly of the nonlinear static response for multiple floors Similarly, simplified modelling can be utilised to determine the nonlinear static response of multiple floors system above the damaged column though the assembly of the responses of individual floors. Assuming an SDOF deformation mode as shown in Figure 48 (Izzuddin, 2010) in which the floor displacement ( 𝑢+,F ), measured along the failed column line, is constant for all floors, the overall response from individual floors can be expressed as: 𝑃=1 𝛼v𝛼F𝑃F F (42) where 𝛼F7 is the work-related factor for floor (j) (i.e., 0.25 for uniformly distributed load). While 𝛼7 is the overall work-related factor for the whole system (i.e., 0.25 for uniformly distributed load). Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 79 5.3 ALTERNATIVE LOAD PATH METHODS Figure 48. Simplified model for multiple floor system (Izzuddin, 2010) Lastly, it is worth mentioning that detailed modelling can be applied at bay, multiple floors and single floor levels, where shell elements can be utilised accounting for material and geometric nonlinearity coupled to the beam elements and can capture the 2D membrane effects within the floor slab. This would be more accurate than the case of simplified modelling of single floors using a grillage approximation which inherently cannot account for the membrane floor action. Additionally, detailed models can be used in combination with simplified models where detailed modelling can be applied on the beam level and the nonlinear static response at the higher levels of structural idealisation can then be assembled using simplified modelling. 5.3.3.6 Simplified dynamic assessment In the event of a sudden column loss, the typical response of a building structure is highly nonlinear and dynamic, therefore, the maximum dynamic response of the structure should be considered when assessing the resulting ductility demands. In this framework, the maximum dynamic response is determined through a simplified approach, as illustrated in Section 5.3.5, without the need of any complex nonlinear dynamic analysis which is not practical for typical/common design situations. The proposed approach is more accurate than the traditional dynamic amplification factor approach with the amplification factor depending on both the level of gravity loading and the nature of the nonlinear response thus lacking generality for common forms of nonlinear static response (Izzuddin, 2010). 5.3.3.7 Ductility assessment The last stage of the proposed assessment framework is to compare the maximum dynamic displacement ( 𝑢4 ) obtained from the pseudo-static response at ( 𝑃=𝑃$ ) with the ductility limit ( 𝑢* ) to evaluate the limit state as shown in Figure 49. The ductility limit ( 𝑢* ) is determined as the minimum value of ( 𝑢4) such that the deformation demand exceeds the ductility supply in any of the joints as discussed in other sections of this document. Alternatively, the limit state can be established by comparing 𝑃$ to the pseudo-static capacity ( 𝑃* ), where 𝑃* is defined as: 𝑃*=max(𝑃-)7777777for777777770≤𝑢4,- ≤𝑢* (43) 𝑃* would normally corresponds to 𝑢* on the pseudo-static response curve, however, this wouldn’t be the case if the response undergoes a softening behaviour due to compressive arching. In the case of using simplified modelling at the system assessment level where the system response is obtained from simplified assembly of lower-level models, the displacements of the sub-systems can be determined from 𝑢4 using the appropriate compatibility conditions. The deformations experienced by the joints can then be determined for the displacements at the lowest level of the considered subsystem which would be either represented by detailed beam/floor models or by simplified beam 80 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 5. UNIDENTIFIED THREATS models. Both the rotational and axial joint deformations must be considered, particularly when sufficient axial restraint is present that can lead to the development of catenary action. The ductility demands in the different components of the joint can then be obtained from the total joint deformations and compared to the ductility supply of the different components. It is important to note here that the system limit state is defined by the failure of a single joint such that the ductility demand exceeds the ductility supply in one or more of the joint components. However, if the failure of a single joint would not lead to a system failure in the presence of sufficient residual redundancy and ductility, this limit state can then be re-established for the system with the exclusion of the failed joint and any affected sub-systems beyond the associated ductility limit. 5.3.3.8 Assessment of floor systems subject to failed floor impact The collapse of only one floor can lead to onerous demands on the lower impacted floors that also have to sustain the debris loading which will in turn increase the vulnerability of the structure to progressive/disproportionate collapse. However, under specific circumstances, it may be possible for the lower part of the structure to arrest impact and prevent progressive collapse. The factors that primarily influence such possibility include: (i) the number of failed floors above the level under consideration, (ii) the reduction in kinetic energy through energy absorption within the failed floors as well as energy loss upon impact, and (iii) the ability of the lower structural floor system to sustain the additional load from debris, accounting for the associated dynamic effects. Vlassis et al. (2007; 2009) proposed a design-oriented methodology for the assessment of progressive collapse resistance of floor systems in multi-storey buildings subject to impact from one upper failed floor. The proposed method can also be generalised to deal with the initial failure of more than one floor. The underlying basis of the proposed framework is that the ability of the lower floor to arrest the falling floor mainly depends on the amount of kinetic energy that is transmitted from the upper floor during impact. Similar to the simplified assessment procedure discussed above for multi-storey buildings under sudden column loss scenarios discussed above, the proposed approach uses the nonlinear static response of the impacted floor along with an energy balance approach to estimate the maximum dynamic deformation demands without the need for detailed nonlinear dynamic analysis. The study demonstrates the extremely onerous conditions imposed on the impacted floor that can result in an increased vulnerability to progressive collapse for structures of this type. Importantly, the likelihood of shear failure modes in addition to inadequate ductility supply under combined bending/axial actions is identified, thus establishing the need for further research work on the dynamic shear capacity of various joint types subject to extreme events. 5.3.4 Full numerical approach In recent years, the increased computational capacities and the availability of advanced numerical programs (FEM, AEM, DEM) able to manage most of the phenomena characterising the building response in accidental loading conditions opened the way to design solutions based on a full numerical approach. The effectiveness of this approach, which is nowadays commonly used, strongly depends on the ability of the designer to identify and model the key factors affecting the structural response. In this framework, great attention should be paid to phenomena associated with energy dissipation due to the activation of local plasticity, such as plastic hinges and yield lines, and failures associated with the constitutive behavioural laws adopted for the materials. Different degree of accuracy can be used when modelling the materials, ranging from the simplest ones, i.e., the linear elastic models, to the more complex non-linear ones, also incorporating strength and stiffness degradation. The linear elastic laws can be used in elastic models which can be adopted in the preliminary design phases to identify critical issues of the structural response to be investigated Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 81 5.3 ALTERNATIVE LOAD PATH METHODS in further more accurate studies. However, collapse scenarios induce large displacements into the structure and activate the non-linear-response of materials, non-linear material models are the most appropriate. Materials yielding provides the main contribution to the energy dissipation capacity and to the redistribution of the internal forces. Steel yielding must be properly represented because it enables development of plastic hinges and activation of the catenary effect in beams. At this aim, models of different degree of accuracy and complexity can be used. A useful guide about the steel stress-strain relationships to be adopted can be found in EN 1993-1-14 (2020). For concrete also, the constitutive law should be properly modelled, incorporating its asymmetric response in tension and compression, in order to enable simulation of cracking, which is vital for catching the development of yielding lines in the concrete slab. Besides, highly refined materials models can be adopted incorporating the unloading and reloading branches from an inelastic state. Moreover, depending on the level of complexity and accuracy of the analysis, considering the materials’ cumulative damage would allow to catch local collapses as well as the potential detachment of the components. When required by the specific design scenario, other material features should be properly modelled. As an example, when investigating fire scenarios, the temperature dependence of the mechanical properties of the materials should be accounted for. At this aim, a guide is provided by part 1-2 of the Eurocodes and in particular EN 1992-1-2 (2004) and the EN 1993-1-2 (2005), for concrete and steel, respectively. Similarly, when the scenarios involve dynamically applied actions (e.g., explosions or impact loading), the strain rate sensitivity of the material properties should be considered. The effects of strain rate on material strength are usually implemented into models considering a dynamic increase factor (DIF) (Johnson and Cook, 1983; Malvar and Crawford, 1998). A second key element of the modelling phase is the choice of the finite element types (line, surface, volume or special elements such as mass, spring…). In detail, the order and type of the chosen finite elements are related to the structural behaviour (magnitude of deflections, strains, rotations, stresses), the chosen method of analysis (linear and non-linear) and the material representation (linear or non-linear). In framed structures, beams and columns are usually modelled via beam elements with centroidal axis coincident with the centroid of the cross-sections. Nevertheless, when significant for the structural response, eccentricities have either to be accounted for explicitly or considered in the interpretation of the results of analysis. The selection of the beam element, in terms of DOFs depends on the investigated problem. Local behaviour such as web crippling or plate buckling are not covered by the beam modelling and they should be taken into account with more sophisticated models or additional calculations. Shell or solid elements are usually used to account for the slab contribution in 3D models. The first approach, although characterised by high computational efficiency, makes difficult to catch in detail the behaviour of slabs in the various phases of the response from flexural to membrane-like. A full 3D solution with solid elements should hence be adopted to account for the various combined effects of the composite floor response, such as the yielding and fracture in the steel reinforcement mesh and deck, the crushing in the concrete slab, the nonlinear behaviour of the shear connectors. In order to reduce the computational demand a hybrid approach may offer a “mid-way” solution, which consists in the use of shell elements combined with a smeared steel layer for modelling the reinforcement in the two directions. In addition, the possible steel deck can be simulated with beam elements in the direction of the steel deck ribs and then connected to the slab through tie constraints. This approach 82 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 5. UNIDENTIFIED THREATS allows considering the steel components needed to simulate the tensile resistance of the slab when the membrane effect develops. Eventually, shear connections between beam and slab can be simply modelled through links characterised by laws suitable to represent the shear connection. As the joints (in particular the beam-to-column joints) are key structural components in preventing progressive collapse, an adequate modelling is required. In detail, depending on the level of the analysis, the joints may be modelled either in a “sophisticated” way (i.e., using solid or shell elements) or through a simplified approach, i.e., using beam elements, constraints or springs. To limit the complexity of the analysis, simplified models, such as the component method (EN 1993-1-8, 2005; EN 1994-1-1, 2004), are usually adopted with the requirement that the key parameters of stiffness, strength and deformation capacity of the steel joints are caught with adequate accuracy. More details about the characterisation of joints are provided in Section 2.2. Another important issue is the definition of the boundary conditions: they should reflect in a realistic way the actual restraint conditions providing a kinematically stable static system, and should be consistent with the DOFs of the type of finite element used. Interaction between different parts or components of a model usually requires definition of contacts. The FE programs nowadays available allow the designer to select different types of contact models. Their calibration requires a set of parameters to be accurately identified. For this reason, incorporating contacts between the parts in the model enables a more realistic simulation of the structural response but at the cost of higher design and computational time. Finally, the choice of the type of analysis: it depends on the problem to be investigated. Linear analysis is simpler to be developed and can be performed via commercial software. Nevertheless, linear analysis cannot activate the main source of non-linearities typical of progressive collapse scenarios which arise from: i) large displacements and large strains (geometric non-linearity); ii) non-linear stress-strain relationships (yield and material non-linearity); iii) change of contacts between elements (topological/contact, non-linearity). Therefore, non-linear analysis, which requires the use of advanced design tools, should be performed. The numerical analyses should aim at providing the background necessary to evaluate the structural ability to activate alternative load paths. Based on the displacement field, it is possible to estimate the deformation capacities required in the plastic zones and evaluate the additional design forces in the structural elements; accordingly, it is possible to check if the structure is sufficiently robust to reach this new state of equilibrium (Demonceau et al., 2018). These additional forces may lead to different potential failure modes which needs to be considered: • Joint failure: the beam-to-column joints which are initially designed for bending moment and shear forces have to support additional tension forces which arise from the presence of the catenary action. This may lead to failure of some joint components. Also, if partial-strength joints are used, the latter will yield and failure may occur due to excessive deformations, i.e., by lack of ductility. • Beam failure: for structures with full-strength joints, the entire plastic zone may develop at the beam extremities. As plastic hinge develops due to bending moment, followed by significant deformations under M-N interaction, this yielded zone may fail by lack of deformation capacity. Also, the beams at the top of the frames may fail by instability under bending and compression, this compression being associated with the development of an arching effect in the structure. Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 83 5.3 ALTERNATIVE LOAD PATH METHODS • Column instability: extra compression forces are developing in the columns adjacent to the lost one which may lead to column buckling. In addition, columns on which catenary forces act may be more sensible to buckling as high forces can lead to significant out of plane displacements. Detailed numerical simulations of explosive events may also be contemplated. Nevertheless, it is important to be aware that numerical models and analysis procedures still need experimental validation. One such tool is the Extreme Loading for Structures (ELS) software, which allows structural engineers to design and analyse a structure subjected to blast loads with full 3-D nonlinear dynamic analysis. The results allow users to visualize in 3D how the building or different structural components inside the building will behave under the prescribed conditions. Moreover, because ELS is based on the Applied Element Method (AEM), engineers can visualize the after-blast effect of the resultant debris and its effect on other structural components, creating a “true damage” picture of the occurrence. In this software, blast pressure loading curves can be created automatically using UFC 3340-02 (Structures to resist the effects of accidental explosions) or by importing custom pressure time history loads. 5.3.5 Prediction of the dynamic response from the static one The maximum dynamic response can be determined from the nonlinear static response through a simplified approach. The main concept behind this proposed simplified approach is that the sudden column loss resembles in effect the sudden application of the gravity load on the directly affected substructure, especially when large deformations are sustained. Immediately after column loss, the structure accelerates from rest where the gravity load exceeds the static structural resistance and where the difference between the work done by the load and the strain energy stored is transformed into kinetic energy. As the deformations increase, the static resistance exceeds the applied loading and the strain energy stored becomes more than the work done by the gravity load, which consequently leads to a continuous reduction in kinetic energy until the structure is brought back to rest at a maximum dynamic displacement. Considering the response being dominated by a single deformation mode, the maximum dynamic response is reached when the kinetic energy is reduced back to zero, or in other words, when the work done by the gravity loads becomes identical to the energy absorbed by the structure. This gives rise to the concept of a pseudo-static response. Considering the nonlinear static load-deflection response for a given appropriate level of idealisation of the structural system at two levels of suddenly applied loading (P = λ1Po) and (P = λ2Po) as shown in Figure 49a and Figure 49b (Izzuddin et al., 2008), the maximum dynamic displacements ( 𝑢4,7,𝑢4,5 ) associated with the sudden application of gravity load (λPo) can be determined from energy balance between the work done by the load and the internal energy stored. Figure 49. Simplified dynamic assessment and definition of pseudo-static response (Izzuddin et al., 2008) 84 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 5. UNIDENTIFIED THREATS With the assumption of a SDOF mode, the equivalence between external work ( 𝑊- ) and internal energy ( 𝑈- ) can be obtained such that the two depicted hatched areas become identical. Utilising the nonlinear static load-deflection response allows the level of the suddenly applied gravity loading (Pn = λnPo) that result in a certain maximum dynamic displacement ( 𝑢4,- ) to be obtained as follows: 𝑊-=𝛼λ-𝑃$𝑢4,-;77777777𝑈-=Œ 𝛼𝑃d𝑢+ !%,. ,;77777777𝑊-=7𝑈- (44) 𝑃-=λ-𝑃$=1 𝑢4,- Œ 𝑃d𝑢+ !%,. , (45) such that the integral represents the area under the nonlinear static ( 𝑃 , 𝑢+ ) curve up to 𝑢4,- . If the suddenly applied gravity loading ( 𝑃-) is plotted against the maximum dynamic displacement ( 𝑢4,- ) for different levels of loading ( λ- ), the “pseudo-static” response can then be obtained as shown in Figure 49c. For the actual gravity loading ( 𝑃$) , the maximum dynamic displacement can be easily obtained from the pseudo-static response at ( 𝑃=𝑃$ ). In addition, the complete pseudo-static response provides useful information about the impact of different levels of gravity loading in the event of sudden column loss and the sensitivity of the maximum dynamic displacement to the slight changes in the applied gravity load. Ultimately, this proposed simplified approach allows the pseudostatic response to be directly obtained from the nonlinear static response, unlike the use of detailed nonlinear dynamic analysis that would require a large number of simulations under different levels of gravity loading. A simple and straightforward procedure for establishing the pseudo-static response curve and the maximum dynamic displacement is provided as follows (Izzuddin et al., 2008). Assuming a nonlinear static response defined as a ( 𝑃 , 𝑢+ ) curve, whether from detailed finite element modelling or using simplified analytical expressions, the presented algorithm can be used to establish the pseudo-static response ( 𝑃 , 𝑢4 ) curve and the dynamic displacement corresponding to the suddenly applied gravity loading ( 𝑃=𝑃$ ). In the following proposed algorithm, 𝑃0\- refers to the suddenly applied load ( λ0\-𝑃$ ), while 𝑃4,0\- refers to the amplified static load ( λ4,0\-𝑃$ ), with m and n indicating the start and end of the current increment, respectively. 1. Initialise: 𝑃4,0 =𝑃0=0 , 𝑢4,0 =0 , 𝐴0=0 ; choose a small displacement increment ∆𝑢4 . 2. Set: 𝑢4,- =𝑢4,0 +∆𝑢4 . 3. Determine 𝑃4,- corresponding to 𝑢4,- from nonlinear static response ( 𝑃 , 𝑢+ ) curve; obtain current area under the ( 𝑃 , 𝑢+ ) curve: 𝐴-=𝐴0+(𝑃4,0 +𝑃4,-)∆𝑢4/2 . 4. Determine current pseudo-static load: 𝑃-=𝐴-/𝑢4,- ; establish new point ( 𝑃- , 𝑢4,- ) on pseudo-static response ( 𝑃 , 𝑢4 ) curve. 5. If (𝑃0<𝑃$≤𝑃-) , obtain and output dynamic displacement corresponding to 𝑃$ : 𝑢4= 𝑢4,0 +(𝑢4,- −𝑢4,0)(𝑃$−𝑃0)/(𝑃-−𝑃0) . If more points are required for pseudo-static response curve: update: 𝑃𝑑,𝑚 =𝑃𝑑,𝑛 , 𝑃𝑚=𝑃𝑛 , 𝑢𝑑,𝑚 = 𝑢𝑑,𝑛 , 𝐴𝑚=𝐴𝑛 ; repeat from step 2. 5.4 Key element method According to the literature, a key element is a structural component or a part of the structure whose failure entails further damage that violates the performance objective. In order to avoid local damages exceeding an assumed limit value, such elements have to be properly identified and designed. Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 85 5.5 SEGMENTATION METHOD Following the “recent” codes (EN 1991-1-7, 2006), the strength of the key elements has to be enhanced to withstand a specified level of load. This design strategy is frequently adopted for structures possessing a limited level of redundancy such as tensile structures, 2D and 3D trussed systems, cable stayed and suspension structures. Key elements can also be used in addition to other design features to improve the robustness of high-risk buildings (Arup, 2011). Furthermore, this design approach is often the only rational approach when retrofitting existing buildings. Depending on the context, examples of potential key elements could be columns, load-bearing walls of a building, piers of continuous bridges or cables in a cable-supported structure (Starossek and Haberland, 2012). According to EN 1991-1-7 (2006), the accidental design action for checking key elements is of 34 kN/m2 applied in any direction. This load, based on the Ronan Point collapse in London, 1968 (Way, 2011), is intended to represent a possible range of impact and blast events and is used as a tool for designing key elements to be more robust than what is required for normal design cases. The key elements must be designed to develop their full resistance without failure of either the member itself or of its joints. Therefore, the design action should be applied to the key element and any components attached to it, unless the attached components or their joints cannot sustain the 34 kN/m2. Hence, for the design of a key element, it is necessary to consider which components, or portion of components, will remain attached to the element in the event of an accident. This implies that various cases of loading would need to be considered for a wall or slab attached to the member, with due account of upper and lower limits of the attachment capacity. In this design approach no capacity for load redistribution needs to be provided. Therefore, the key element approach includes the following steps: § Identification of the key structural members. § Design of the key elements to resist to an accidental design action Ad applied in the horizontal and vertical direction, one direction at a time. According to EN 1991-1-7, the recommended value for Ad is 34 kN/m2. However, if appropriate, other accidental actions can be considered. § The accidental design action has to be applied to the key element and to any attached component. In the design process, the accidental load combination of Eurocode 0 (EN 1990, 2002) should be used in the design of key elements and their attached components. 5.5 Segmentation method Segmentation/compartmentalisation is a design strategy that can offer a possibility to enhance the robustness of a structure. In such an approach, the spreading of failure following an initial damage can be prevented or limited by isolating the failing part of a structure from the remaining structure by what can be referred to as segment/compartment borders. Such approach would ensure that each part/compartment/segment is able to collapse independently without affecting the safety of the other parts. Segmentation strategies can generally be based on either weak segment borders or strong segment borders where the locations of the segment borders are selected by the design engineer within the scope of the design objectives and in accordance with the requirements of the client and the relevant authorities depending on the type and importance of the structure (Starossek, 2007; Starossek and Haberland, 2012; CEN/TC250/WG6, 2020). In alternative load path methods, the extent of collapse increases, and the effectiveness of the method decreases with an increase in initial damage size. It is thus preferable in the case when the size of the 86 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 5. UNIDENTIFIED THREATS initial damage is assumed to be small. On the other hand, when using the segmentation strategy, the extent of collapse and the effectiveness of the method are considered to be insensitive to the size of the initial damage, provided that the segments sizes are not too small. However, the fixed extent of collapse due to segmentation is relatively large corresponding to the failure of the whole segment. Consequently, such method is desirable when the initial damage size is assumed to be of a large value. Segmentation can also be combined with alternative load path methods, where alternative paths can be provided within the individual segments. In such case, the extent of failure spreading will not be significantly larger than the initial assumed damage for both small and large initial damage sizes (Starossek and Haberland, 2012). 5.5.1 Weak segment borders Segmentation achieved using weak segment borders would allow the failure of a specific segment to take place without the progression of failure to other adjacent segments. In such mode, segmentation can act as a structural fuse, where failing parts can safely disconnect from the structure. This segmentation method can be achieved by eliminating continuity between adjacent segments/ compartments or reducing the stiffness to accommodate large deformations and displacements at the segment borders and thus limiting the amount of force transmitted to the surrounding structure (Starossek, 2007; Starossek and Haberland, 2012; CEN/TC250/WG6, 2020). It should be also noted that providing continuity in general has a desirable effect on the overall performance of the structure in extreme events; however, continuity can be detrimental when the resulting alternate load paths are not provided with the required strength that is able to withstand the forces transmitted by continuity. Therefore, in the case where alternative load paths are impractical, or too expensive to be provided, segmentation by selectively eliminating continuity would be advantageous. This is also the case if alternate load paths (or collapse-isolating elements) are strong enough, but the corresponding verification proves difficult or unconvincing (Starossek, 2006). For building structures, such a form of segmentation is commonly applied to horizontal low-rise buildings which have a relatively large footprint. In such low structures, it can be assumed that collapse would involve the full height of the building; however, it is limited in horizontal extent at locations where collapse forces cannot be transferred across the boundary to the surrounding structure. As stated, it is desirable that alternative paths are provided within the individual segments. It should mentioned that the surrounding structure should be checked under the highest possible level of tying forces such that failure in adjacent segments should be avoided. 5.5.2 Strong segment borders Segmentation based on strong segment borders is designed to prevent an incipient collapse providing high local resistance that is able to accommodate relatively large forces. In this mode, segmentation can offer an alternate load path, such that resistance to local damage is achieved at relatively small deformations, or it can stop the collapse of part of the structure. This form of segmentation can be considered for vertical structures, such as the case of multi-storey buildings with outrigger or belt trusses at regular intervals, where such trusses can act along with vertical tying to allow for the redistribution of the loads following local damage arresting falling debris and adding stability to the surrounding structure (CEN/TC250/WG6, 2020; Starossek, 2007; Starossek and Haberland, 2012; Starossek, 2018; Ellingwood et al., 2007). A third possibility of creating segment borders is to provide them with high ductility and large energy dissipation capacity (to accommodate large forces and large displacements at the same time) (Starossek, 2009). Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 87 6. RISK ASSESSMENT 6 Risk assessment A risk analysis is based on the assessment and mitigation of the risk of structural damage and the consequences that could arise from the damage state, after an occurrence of low-probability, highconsequence accidental hazards, such as impact, fire, explosions, human errors, etc. Within the Eurocode framework, a risk analysis is only required for buildings falling into the high consequences class CC3 according to EN 1991-1-7. Two types of risk analysis can be used, namely, i) qualitative and ii) quantitative analysis, being the main steps required for both analyses summarized in Figure 50. In practice, a risk analysis based on a quantitative approach is quite complex to carry out since it requires the quantification, in terms of probabilities, of the likelihood of occurrence of each considered hazard as well as all of the possible consequences of its occurrence in the building, requiring the use of robust risk models and high amounts of data. For these reasons, the quantitative approach is rarely applicable by designers. However, if necessary, some guidelines on quantitative structural risk analysis are provided in EN 1991-1-7. On the other hand, a risk analysis based on a qualitative assessment can be performed at any time or stage of a project even if it is strongly recommended to initiate it at an early stage of the design process. One of the crucial tasks to be achieved is the identification of hazards to be considered. In Annex B (informative) of EN 1991-1-7, conditions which could present hazards to a structure are identified (see Section 4 dedicated to identified threats); the identification of the hazards should be performed in close interaction with the future owner of the building and/or with the authorities. Then, for the soidentified hazards, it is asked to describe the possible consequences in case of occurrence of the latter and to define the required measures if these consequences are not acceptable. The qualitative assessment is easier to apply than the quantitative approach, therefore is most often the preferable approach even if it tends to be more subjective. Figure 50. Risk assessment 94 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 8. INTRODUCTION b) Figure 51. Presentation of the structural systems: a) non-seismic structures; b) seismic structures (cont.) 8.3 Actions, combination of actions The actions that were used in the design of each structural typology are presented in Table 11. Combination of actions for ULS and SLS were considered in compliance with EN 1990. Additionally, according to EN 1998, damage limitation limit state (DL) was considered for SS/S and CS/S cases. Table 11. Actions considered in the design process Loads Structures SS/S & CS/S CS/NS SS/NS Location Timișoara, RO Luxembourg Aachen, DE Dead load - Floors: gk = 5 kN/m2 - Façade (supported by the perimeter beams): gk= 4 kN/m Live load - Live load for office buildings: qk = 3 kN/m2 - construction load qk = 1 kN/ m2 (general floors and roof). WIND Wind speed vb,0 = 25 m/s vb,0 = 24 m/s vb,0 = 25 m/s Equiv. wind pressure qb = 0.4 kN/m2 qb = 0.36 kN/m2 qp = 0.9 kN/m2* Terrain category III III “Binnenland”* Snow load sk = 1.5 kN/m2 sk = 0.5 kN/m2 sk = 0.85 kN/m2** Seismic load Elastic response spectrum Type 1 Ground type B Design ground acceleration, ag 0.25 g Behaviour factor, q q = 4.8 (dual frame CBF+MRF) * Simplified wind pressure acc. to DIN EN 1991-1-4/NA Tab. NA.B.3 as commonly used in Germany. This replaces the concept of terrain category. “Binnenland” can be translated with “inland region” or “interior region” and is used to be distinguished from island and coastal regions. ** Snow zone 2 according to DIN EN 1991-1-3/NA 8.4 Design requirements and output The structural analysis was carried out using 3D models and linear elastic analyses. For SS/NS, calculations are performed using the following software: Inner Braced Core Rigid frame Pinned elements MRF Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 95 8.4 DESIGN REQUIREMENTS AND OUTPUT • Dlubal RSTAB 8.22 for FE analyses including the STEEL EC3 module for cross-section member verifications; • COP 2.1.3 Premium for the verification of connections. For CS/NS, the design of the building was performed using the software SCIA (version 2019), while the connections were designed using calculation spreadsheets. For the structures designed in seismic areas (SS/S and CS/S), Etabs v.19 and SAP2000 v23 software were used. The design of connections was performed using STeelCON software. For the seismic design, a modal response spectrum analysis was conducted. Also, the plastic mechanism and seismic response by means of non-linear static analysis procedure (push-over analysis) was evaluated using the N2 method. The verifications performed for all structures included: • ULS verifications for which the results are reported through utilization factors (UFs). • SLS verifications, which were done using the following admissibility criteria: 1. The maximum deflection of secondary beams limited at L/250; 2. The maximum deflection of main beams limited at L/350; 3. The maximum top displacement under wind action limited at H/500; where L is the length of the beams and H is the height of the structure. Additionally, for the seismic resistant structures, the following verifications were performed: 1. Interstorey drift limited at 0.75% Hst to comply with the damage limitation requirement (buildings with ductile non-structural elements); 2. Second order effects: θ ≤ 0.2 ; 3. Verification of dissipative members and connections in CBFs and MRFs; 4. Verification of non-dissipative members and connections in CBFs and MRFs; where Hst is the storey height and θ is the interstorey drift sensitivity coefficient. The output of the design is presented in Table 12 to Table 14. Table 12 shows the cross-sections for the different categories of beams and the utilization factors for strength (including buckling resistance where appropriate) and stiffness. Table 13 presents the cross-sections for the different categories of columns and the utilization factors for strength (including buckling resistance). For the structures designed in the seismic area, utilization factors for the columns of the Lateral Load Resisting System LLRS refer to maximum demand between combinations with wind or seismic action. The SLS verification for all structures subjected to the wind action is presented in Table 16. All structures having the same height H (24 m), the ratio between the lateral top displacement and the acceptable limit has a maximum value of approximately 0.5. Regarding the specific verifications for the structures in the seismic area, Table 17 presents the interstorey drift check at damage limitation state. As it may be observed, the structures successfully fulfil the limitation to 0.75%, having a maximum interstorey drift of 0.24%. The SS/S and CS/S have also been checked at ULS in terms of interstorey drift limitation using the following equation: 96 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 8. INTRODUCTION 𝑑) Q/R =𝑐∙𝑞∙𝑑)B ≤𝑑),1 Q/R (46) where c is the amplification factor (considered 1 since 𝑇7≥𝑇S ), q is the behaviour factor, and 𝑑)B is the relative displacement obtained from static calculation. The acceptable limit for this verification is 2.5% Hst. As presented in Table 18, all values are below this limit, the largest being of 0.49%. In addition, the results for the second-order verification are provided in Table 19. As it may be observed, the largest value for θ is 0.096. Consequently, as it is mentioned in Eurocode 8, the second order effects may be neglected, having a value for θ smaller than 0.1. The seismic loading for the design of the non-dissipative elements takes into account the utilization factor (UF) of the braces. Consequently, having an UF of 0.46 for the most stressed brace, an overstrength factor of 1/0.46 = 2.16 was obtained. Considering also the strain hardening effect, the total overstrength factor considered for the design of the non-dissipative elements was ΩT = 3.0. Finally, the contribution of the perimeter MRFs was checked. In (RFCS, 2017), it is mentioned that the duality should be checked by verifying that the MRFs carry at least 25% of the seismic force. Considering the equilibrium of a simple frame and the development of plastic hinges at the ends of the beams, the capacity of a MRF is twice the plastic capacity of the beam divided by the storey height. The necessary flexural resistance of the beam may be determined using the following expression: 𝑀=@," =𝐹# LCI 27∙𝐻+3 𝑛 (47) where 7𝐹# LCI is the capacity of the frame ,𝐻+3 is storey height, and 7𝑛 is the number of beams. In the above formula, the capacity of the frame is taken as equal to 0.25 of the storey seismic force and 𝑛 as equal to 12 since there are 6 beams per frame and 2 frames per direction resisting the seismic actions. As presented in Table 20, the necessary flexural capacity is smaller than the efficient one in both directions; so, the duality condition is checked. Table 12. Sections and utilization factors for beams Case Element Direction4 Storey Section Utilization factor (UF) Strength Deflection1 SS/S Perimeter beams X 1-6 IPE550 0.278 0.023 Y 1-6 IPE600 0.302 0.153 Interior beams X 1-6 IPE550 0.546 0.85 Y 1-6 IPE550 0.909 0.928 5Inner core beams X 1-3 6H800* 0.936 - 4-5 HEM800 0.953 - 6 HEM700 0.789 - Y 1-3 HEM500 0.859 - 4-6 HEB500 0.878 - Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 97 8.4 DESIGN REQUIREMENTS AND OUTPUT Table 12. Sections and utilization factors for beams (cont) Case Element Direction4 Storey Section Utilization factor (UF) Strength Deflection1 CS/S Perimeter beams2 X 1-6 IPE550 0.278 0.178 Y 1-6 IPE600 0.302 0.157 Interior beams2 X 1-6 IPE400 0.627 0.971 Y 1-6 IPE450 0.874 0.94 5Inner core beams X 1-3 6H800* 0.936 - 4-5 HEM800 0.953 - 6 HEM700 0.789 - Y 1-3 HEM500 0.859 - 4-5 HEB500 0.878 - SS/NS Perimeter beams X 1-6 IPE500 0.51 0.89 Y 1-6 IPE500 0.75 0.83 Interior beams X 1-6 IPE550 0.62 0.93 Y 1-6 IPE600 0.87 0.89 Inner core beams X, Y 1-6 HEA300 0.9 0.19 CS/NS Perimeter beams3 X, Y 1-6 IPE 450 0.93 0.8 Interior beams3 X 1-6 IPE360 0.95 0.98 Y 1-6 IPE500 0.96 0.86 Inner core beams X, Y 1-6 IPE500 0.45 - 1Deflection verification criterion: L/250 for secondary beams, L/350 for main beams 2Nelson studs d=19mm, h=100 mm / 160 mm – steel beams fully connected to a solid slab of 12cm 3Nelson studs d=19mm, h=100 mm / 160 mm – steel beams connected to a composite slab of 13 cm and with a Cofraplus 60 decking (0.88 mm) 4See Figure 51 for the orientation of the axes 5S460 steel grade used for the inner core beams. 6H800* is a built-up section, having the same height as regular HEM800, with b = 380mm, tf = 50 mm, and tw = 30 mm. Table 13. Sections and utilization factors for columns Case Element Section UF SS/S Corner columns HE550B 0.49 Perimeter columns HE500B 0.71 Inner core columns HD400X463 0.95 CS/S Corner columns HE550B 0.48 Perimeter columns HE500B 0.71 Inner core columns HD400X463 0.95 SS/NS Perimeter columns X HEB 360 0.97 Y HEB 340 0.94 Inner core columns HEM300 0.95 CS/NS Perimeter columns HD360X162 0.61 Inner columns HD400X216 0.78 98 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 8. INTRODUCTION Table 14. Sections and utilization factors for braces Case Element Direction Storey Section UF SS/S Brace Y 1-3 HEA320 0.41 4 HEA260 0.43 5 HEA220 0.46 6 HEA200 0.39 X 1-3 HEB340 0.41 4-5 HEA320 0.27 6 HEA260 0.26 CS/S Y 1-3 HEA320 0.41 4 HEA260 0.43 5 HEA220 0.46 6 HEA200 0.40 X 1-3 HEB340 0.41 4-5 HEA320 0.39 6 HEA260 0.26 SS/NS X, Y 1-6 CHS 219.1x6.3 0.90 CS/NS X, Y 1-6 CHS 219.1x5 0.71 It may be observed that, for SS/S and CS/S structures, the condition for homogeneity (25% maximum difference between UF elements on elevation) was fulfilled for most elements. The difference between the most stressed and least stressed braces is 16% in case of Y direction. However, on X direction, the condition was not fulfilled on the last two stories due to the requirement of using Class 1 cross-sections for high ductility class. Table 15 presents the slenderness verification for diagonal members according to the seismic design. It may be observed that all the braces fulfilled the condition, the maximum value of the nondimensional slenderness 𝜆 ’ 7 being 0.76, which is lower than the admissible limit of 2.0. Table 15. Slenderness check Case Direction Storey Section A (mm2) fy (MPa) I (mm4) Lcr (mm) Ncr (kN) 𝝀7 (-) SS/S and CS/S X 6 HEA260 8680 275 36680000 3605500 5848.1 0.639 5-4 HEA320 12400 275 36950000 3605500 5891.2 0.761 1-3 HEB340 17090 275 96900000 3605500 15449.4 0.552 Y 6 HEA200 2570 275 13360000 2828500 3461.1 0.654 5 HEA220 3030 275 19950000 2828500 5168.3 0.585 4 HEA260 3310 275 36680000 2828500 9502.5 0.501 1-3 HEA320 3710 275 69850000 2828500 18095.6 0.434 Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 99 8.4 DESIGN REQUIREMENTS AND OUTPUT Table 16. SLS check for LLRS against wind action Case Direction Top displacement (mm) Maximum allowable displacement (mm) SS/S X 4.62 48 Y 3.2 CS/S X 4.61 Y 3.16 SS/NS X 12.4 Y 7.3 CS/NS X 8.6 Y 5.6 Table 17. Interstorey drifts for the structures in seismic zones – DL Case Storey Direction Drift (%) Case Storey Direction Drift (%) SS/S 6 X 0.171 CS/S 6 X 0.172 5 0.209 5 0.210 4 0.244 4 0.243 3 0.222 3 0.220 2 0.224 2 0.222 1 0.183 1 0.182 6 Y 0.190 6 Y 0.190 5 0.241 5 0.241 4 0.238 4 0.238 3 0.203 3 0.203 2 0.193 2 0.192 1 0.148 1 0.148 Table 18. Interstorey drifts for the structures in seismic zones - ULS Case Storey Direction Drift (%) Case Storey Direction Drift (%) SS/S 6 X 0.343 CS/S 6 X 0.343 5 0.419 5 0.419 4 0.486 4 0.486 3 0.440 3 0.440 2 0.445 2 0.444 1 0.364 1 0.364 6 Y 0.380 6 Y 0.381 5 0.482 5 0.482 4 0.476 4 0.476 3 0.406 3 0.406 2 0.385 2 0.385 1 0.297 1 0.296 100 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 8. INTRODUCTION Table 19. Second order effects for the structures in seismic zones Case Storey h (mm) Px (kN) Vx (kN) dx (mm) θx (rad) Case Storey h (mm) Py (kN) Vy (kN) dy (mm) θy (rad) SS/S 6 4000 10867 1753 60.77 0.094 SS/S 6 4000 10867 1881 59.12 0.085 5 4000 21734 2983 52.77 0.096 5 4000 21734 3176 50.10 0.086 4 4000 32602 3912 42.80 0.089 4 4000 32602 4094 38.57 0.077 3 4000 43469 4628 31.02 0.073 3 4000 43469 4810 27.01 0.061 2 4000 54336 5193 20.18 0.053 2 4000 54336 5376 17.01 0.043 1 4000 65203 5524 9.09 0.027 1 4000 65203 5707 7.42 0.021 CS/S 6 4000 10867 1753 60.73 0.094 CS/S 6 4000 10867 1883 59.11 0.085 5 4000 21734 2985 52.73 0.096 5 4000 21734 3178 50.08 0.086 4 4000 32602 3914 42.76 0.089 4 4000 32602 4097 38.54 0.077 3 4000 43469 4630 30.99 0.073 3 4000 43469 4813 26.98 0.061 2 4000 54336 5195 20.16 0.053 2 4000 54336 5379 16.98 0.043 1 4000 65203 5526 9.10 0.027 1 4000 65203 5710 7.40 0.021 Table 20. Contribution of the MRF frames for the LLRS – SS/S and CS/S Case Storey label Direction Vi (kN) 0.25Vi (kN) n MRd,nec (kNm) Wnec (mm3) Section Weff (mm3) MRD,eff (kNm) SS/S 6 X 1752.5 438.1 12 73.0 205695.6 IPE550 2787000 989.4 5 2983.3 745.8 12 124.3 350149.8 IPE550 2787000 989.4 4 3911.9 978.0 12 163.0 459139.5 IPE550 2787000 989.4 3 4628.3 1157.1 12 192.8 543229.7 IPE550 2787000 989.4 2 5192.7 1298.2 12 216.4 609469.1 IPE550 2787000 989.4 1 5523.6 1380.9 12 230.2 648313.6 IPE550 2787000 989.4 6 x 1881.3 470.3 12 78.4 220813.2 IPE600 35112000 12464.8 5 3176.0 794.0 12 132.3 372765.1 IPE600 35112000 12464.8 4 4094.4 1023.6 12 170.6 480560.5 IPE600 35112000 12464.8 3 4810.2 1202.5 12 200.4 564574.4 IPE600 35112000 12464.8 2 5376.1 1344.0 12 224.0 630999.7 IPE600 35112000 12464.8 1 5707.5 1426.9 12 237.8 669894.1 IPE600 35112000 12464.8 CS/S 6 X 1753.4 438.3 12 73.1 205796.4 IPE550 2787000 989.4 5 2984.7 746.2 12 124.4 350314.6 IPE550 2787000 989.4 4 3913.5 978.4 12 163.1 459332.4 IPE550 2787000 989.4 3 4630.1 1157.5 12 192.9 543444.7 IPE550 2787000 989.4 2 5194.7 1298.7 12 216.4 609711.1 IPE550 2787000 989.4 1 5526.1 1381.5 12 230.3 648600.5 IPE550 2787000 989.4 6 x 1882.8 470.7 12 78.4 220980.2 IPE600 35112000 12464.8 5 3178.0 794.5 12 132.4 373009.1 IPE600 35112000 12464.8 4 4096.9 1024.2 12 170.7 480855.4 IPE600 35112000 12464.8 3 4813.0 1203.2 12 200.5 564905.2 IPE600 35112000 12464.8 2 5378.9 1344.7 12 224.1 631327.2 IPE600 35112000 12464.8 1 5710.0 1427.5 12 237.9 670185.7 IPE600 35112000 12464.8 Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 101 8.5 JOINTS 8.5 Joints 8.5.1 SS/NS Beam-to-beam as well as beam-to-column joints are pinned fin plate joints. Brace joints as well as column base joints are not detailed here. Column splices are moment resisting end-plate joints. The position of column splices is assumed approximately at mid-height of the building. The design of column splices is constructive (only compression forces and negligible bending moments). The nomenclature of the joints throughout the worked examples is based on members IDs reported in Figure 52. Joint labels, ULS shear forces, and resistances are summarized in Table 21. Figure 52. Joint positions Table 21. Verifications of joints at ULS, SS/NS Position s = strong axis w = weak axis Connection type Shear resistance (kN) Moment resistance (kNm) Failure mode UF A1s / A2 Fin plate 196 - Fin plate in bearing 0.66 A1w Fin plate 255 - Fin plate in bearing 0.94 B1 / B3 Fin plate 196 - Fin plate in bearing 0.92 C2w / C3w Fin plate 443 - Fin plate in bearing 0.97 D3s Fin plate 102 - Beam web in bearing 0.59 D3w Fin plate 102 - Beam web in bearing 0.88 BA / BC Fin plate 196 - Fin plate in bearing 0.92 BD Fin plate 185 - Fin plate in bearing 0.97 102 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 8. INTRODUCTION The design of joints has been performed using the aforementioned software COP. Notice that the design of such joints is not directly covered by the current version of the Eurocode; so the verification is based on the document from ECCS (ECCS, 2009). These verifications also contain ductility requirements for a proper pinned assumption of the joints. All failure modes are here ductile (fin plate or beam web in bearing). 8.5.2 CS/NS Two different types of connections were calculated: • Header plate; • Fin plate. A comparison between header plate and fin plate connections was performed for the joints of the perimeter beams (IPE450) and internal beams (IPE360) to the columns (HD360x162). The summary of the results for the joints may be found in the Table 22. Table 22. Verifications of joints at ULS, CS-NS Position Connection type Shear resistance (kN) Moment resistance (kNm) Failure mode UF Perimeter Header plate 289.38 - Shear resistance of bolt group 0.73 Fin plate 297.96 - Shear resistance of bolt group 0.71 Internal Header plate 289.38 - Shear resistance of bolt group 0.64 Fin plate 265.89 - Plate bearing in supported beam web 0.70 8.5.3 SS/S and CS/S Prequalified seismic moment resisting joints were adopted for the perimeter MRFs of both SS/S and CS/S. Extended end-plate joint configuration was preferred from the typologies available from the European RFCS EqualJoints project. Equal strength joints were chosen for MRFs and the joints adopted for the SS/S were also used for CS/S since no cross-sectional changes were made for the MRFs. Moreover, as the slab is considered totally disconnected from the steel frame in a circular zone around a column (see EN 1998-2), the composite character of beams with the slab was disregarded in the calculation of the joints. For the other elements (beam-to-beam as well as beam-to-column, except the MRFs and the braced core) pinned joints were used. Angle cleats were used in both cases (SS/S and CS/S), with minor changers from one case to another. The summary of the results for the moment resisting joints may be found in Table 23, while Table 24 provides the verification of pinned joints. Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 103 8.6 COMMENTS ON THE FINAL SELECTION OF THE WORKED EXAMPLE STRUCTURES Table 23. Verifications of moment resisting joints at ULS, SS/S and CS/S Position Connection type Moment resistance (kNm) Shear resistance (kN) Failure mode in bending UF* 𝑴𝑹𝒅 𝑴𝒑𝒍,𝒃 A/1, A/7 IPE600-HEB550 Extended end-plate 1173 1516 End-plate in bending 0.29 0.94 A/1, A/7, A/2-6 IPE600-HEB500 Extended end-plate 1169 1387 End-plate in bending 0.26 0.94 1/A - 1/D IPE550-HEB500 Extended end-plate 957 1409 End-plate in bending 0.15 0.97 Note: * Utilization factor is defined for ULS, persistent design situation only Table 24. Verifications of pinned joints at ULS, SS/S and CS/S Case Position Storey Connection type Shear resistance (kN) Failure mode UF* SS/S A/1-7, D/1-7 IPE550-IPE600 1-6 Cleat angle 196 Sec. beam bolts in shear 0.72 B/1-7, C/1-7 IPE550-IPE550 1-6 Cleat angle 196 Sec. beam bolts in shear 0.72 B/2, B/5, C/2, C/5 IPE550-HEM500 1-3 Cleat angle 196 Sec. beam at notch 0.67 B/2, B/5, C/2, C/5 IPE550-HEB500 4-6 Cleat angle 196 Sec. beam bolts in shear 0.65 CS/S A/1-7, D/1-7 IPE400-IPE600 1-6 Cleat angle 196 Sec. beam in bearing 0.90 B/1-7, C/1-7 IPE400-IPE450 1-6 Cleat angle 196 Sec. beam in bearing 0.97 B/2, B/5, C/2, C/5IPE550-HEM500 1-3 Cleat angle 196 Sec. beam at notch 0.74 B/2, B/5, C/2, C/5 IPE550-HEB500 4-6 Cleat angle 196 Sec. beam at notch 0.84 Note: * Utilization factor is defined for ULS, persistent design situation, only 8.6 Comments on the final selection of the worked example structures 8.6.1 Seismic vs. non-seismic The structural configurations were mainly designed to cover both seismic and non-seismic areas but keeping similar main structural schemes to allow for some direct comparisons in the design against accidental actions. Thus, same spans, bays, and storey heights were adopted. However, some adjustments were necessary for seismic resistant structures, i.e.: • The position of the braced spans close to the centre of rigidity (Figure 51a) makes the structure sensitive to torsional effects (Figure 53a). For seismic design, this is a feature to avoid, as it 110 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 8. INTRODUCTION Worked example I.1.2 / CS/S Design for impact using simplified dynamic approach – CS/S 2 of 3 pages 2nd step: the impact force is applied transversally on the weak axis direction using a dynamic nonlinear analysis and hard impact approach as follows: Computation 𝑭=𝒗𝒓√𝒌⋅𝒎 EN1991-1-7, formula C.1 where vr is the impact velocity, m is the impact mass, and K – the stiffness of the impact object. The parameters are calculated considering the same type of road (Motorways and country national main roads): K= 300 kN/m = 300000 N/m EN1991-1-7 vr= 90 km/h = 25 m/s Hypothesis m = 3500 kg Hypothesis This results in: 𝐹=𝑣)√𝑘⋅𝑚=25√300000⋅3500=8107𝑘𝑁 Note: If the impact force is amplified by the DLF (recommended value of DLF = 1.4), for a vehicle velocity of 90 km/h (see Table C1 of EN1991-1-7) the equivalent dynamic impact force, Fequiv, is close to the one applied in the static analysis (see W.E I.1.1 / CS/S): 7𝐹BZ!;% =1.4∙25√300000⋅3500=71134.17𝑘𝑁 In the dynamic analysis, the force is applied using a ramp function with instant rise and a duration of: Formula (4.1.5) from (Vrouwenvelder et al., 2005) Δt7=(𝑘/𝑚=(300000/3500=0.108 s EN1991-1-7 The total duration of the dynamic analysis is one second (larger than the ramp function duration Δt), to verify if the column remains stable after the ramp function ends. The nonlinear behaviour is modelled using plastic hinges at each column end and at the point of impact using P-M2-M3 interaction. The plastic hinges are modelled using fibres. SAP2000 The effects of the fast impact loading (strain rate effects) are considered using a dynamic increase factor (DIF) applied to the strength of material. The DIF formulation for hot-rolled steel with yield strength up to 420 N/mm2 can be expressed according to (CEB 1988) method. The strain rate ( 𝜀 I) is obtained through an iterative procedure. In the first iteration, the ratio between the specific deformation and the time up to the point of yielding is computed based on the analysis results without applying a DIF. Afterwards, the analysis is performed again with the modified material properties by using a DIF, followed by DIF recalculation. If the new DIF values are comparable with the ones from the previous step (convergence), no further iterations are needed. Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 111 8.7 IDENTIFIED EXCEPTIONAL EVENTS Worked example I.1.2 / CS/S Design for impact using simplified dynamic approach – CS/S 3 of 3 pages DIF=𝑓4# 𝑓#=1+6.0 𝑓#ln 𝜀I 5×106[ DIF=𝑓4! 𝑓!=1+7.0 𝑓!𝑙𝑛 𝜀I 5×106[ At the end of the iterative process, one obtains DIF (fy) = 1.118 Results The column can sustain the impact force, but with incipient plastic deformations at the point of impact 0.054% normal strain, 0.073% at the bottom end and 0.036% at the top end of the column. The figure below shows the lateral displacement time history of the column at the impact point. The peak horizontal displacement is 29.12 mm, with a residual deflection of 16.47 mm. Figure 56. Lateral displacement time history at point of impact – CS S Figure 57. Plastic hinges – CS S The application of equivalent static approach (W.E. I.1.1 / CS/S) indicated that the utilization factor exceeds unity è redesign is needed. However, if plastic deformations are allowed to develop in the column, the design becomes acceptable by applying a simplified dynamic approach è end of design. Flowchart Figure 3 – Box B.6 è End of design 0 5 10 15 20 25 30 35 0 0.2 0.4 0.6 0.8 1 Lateral displacement [mm] Time [s] Impact - simpl. dyn 112 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 8. INTRODUCTION 8.7.1.3 Design for impact using full dynamic approach (CS/S) Worked example Title Design for impact using full dynamic approach 1 of 4 pages Structure Composite structure in seismic zone Made by UPT Date: 06/2021 Document ref. I.1.3 / CS/S Example: Design for impact of first storey perimeter columns in a composite structure in seismic zone using the full dynamic approach Design manual § 4.2.2.3 This example gives information about the design against impact due to accidental collision of a vehicle. Basic data of structure • For geometry, sections, and materials, see Section 8.2. Design manual § 8.2. Actions for Accidental Design Situation The following actions are considered: • Permanent loads DL (see Table 11); • Live loads LL (see Table 11 for CS/S structure); • Impact action AEd (see section below). Combination of actions for Accidental Design Situation The combination of actions is: 𝐷𝐿7+70.5×𝐿𝐿7+7𝐴.4 EN 1990 §6.4.3.3, Eq 6.11b Definition of impact scenarios • For definition of impact scenarios, see example W.E. I.1.1 / CS/S, with specific details reported in W.E. I.1.2 / CS/S. • The impact parameters are calculated considering the same type of road (Motorways and country national main roads): W.E. I.1.1 / CS/S and W.E. I.1.2 / CS/S K= 300 kN/m = 300000 N/m - stiffness of the impact object; EN 1991-1-7 vr= 90 km/h = 25 m/s - impact velocity; m = 3500 kg - impacting mass. Structural analysis To analyse a complex structural behaviour, such as an object collision followed by separation of elements and possible collapse, the impact with a vehicle was explicitly modelled. A nonlinear dynamic analysis was conducted on a full 3D model using the ELS software. ELS uses a nonlinear solver based on AEM (Tagel-Din and Meguro, 2000) and allows the automatic detection and computation of yielding, hardening, failure of materials, separation of elements, contact at impact, buckling/post-buckling, crack propagation, membrane action, and P-Δ effect. In the AEM modelling technique the structural elements are modelled as small solid elements (discretization is made both along the length of the member and of the cross-section) connected by normal and shear springs that follow the constitutive law of the corresponding material (including plastic Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 113 8.7 IDENTIFIED EXCEPTIONAL EVENTS Worked example I.1.3 / CS/S Design for impact using full dynamic approach – CS/S 2 of 4 pages behaviour, separation, contact). After reaching the separation strain, springs are removed. Then, if the separated elements come in contact, springs are generated at the surface of elements that are forced towards each other (Applied Science International, 2021). Columns and beams were defined as solid objects with a constant I / H shape crosssection. The objects were discretized into small solid elements, generating 25 sets of springs at each surface. Link elements were used to model vertical braces and horizontal ties (anchored to perimeter columns). Beam-to-column joint properties were modelled with 8-node objects for end-plates and individual springs for each bolt. Pinned joints were defined by connecting the secondary beams with the main beams using just the springs representing the bolts. Column bases were considered as fixed. Reinforced concrete (RC) slabs were modelled as solid concrete elements with steel springs at the level of the reinforcement. Springs also simulated the connectors linking the beams to the RC slab. To take into account the inertial effects, dead and live loads were assigned on the floors using lumped masses, which simulate better inertia effects in comparison to load assignments. Figure 58. CS/S structure model (general view and connection detail) To improve the accuracy of the AEM model, fine meshing was applied to the structural elements and joints which are contributing to the load redistribution capacity. The calibration was done against relevant experimental data from tests on subassemblies and joints (see Figure 59). Thus, Figure 59a shows the forcedisplacement curves in a column loss scenario from an experimental test and the corresponding numerical prediction in ELS, while Figure 59b shows the beam-tocolumn hysteretic and backbone curves from tests on joints. Based on these two comparisons, the accuracy of the numerical model in reproducing the structural response is considered adequate. 114 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 8. INTRODUCTION Worked example I.1.3 / CS/S Design for impact using full dynamic approach – CS/S 3 of 4 pages a) b) Figure 59. System calibration on CODEC Tests and Connections calibration on Equaljoints Tests: a) force-displacement in a column loss scenario (Dinu et al., 2016); beam-to-column hysteretic and backbone curves (Landolfo et al., 2018) The analysis is performed in two steps. 1st step: the permanent and live loads are applied on the structure in a static nonlinear analysis 2nd step: the impact body is colliding with the C2 column in a dynamic nonlinear analysis. Model assumptions for impact The impacting body (i.e., the vehicle) is allowed to slide on the horizontal plane only, at a height of 1.5 m, and has a mass of 3.5 tones. The initial velocity of the object is 25 m/s. The impacting body is composed of a contact plate, a plate with assigned mass, and axial springs between them. The height of the contact zone between the lorry and the column is considered as equal to 0.6 m. The stiffness of 300 kN/m is modelled through elastic springs. Figure 60. Collision object moving towards the column Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 115 8.7 IDENTIFIED EXCEPTIONAL EVENTS Worked example I.1.3 / CS/S Design for impact using full dynamic approach – CS/S 4 of 4 pages Results a) b) c) Figure 61. Results for impacted column: a) strains; b) deformations; c) horizontal base reaction force (orange) and horizontal displacement at impact point (blue) The results show limited plastic deformations in the impacted column, with a maximum lateral deflection of 10.6 mm. Conclusions Figure 62. Lateral displacement in time – comparison of dynamic approaches Compared with the W.E. I.1.2 / CS/S, full dynamic approach results in less deformation (as presented in Figure 62), as the restraining provided by the adjacent structure (especially the vertical restraining) is taken into account, and the “real” rise function of the impact force is less steep than the one applied for simplified dynamic approach. Note that explicit consideration of impact object-structure interaction may result in much higher demands than typically considered in simplified dynamic analysis (Dubina et al., 2019). Flowchart Figure 3 – Box B.6 è End of design 0 5 10 15 20 25 30 35 0 0.2 0.4 0.6 0.8 1 Lateral displacement [mm] Time [s] Impact - simpl. dyn. Impact - full dyn. 116 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 8. INTRODUCTION 8.7.1.4 Design for impact using equivalent static approach (CS/NS) Worked example Title Design for impact using equivalent static approach 1 of 3 pages Structure Composite structure in non-seismic zone Made by AM Date: 06/2021 Document ref. I.1.4 / CS/NS Example: Design for impact of first storey perimeter columns in a composite structure in non-seismic zone using the equivalent static approach Design manual § 4.2.2.1 This example gives information about the design against impact due to accidental collision of a vehicle. Basic data of structure • For geometry, sections, and materials, see Section 8.2. Design manual § 8.2. Actions for Accidental Design Situation The following actions are considered: • Permanent loads DL (see Table 11); • Live loads LL (see Table 11 for CS/NS structure); • Impact action AEd (see section below). Combination of actions for Accidental Design Situation The combination of actions is: 𝐷𝐿7+70.5×𝐿𝐿7+7𝐴.4 EN 1990 §6.4.3.3, Eq 6.11b Definition of impact scenarios Impact scenarios include perimeter columns along two traffic lanes (see Figure 63). In this example, both long façade and short façade are exposed. The impact gives rise to a collision force that has components parallel and perpendicular to the direction of travel. Each impact direction (short side – case A, long side – case B) results in two loading situations (according to the traffic flow) for the columns located at the ground floor of the building, i.e., one along the lane and one perpendicular to the lane. The location of the columns considered in the analysis is presented in Figure 63. Figure 63. Plan view with columns layout, traffic lanes and position of columns under impact Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 117 8.7 IDENTIFIED EXCEPTIONAL EVENTS Worked example I.1.4 / CS/NS Design for impact using equivalent static approach – CS/NS 2 of 3 pages The impact loads are calculated using table 4.1 of EN 1991-1-7, considering the case Country roads in rural area. Table 28. Impact forces for linear static analysis CS/NS Case Fdx (kN) Fdy (kN) A.1 750 375 A.2 750 375 B.1 375 750 B.2 375 750 EN 1991-1-7, 2006 Structural analysis The linear elastic analysis is performed on a full 3D model using the software SCIA®. In a first step, the cross-sections of the members are those resulting from the initial design (persistent design situation). In a second step, the use of composite columns instead of steel ones is considered; the composite columns are designed using the software A3C®(see the selected cross-section here below). The acceptance criteria reported here are given in terms of utilization factors (UFs) for accidental combinations only. Results Table 29. Results of linear static analysis for impact on steel columns Case Section Loading Bottom support UF (-) Fdx (kN) Fdy (kN) S355 S460 A.1 HD 360x162 750 375 Fixed 1.30 0.91 Hinged 1.50 1.05 A.2 HD 360x162 750 375 Fixed 1.08 0.78 Hinged 1.23 0.92 B.1 HD 360x162 375 750 Fixed 1.29 0.98 Hinged 1.54 1.17 B.2 HD 360x162 375 750 Fixed 1.45 1.10 Hinged 1.72 1.30 Table 30. Results of linear static analysis for impact on composite columns Case Loading Upper and bottom supports UF (-) S355 Fdx (kN) Fdy (kN) A.1 750 375 Hinged 2.63 A.2 750 375 Hinged 2.04 B.1 375 750 Hinged 2.25 B.2 375 750 Hinged 2.34 Details of the composite columns: • Steel section - HE200M • Concrete class – C30/37 • Rebar (A500) – φ20 mm / φ6 mm 118 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 8. INTRODUCTION Worked example I.1.4 / CS/NS Design for impact using equivalent static approach – CS/NS 3 of 3 pages Conclusions • Standard steel columns The results for the columns made of S355 steel grade show a surpass of the yield strength for both pinned and fixed conditions with UFs up to 1.72. When using S460 steel grade, a considerable improvement is observed in terms of utilization factors. Flowchart Figure 3 – Box B.5 è Box B.II OR Box B.6 • Composite steel-concrete columns Regarding the composite columns, the utilization factors are substantially higher. This is mainly related to the pre-design of the sections and supporting conditions. The columns were pre-designed considering the same capacity as the steel columns and pinned supports at both extremities (the steel cross-sections used for the composite elements are substantially smaller). When an impact load is applied (considering an equivalent static approach), the element will be subjected to bending which will be taken for the most part by the steel profile when it comes to the composite section (approximately 65% to 70%). Due to this, the composite columns show a higher utilization factor for impact analysis. It is concluded that, for the non-composite steel columns, if the standard design is made considering around 60% to 65% utilitzation, the columns can still be able to sustain the impact load (static approach), assuming that the bottom supports remain fixed. For the sections that are failing using this approach, a capacity assessment with more sophisticated approaches should be made. It is reminded that this example considered less demanding road conditions for impact with respect to W.E. I.1.1 / CS/S. As shown previously, the main improvement that can be made is by increasing the steel grade to S460; by doing so, the columns have a better behaviour for the majority of cases. Other measures can also be implemented to improve the response to the impact load: • Orientate the columns (acording to their cross-sections’s strong axis) to maximize the resistance to impact; • Increase the size of the sections; • Design the end-connections of the columns with higher stiffness and resistance (i.e., fixed (rigid) column bases); • Use of composite columns, to achieve an optimum solution in terms of size, used grade of steel, used concrete; Flowchart Figure 3 – Box B.5 è Box B.II OR Box B.6 Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 119 8.7 IDENTIFIED EXCEPTIONAL EVENTS 8.7.2 Blast analysis 8.7.2.1 External blast 8.7.2.1.1 Design for external blast using equivalent single-degree-of-freedom approach (CS/NS) Worked example Title Design for external blast using equivalent SDOF approach 1 of 6 pages Structure Composite structure in non-seismic zone Made by AM Date: 06/2021 Document ref. I.2.1 / CS/NS Example: Design for external blast of perimeter columns of a composite structure in non-seismic zone using the equivalent SDOF approach Design manual, § 4.3.2.2 This example gives information about the design against blast due to accidental external explosion. Basic data of structure • For geometry, sections, and materials, see Section 8.2 for the steel column solution and W.E. I.1.4 / CS/NS for the composite column. Design manual, § 8.2. Actions for Accidental Design Situation The following action is considered: • Blast action AEd (see section below). Note: No other loads are considered as acting on the column. Definition of blast scenario The column considered in the analysis is a perimeter column located in the middle of the longest façade of the building – see Figure 64. The blast scenario assumes that a car is placed at a standoff distance of 20 m from the column and carries an explosive charge equal to 100 kg of TNT (or equivalent). The burst is defined as a free-air burst with a free height from the ground of 1 m. Figure 64. Plan view of the columns under blast load – CS/NS R = 20 m 126 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 8. INTRODUCTION Worked example I.2.2 / SS/S Design for external blast using equivalent SDOF approach – SS/S 2 of 4 pages Computation The blast loading parameters (incident pressure, incident impulse, reflected pressure, reflected impulse, time of arrival, positive phase duration, blast wavelength, shock front velocity) are identical to W.E. I.2.1/ CS/S. Additionally, the parameters which follow (sound velocity, peak dynamic pressure, fictitious durations, clearing time) have the same values. W.E. I.2.1/ CS/S Single degree of freedom approach (SDOF) The first step in applying the SDOF method consists in calculating the uniformly distributed load (Fd) and point load (Fp) caused by the blast on the column. Reflected pressure 𝑃)=137.377𝑘𝑃𝑎 Height of the column ℎ(=3.57𝑚 Assumption Note: If the rigid zone formed by the connection is accounted for, the height of the column can be assumed less than 4 m as effective length. Width of the panel in front of the column 𝑤==5𝑚7 Self weight of the column 𝐺(=1.8347𝑘𝑁 𝑚 Distributed load from the blast on the column 𝐹4=𝑃)𝑤==137.37×5=686.857𝑘𝑁 𝑚 Point load from the blast on the column 𝐹==𝐹4ℎ(=686.85×3.5=24047𝑘𝑁 Dynamic load factor 𝐷𝐿𝐹=1.4 Loading factor 𝐾/=0.64 Mass factor 𝐾L=0.50 Plastic section modulus 𝑊=@.( =12927𝑐𝑚E Second moment of area 𝐼(=126207𝑐𝑚] Dynamic increase factor 𝐷𝐼𝐹=1.2 Yield strength affected by an amplification factor of 1.2 for the strain rate Steel yield strength 𝑓#=355×1.2=4267𝑀𝑃𝑎 Steel elastic modulus 𝐸=2107𝐺𝑃𝑎 Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 127 8.7 IDENTIFIED EXCEPTIONAL EVENTS Worked example I.2.2 / SS/S Design for external blast using equivalent SDOF approach – SS/S 3 of 4 pages Column stiffness 𝐾(=384.𝐼( 5ℎ( E=384×210×10e×12620×106h 5×3.5E7=474727𝑘𝑁 𝑚 Maximum resistant moment 𝑀C4 =𝑊=@.(.𝑓#.𝐷𝐼𝐹=1292×106e ×426×10E=550.47𝑘𝑁𝑚 Maximum applied moment 𝑀012 =𝐹=.ℎ( 8𝐷𝐿𝐹=2747.4×3.5 8×1.4=14727𝑘𝑁𝑚 Effective mass 𝑀B=𝐺(.ℎ(.𝐾L 𝑔=1.834×3.5×0.50 9.81 7=327.37𝑘𝑔 Effective stiffness 𝐾B=𝐾(𝐾/=47471.8×0.64=303827𝑘𝑁 𝑚 Natural period of vibration 𝑇(=2𝜋«𝑀B 𝐾B=2×𝜋«327.3 30382 7=0.0206 Ratio between the fictious duration of the reflected wave and the natural period 𝑡)* 𝑇(=0.49 The new determined ratio allows for a second, more precise iteration. Second iteration 𝐷𝐿𝐹=1.6 Maximum applied moment 𝑀012 =𝐹=.ℎ( 8𝐷𝐿𝐹=2747.4×3.5 8×1.6=16837𝑘𝑁𝑚 Resistance force 𝑅0=8(2𝑀C4) ℎ(=8×2×550.4 3.5 =25167𝑘𝑁 Dynamic reaction 𝑉0=0.39𝑅0+0.11𝐹=+𝐺(.ℎ(0.5 𝑉0=0.39×2516+0.11×2747.4+1.834×3.5×0.5=1248.927𝑘𝑁 Ratio 𝑅0 𝐹f=1.05 The ratio between the maximum resistance and the point load is used to determine the ductility demand 𝜇 through Figure 148 from Annex A.6.2. Figure 148 from §A.6.2. 128 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 8. INTRODUCTION Worked example I.2.2 / SS/S Design for external blast using equivalent SDOF approach – SS/S 4 of 4 pages Results Ratio 𝜇7=1.05 (χM/χE) 𝜇5=0.82 (tm/T) Yield displacement 𝜒B=𝑅0 𝐾B=2516 30382=82.827𝑚𝑚 Maximum displacement 𝜒L=𝜇7×𝜒B=1.05×82.82=86.967𝑚𝑚 Maximum response time 𝑡0=𝜇5×𝑇(=0.82×0.0206=16.907𝑚𝑠 Simplified dynamic approach (Pressure-impulse relationships) Design manual, §4.3.2.3, Table 5 𝜇012 =1 Flexure - > Beam -column with compact section -> B1 Flowchart Figure 3 – Box B.5 Check g/ g012 =1.05 Flowchart Figure 3 – Box B.6 è End of design Conclusions According to the results, the column can withstand the blast load (the value may be considered admissible), the requirement from class B1 (superficial damage) being fulfilled. Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 129 8.7 IDENTIFIED EXCEPTIONAL EVENTS 8.7.2.1.3 Design for external blast using full dynamic approach (SS/S) Worked example Title Design for external blast using full dynamic approach 1 of 3 pages Structure Steel structure in seismic zone Made by UPT Date: 06/2021 Document ref. I.2.3 / SS/S Example: Design for external blast of perimeter columns of a steel structure in seismic zone using the full dynamic approach Design manual § 4.3.2.4 This example gives information about the design against blast due to accidental external explosion. Basic data of structure • For geometry, sections, and materials, see Section 8.2. Design manual § 8.2. Actions for Accidental Design Situation The following action is considered: • Blast action AEd (see section below). Definition of blast scenario The column considered in the analysis is a perimeter column located in the middle of the long façade of the building. Loading parameters: • standoff distance = 20 m; • explosive charge = 100 kg of TNT; • tributary width of the column 5 m (2,5 m on each side); • the blast pressure is considered to act on the 1st and 2nd storeys columns. Figure 66. 3D model with the position of the charge Note that, for a relevant comparison, the blast scenario considered in this example is the same with the one employed in W.E. I.2.1 / CS/S. W.E. I.2.1/ CS/S Structural analysis The numerical analysis has been performed in ELS (Extreme Loading for Structure) software, using a full 3D model where the entire structure has been modelled. Model assumptions in AEM – see W.E. I.1.3 / CS/S for details. W.E. I.1.3 / CS/S 130 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 8. INTRODUCTION Worked example I.2.3 / SS/S Design for external blast using full dynamic approach – SS/S 2 of 3 pages To account for the tributary area loaded by the blast, rigid plates were modelled to transfer the pressure horizontally to the 1st and 2nd storey columns. The blast loading parameters given below are computed automatically by the integrated blast pressure generator of ELS: Figure 67. Blast parameters computed automatically in ELS software The analysis is performed in two steps. 1st step: the permanent and live loads are applied on the structure in a nonlinear static analysis. 2nd step: the charge is detonated, and the blast load is applied in a nonlinear dynamic analysis. The time step for this analysis is 1E-6 s. Only the positive phase of the blast is considered; no reflection from the ground is considered in the analysis. Results The maximum horizontal displacement at the mid-height of the column is 24 mm – see Figure 68 (left). The maximum reached plastic strain is 1%. Figure 68. Horizontal deformation vs time at column mid-height (left) and Von Mises strains (right) Flowchart Figure 3 – Box B.5 Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 131 8.7 IDENTIFIED EXCEPTIONAL EVENTS Worked example I.2.3 / SS/S Design for external blast using full dynamic approach – SS/S 3 of 3 pages Conclusions Full dynamic approach vs. equivalent SDOF approach: • The displacement in the full nonlinear dynamic analysis is less than the value obtained using tabular method (24 mm vs. 87 mm, see W.E. I.2.2 / SS/S); • Nonlinear analysis can account for distribution of plasticity in the element; • Full 3D model can account for real boundary conditions and interactions between elements; • Full dynamic approach and 3D modelling can account for sequential application of blast pressure on the surface (different arrival times along the column length). Note that, in case of near field blasts, the effects can be amplified by the uplift pressure against the adjoining floors, which can result in higher dynamic effects and even risk of progressive collapse (Dinu et al. 2018). Flowchart Figure 3 – Box B.6 è End of design 132 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 8. INTRODUCTION 8.7.2.2 Internal explosions 8.7.2.2.1 Design for internal explosions using equivalent static approach (SS/S) Worked example Title Design for internal explosions using equivalent static approach 1 of 3 pages Structure Steel structure in seismic zone Made by UPT Date: 06/2021 Document ref. I.3.1 / SS/S Checked by Example: Design for internal explosions on columns of a steel structure in seismic zone using equivalent static approach Design manual § 4.3.3.2 This example gives information about the design against internal blast due to accidental internal gas explosion. § 5.4, EN19911-7 Basic data of structure • For geometry, sections, and materials, see section 8.2. Design manual § 8.2. Actions for Accidental Design Situation The following actions are considered: • Permanent loads DL (see Table 11); • Live loads LL (see Table 11 for SS/S structure); • Gas pressure AEd (see section below). Combination of actions for Accidental Design Situation The combination of actions is: 𝐷𝐿7+70.5×𝐿𝐿7+7𝐴.4 EN 1990 §6.4.3.3, Eq 6.11b Definition of gas explosion scenario 7 Figure 69. Position of the confined compartment and checked column – SS/S 8 Confined compartment Column checked Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 133 8.7 IDENTIFIED EXCEPTIONAL EVENTS Worked example I.3.1 / SS/S Design for internal gas explosions using equivalent static approach – SS/S 2 of 3 pages The compartment is located at the ground floor. The venting surface is considered on the external wall and is made of glass windows, while the other 3 internal walls are made of stronger materials. The column considered for the verification is circled in green in Figure 69. Computation Table 31. Geometry of the compartment 8 L 12 m length B 8 m width H 4 m height Av 48 m2 venting area V 384 m3 compartment volume The venting area and volume of the enclosure were computed considering that the glass wall is placed on the enclosure of the building and on the entire storey height. After succesfully checking that the pressure model from EN 1991-1-7 can be applied for the current example (limits function of the venting area and volume of the enclosure), the following equivalent static pressure for the internal gas explosion was obtained: 𝑝47=737+𝑝+313 or 𝑝47=737+𝑝+313 2+0.04 (𝐴%𝑉 ⁄)5 whichever is the greater. It was assumed that 𝑝+313 =37𝑘𝑁/𝑚5, which represents the static uniformly distributed pressure at which venting components fail. Consequently, the design pressure in case of accidental situation is: 𝑝4=77.067𝑘𝑁/𝑚5 Hereinafter, the pressure was applied as a linear load acting on the height of the column considering a tributary width of 6 m. Structural analysis A linear elastic analysis is conducted on a full 3D model using SAP2000 software. The sections of the elements are those resulted from the initial design (persistent and seismic design situations). The acceptance criteria are given in terms of utilization factors (UFs) for accidental combinations only. Results The results of the linear static analysis of the column is presented in Table 32. 7 134 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 8. INTRODUCTION Worked example I.3.1 / SS/S Design for internal gas explosions using equivalent static approach – SS/S 3 of 3 pages Table 32. Results of linear static analysis Section Axis Bottom support N (kN) M (kNm) UF (-) Lateral deflection (mm) HEB500 Minor Fixed 612 72 0.279 0.57 Conclusions The column analysed with this approach does not exceed its capacity and does not require a redesign. However, since no local damage occurs, more sophisticated approaches may be used to quantify the damage that might appear. Flowchart Figure 3 – Box B.4è End of design Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 135 8.7 IDENTIFIED EXCEPTIONAL EVENTS 8.7.2.2.2 Design for internal explosions using dynamic approach – TNT equivalence method (SS/S) Worked example Title Design for internal explosions using dynamic approach 1 of 6 pages Structure Steel structure in seismic zone Made by UPT Date: 06/2021 Document ref. I.3.2 / SS/S Example: Design for internal gas explosion of a steel structure in seismic zone using dynamic approach – TNT equivalence method Design manual § 4.3.3.3 This example gives information about the design against internal gas explosions. Under specific conditions, an internal gas explosion may be approximated with an equivalent TNT explosion (Bjerketvedt et al., 1997b). Note: The procedure proposed to solve this case is a simplification of the actual procedure. The volume of the gas is replaced in the computations with an equivalent TNT charge. Onwards, the procedure applied in case of external blast, as described in W.E. I.2.1 / CS/NS and I.2.2 / SS/S is used for this example also. Thus, the effect of the frangibility of the walls, pressure leakage from the compartment etc. are neglected. However, a very complex procedure based on the recommendations from (DoD, 2008) is shown in the Deliverable D2-2 of the FAILNOMORE project available on the following website: https://www.steelconstruct.com/eu-projects/failnomore/. (Bjerketvedt et al., 1997b), (DoD, 2008) Basic data of structure • For geometry, sections, and materials, see Section 8.2. Design manual § 8.2. Actions for Accidental Design Situation The following action is considered: • Gas action AEd (see section below). Note: No other loads are considered to act on the column. Definition of gas explosion scenario For the internal explosion scenario, a 48 m3 compartment and 6% methane concentration in the air were assumed. Computation Equivalent TNT mass According to section 4.3.3.3, the following definition of the equivalent TNT charge may be used: 𝑊898 =𝜂𝑊:×𝐸( 𝐸898 (DoD, 2008) §4.3.3.3 Relation (15) and (16) 142 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 8. INTRODUCTION Worked example I.4.1 / CS/NS Design for localised fire using localised fire models – CS/NS 2 of 2 pages Structural analysis For each scenario, the software OZone® (Cadorin, 2003) is used, applying the LOCAFI (Brasseur et al., 2018) model as well as the equations from EN 1991-1-2, to evaluate the steel temperatures of a bare steel column made of an unprotected hot rolled profile HEB340 (as an example). Conclusions The maximum steel temperatures along the height of the column for the 4 scenarios were calculated and compared (see Figure 70). This comparison highlights that, although different assumptions are made to characterize the localised fire, the same trend and order of magnitude are achieved. Significant temperatures develop at the bottom of the steel columns which can cause buckling or a local plastic failure. Figure 70. Steel temperature variation on column height In another approach performing a full numerical analysis, a study was made where specific columns were removed and the building behaviour evaluated (Alternative load path method), see example II.4.6/ CS-NS. In order to avoid fire damage, fire protection can be used instead of designing the structural elements for specific fire resistance or increase the size of the section. Flowchart Figure 3 – Box B.5 Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 143 8.7 IDENTIFIED EXCEPTIONAL EVENTS 8.7.4 Seismic analysis 8.7.4.1 Seismic design using prescriptive method (SS/NS) Worked example Title Seismic design using prescriptive method 1 of 1 pages Structure Steel structure in non-seismic zone Made by F+W Date: 06/2021 Document ref. I.5.1 / SS/NS Example: Design recommendations for steel structures in non-seismic zone (prescriptive method) Design manual § 4.5 This example gives recommendations about the application of prescriptive measures for improving the response of non-seismically designed steel structures in case of exceptional earthquakes. Basic data of structure • For geometry, sections, and materials, see Section 8.2. Design manual § 8.2. The structure considered in this example has been designed for ULS/SLS conditions only (persistent design situation). No particular calculations have been conducted with respect to any accidental seismic action. So here, the seismic action is considered as exceptional. In practice, simple recommendations as proposed in Section 4.5.2 can be followed when the seismic action is less critical than the wind-based design. This is mainly done for lowrise buildings to optimize engineering costs. Remarks • Due to the symmetry in plan and regularity in elevation, the structure stiffness is well distributed, thus offering a favourable response to the seismic action. • Equal floor heights also contribute to the good behaviour of the structure in case of earthquakes. • Ductility requirements: 1. To increase the overall ductility of the structure, the HEA300 beams can be replaced with HEB300 ones, as HEA300 S355 profiles are class 3 and HEB300 S355 are class 1. All the other members are already class 1 profiles. 2. To optimize the structure response, the originally designed pinned joints could be replaced by ductile semi-rigid joints as described in Section 8.8.4.1 where the alternative load path method is applied (W.E. II.4.1 / SS/NS). This would allow the formation of plastic hinges in the joints and dissipate part of the seismic induced energy. 144 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 8. INTRODUCTION 8.7.4.2 Seismic design using advanced numerical analysis (multi-hazard) (SS/S) Worked example Title Seismic design using advanced numerical analysis (multihazard) 1 of 4 pages Structure Steel structure in seismic zone Made by UPT Date: 06/2021 Document ref. I.5.2 / SS/S Example: Design of a steel structure for multi-hazard scenarios using advanced numerical analysis Design manual § 4.5 This example gives information about the design of a steel structure considering multihazard events, i.e., column failure after an earthquake. Basic data of structure • For geometry, sections, and materials, see Section 8.2. Design manual § 8.2. Actions for Seismic Design Situation The following actions are considered: • Permanent loads DL (see Table 11); • Live loads LL (see Table 11 for SS/S structure); • Seismic action AEd corresponding to ULS (see section below). Combination of actions for Seismic Design Situation The combination of actions is: 𝐷𝐿7+70.3×𝐿𝐿7+7𝐴.4 Definition of hazard scenario After the structure is subjected to an earthquake, a column can be lost, thus making the structure vulnerable to subsequent hazards. In the following, this procedure is applied to verify the capacity of the structure to resist progressive collapse using column loss approach. Step 1: Seismic analysis – The structure is subjected to a design level earthquake Step 2: Column loss scenarios: Lost columns are located at A1, A2, A4, B1, B’ (Figure 71) – they are assumed to be lost one at a time. Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 145 8.7 IDENTIFIED EXCEPTIONAL EVENTS Worked example I.5.2 / SS/S Seismic design using advanced numerical analysis (multi-hazard) – SS/S 2 of 4 pages Figure 71. Position of the columns to be removed after eathquake Structural analysis The seismic analysis is performed using push-over analysis and the damage evaluation is done using the N2 method (EN 1998). After the gravity loads are applied, the structure is subjected to a monotonically increasing pattern of lateral forces, representing the inertial forces which would be experienced by the structure when subjected to ground shaking. Under incrementally increased loads, some structural elements may yield. Consequently, after each plastic hinge is formed, the structure experiences a loss in stiffness and load capacity. To evaluate the seismic demands for ULS, the structure is pushed to its target top displacement Dt. Figure 72 shows the capacity curves for transversal and longitudinal directions and the target points for ULS and DL. Figure 73 shows the plastic mechanisms at failure for transversal and longitudinal directions. No plastic hinges develop in perimeter moment resisting frames in neither X nor Y direction at ULS, but only in the braced frames. a) b) Figure 72. Seismic analysis: a) push-over curve with the position of the target point – X direction; b) push-over curve with the position of the target point – Y direction 0 5000 10000 15000 20000 25000 0 0.05 0.1 0.15 0.2 Base shear force [kN] Top displacement [m] PO analysistarget displacement - X direction ULS DL PO 0 5000 10000 15000 20000 25000 30000 0 0.05 0.1 0.15 0.2 0.25 Base shear force [kN] Top displacement [m] PO analysis - target displacement - Y direction ULS DL PO 146 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 8. INTRODUCTION Worked example I.5.2 / SS/S Seismic design using advanced numerical analysis (multi-hazard) – SS/S 3 of 4 pages a) b) Figure 73. Seismic analysis: a) plastic mechanism at Dt ULS – current transversal frame; b) plastic mechanism at Dt ULS – current longitudinal frame Column removal in the aftermath of the earthquake Five removal scenarios are considered, i.e., perimeter, penultimate, and corner columns located at the ground floor. The scenarios involve columns on the short and long sides of the facade. The assessment of progressive collapse resistance is done using the alternative load path (ALP) method and nonlinear dynamic procedure (NDP), in accordance with the UFC 4-023-03 guidelines. The gravity loads are applied in first stage; then, in the second stage, the element is removed almost instantaneously (removal duration of 0.005 seconds). Results Below are presented the formation of the plastic mechanisms which occur in perimeter frames in the scenarios mentioned above. For each case, the plastic mechanisms (Figure 74a) to e)) and history of vertical displacement above the removed column (Figure 75) are presented. a) Case A4 b) Case A2 Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 147 8.7 IDENTIFIED EXCEPTIONAL EVENTS Worked example I.5.2 / SS/S Seismic design using advanced numerical analysis (multi-hazard) – SS/S 4 of 4 pages Figure 75. Time history response for column removal scenarios Conclusions a) Case A1 b) Case B1 c) Case B’ Figure 74. Plastic mechanism after column removal for the considered scenarios • It may be concluded that the structure has the capacity to resist the progressive collapse even with the loss of a column after an earthquake. • The level of damage in the elements (given by the level of plastic deformation in the plastic hinges) is small. • Other performance objective (e.g., collapse prevention) may be employed to assess the structural behaviour. Flowchart Figure 3 – Box B.5 è End of design -90 -80 -70 -60 -50 -40 -30 -20 -10 0 00.5 11.5 Vertical displacement [mm] Time [s] Case A1 Case A2 Case A4 Case B' Case B1 148 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 8. INTRODUCTION 8.8 Unidentified exceptional events 8.8.1 Prescriptive approach (tying method) 8.8.1.1 Design for unidentified threats using prescriptive approach - tying method (SS/S) Worked example Title Design for unidentified threats using prescriptive approach 1 of 3 pages Structure Steel structure in seismic zone Made by UPT Date: 06/2021 Document ref. II.1.1 / SS/S Example: Design for unidentified threats of a steel structure in seismic zone using prescriptive approach (tying method) Design manual § 5.3.1 This example shows the application of the tying method for beams and their connections (horizontal tying). The vertical tying should also have been checked but this check is not performed in the framework of this worked examples. The check of vertical ties is performed in W.E. II.4.1 / SS/NS. Basic data of structure • For geometry, sections, and materials, see Section 8.2. Design manual § 8.2. Actions for Accidental Design Situation The following actions are considered: • Permanent loads DL (see Table 11); • Live loads LL (see Table 11 for SS/S structure); • No specific accidental action is taken into account. Definition of tensile loading Figure 76. Horizontal ties considered for using prescriptive method – SS/S Horizontal ties • for internal ties: 77𝑇i=0.8∙(gj+ψ∙qj) or 75 kN, whichever is greater • for perimeter ties: 𝑇k=0.4∙(gj+ψ∙qj) or 75 kN, whichever is greater Eq. A1 and A2 from (EN 19911-7 2006) Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 149 8.8 UNIDENTIFIED EXCEPTIONAL EVENTS Worked example II.1.1 / SS/S Design for unidentified threats using prescriptive approach – tying method – SS/S 2 of 3 pages Computation • Internal pinned secondary beams (IPE550, all on short direction, see Figure 77 for joint configuration)7 7 7 Figure 77. Joint configuration of pinned connection for a secondary beam 8 ! Spacing between ties (secondary beams) 𝑠=2.667𝑚7 Span of the tie 𝐿=127𝑚7 Design tensile load for internal ties7 𝑇;=𝑚𝑎𝑥[0.8∙(𝑔<+𝛹∙𝑞<)𝑠.𝐿;7757𝑘𝑁]=𝑚𝑎𝑥[0.8×(5+0.5×3)×2.66× 12;7757𝑘𝑁]7=1667𝑘𝑁7 • Internal pinned main beams (IPE550, all on long direction, see Figure 78 for joint configuration) 7 7 Figure 78. Joint configuration of pinned connection for a main beam 8 Spacing between ties (main beams) Span of the tie 𝑠=12𝑚 𝐿=87𝑚 150 | Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings 8. INTRODUCTION Worked example II.1.1 / SS/S Design for unidentified threats using prescriptive approach – tying method – SS/S 3 of 3 pages Design tensile load for internal ties 𝑇;=𝑚𝑎𝑥[0.8∙(𝑔<+𝛹∙𝑞<)∙𝑠∙𝐿;7757𝑘𝑁] =𝑚𝑎𝑥[0.8×(5+0.5×3)×12×8;7757𝑘𝑁]=499.27𝑘𝑁 Results The shear resistances and UFs for the connections of the internal ties considered for the verification are presented in Table 33. Table 33 Connection check for tying forces according to the prescriptive method Element Tying force (kN) Shear resistance (kN) Failure mode UF (-) Internal pinned secondary beams 166 392 Sec. beam in bearing 0.42 Internal pinned main beams 499.2 392 Main beam bolts in shear 1.27 Note: The capacity of the connection in tension at the extremities of the secondary beams was verified without any verification to the main beam. Care is needed as the main beam web can become the critical component. Conclusions For the connections of the internal pinned secondary beams, the UF of 0.42 results in an appropriate design. Flowchart Figure 3 – Box C.4 è End of design For the connections of the pinned internal main beams, an UF of 1.27 requires a redesign of the joint. Flowchart Figure 3–Box C.4èC.2 Consequently, another bolt row was added (3 rows in total). It increased the shear capacity to 588 kN which gives an UF of 0.85 for the connection – see Figure 79 for the redesigned configuration. 7 7 Figure 79. Redesign of the main beam joints 8 Flowchart Figure 3 – Box C.4 è End of design Design Recommendations Against Progressive Collapse in Steel and Steel-concrete Buildings | 151 8.8 UNIDENTIFIED EXCEPTIONAL EVENTS 8.8.1.2 Design for unidentified threats using prescriptive approach – tying method (CS/S) Worked example Title Design for unidentified threats using prescriptive approach 1 of 2 pages Structure Composite structure in seismic zone Made by UPT Date: 06/2021 Document ref. II.1.2 / CS/S Example: Design for unidentified threats in a composite structure in seismic zone using prescriptive method (tying method) Design manual § 5.3.1 This example shows the application of the tying method for beams and their connections (horizontal tying). The vertical tying should also have been checked but this checked is not performed in the framework of this worked examples. The check of vertical ties is performed in W.E. II.4.1 / SS/NS. Basic data of structure • For geometry, sections, and materials, see Section 8.2. Design manual § 8.2. Actions for Accidental Design Situation The following actions are considered: • Permanent loads DL (see Table 11); • Live loads LL (see Table 11 for CS/S structure); • No specific accidental action is taken into account. Definition of tensile loading The verification is performed similarly to W.E. II.1.1 / SS/S for the main beams. Additionally, the longitudinal reinforcement in the effective length of the beam is taken into consideration. Computation • internal pinned main beams Spacing between ties (main beams) 𝑠=127𝑚 Span of the tie 𝐿=87𝑚 Design tensile load for internal ties 𝑇;=𝑚𝑎𝑥[0.8(𝑔<+𝛹.𝑞<)𝑠.𝐿;7757𝑘𝑁]=𝑚𝑎𝑥[0.8(5+0.5×3)12×8;7757𝑘𝑁] 77777=499.27𝑘𝑁 The axial force capacity of the main beam connection is the sum of the tension force transferred through the bolts and the tension force transferred through longitudinal reinforcement in the effective width of the reinforced concrete slab.