Fatigue Design of Square Hollow Section Joints Strengthened with Gusset Plates Using the Structural Stress Concept

19th International Symposium on Tubular Structures (ISTS 19) Hong Kong, China, December 1st – 3rd, 2025 Edited by Tak-Ming CHAN Fatigue Design of Square Hollow Section Joints Strengthened with Gusset Plates Using the Structural Stress Concept M. WINKLER a, A. DÜRR a, P. LADENDORF b and S. HERION b a Institute for Material and Building Research, University of Applied Sciences Munich, Germany bCCTH Center of Competence for Tubes and Hollow Sections, Karlsruhe, Germany E-mails: mwin[email protected], andre.[email protected], philipp[email protected], [email protected] Keywords fatigue strength; strengthening; gusset plate; structural stress concept.t Abstract Welded tubular joints have a low fatigue strength due to high stress concentrations. Gussets plates can increase the fatigue strength by distributing stresses more uniformly. However, there are few recommendations to consider the influence of the gusset plate in the fatigue design. Therefore, the research project FOSTA P 1442 investigated systematically the fatigue behaviour of tubular joints strengthened with shape-optimized gusset plates. K-Joints with different gusset plate shapes, hollow sections shapes and steel grades were tested to characterize the fatigue strength using small and large specimens. A parametric study was performed using a numerical model verified by strain gauge measurements. Formulae were derived from the parametric study to calculate the stress concentrations factors for different joint configurations and gusset plate shapes. In this paper a recommendation is presented based on the project’s findings for the fatigue design of square hollow section joints strengthened with gusset plates using the structural stress concept. 1 INTRODUCTION The fatigue strength of welded tubular joints is low due to high stress concentrations and secondary bending moments. By adding gusset plates to the joint, stresses can be distributed more uniformly over a larger area resulting in lower stress concentration factors (SCF) and thus a higher fatigue strength, see Figure 1. In the fatigue design according to standards like EN 1993-1-9 [1] of welded tubular joints, the influence of gusset plates cannot be taken into account. As there are only a few studies regarding the fatigue behaviour of tubular joints with gusset plates, see [2], [3], the research project FOSTA P 1442 [4] was carried out by the Center of Competence for Tubes and Hollow Sections (CCTH) in Karlsruhe and the University of Applied Sciences in Munich. Within this project 35 fatigue tests on welded tubular K-joints strengthened with gusset plates were performed. Different gusset plate shapes, steel grades and sections shapes were investigated. A numerical parametric study was performed to extend the area of application of the experimental findings. In this paper a proposal for a fatigue design recommendation for square hollow section (SHS) K-joints using the structural stress concept is presented. 2 STRUCTURAL STRESS CONCEPT The fatigue strength of tubular connections is strongly dependent on the joint geometry. Due to the infinite variety of geometries the nominal stress approach cannot cover all joint configurations in a meaningful manner, often leading to uneconomical designs. The structural stress concept, however, enables the calculation of design stresses, so called hot-spot stresses, for arbitrary joint configurations by determining stress concentrations factors (SCF). In conjunction with structural S-N curves a more geometry-appropriate and economical design is possible. SCFs can be determined numerically, experimentally or by using SCF-formulae like in [5]. Figure 1: Joint of hollow sections strengthened with a gusset plate [4] 3 EXPERIMENTAL INVESTIGATIONS To systematically investigate the effect of gusset plates on the fatigue strength of welded tubular joints 35 fatigue tests on welded K-joints strengthened with shapeoptimized gusset plates, see Figure 1, were carried out. For this purpose, 3 different gusset plate shapes, 2 steel grades - S355H and S700MH - and 2 section shapes – SHS and circular hollow sections (CHS) – were investigated. 33 tests were performed on “small-scale” K-joints specimens and 2 tests were performed on trusses with a height of 1.0 m and a span of 6.0 m. The results showed an increase in fatigue strength in all test series. In the S-N curve in Figure 2 the results of the tests on SHS-joints made from S355H and S700MH with the gusset plate shape as shown in Figure 4 are summarised. It has been shown that through the strengthening with a shapeoptimised gusset plate the fatigue strength could be increased by 31% compared to the design fatigue strength for non-reinforced K-joints acc. to EN 1993-1-9 [1]. More information regarding the experimental investigations can be found in [6]. Figure 2: S-N curve - Joint evaluation of experimental data from [4] 4 NUMERICAL INVESTIGATIONS 4.1 Parametric study To extend the area of application of gusset plate reinforcements a numerical parametric study was conducted. Therefore, the maximum SCFs for various joint configurations and gusset plate shapes as well as loading conditions were calculated using a finite element (FE) model, see Figure 3. The model was validated using strain gauge measurements. More information regarding the FE-model and the results of the parametric study can be found in [7]. The parameter boundaries of the study are summarised in Table 1. 4.2 Development of a SCF-formula On basis of the calculated SCFs a multi-variate regression analysis was performed to determine regression coefficients and variables, see Table 2, for a simple linear formula, see equation (1), to calculate the SCFs for arbitrary joint configurations. The variables consist of dimensionless geometry parameters, see Figure 4 and Table 2. Table 1: boundaries of parametric study parameter symbol parameter boundaries chord width b0 100 - 300 mm chord wall thickness t0 6 - 20 mm brace width b1 80 - 200 mm brace wall thickness t1 4 - 20 mm gap g 25 - 50 mm excentricity e -29 - 19 mm brace angle Θ 45° width ratio β 0,4 - 0,8 chord ratio 2γ 15 - 25 thickness ratio τ 0,5 - 1 𝑆𝐶𝐹𝑝𝑙𝑎𝑡𝑒 =∑𝐾𝑖∗𝑃𝑖 (1) a) b) Figure 3: numerical model – a) investigated loading conditions [5], b) details of FE-model [4], [7] Load c cles Stress range N ailure criterion: N3(through-thickness cracking) S355H S 00MH R 0.1 m 5 e perimental data C,50 C,95 EN 1993-1-9 C,50 9 . N mm C,95 0.0 N mm C,95 53.5 N mm brace chord e Figure 4: geometry parameters Table 2: regression parameters for calculation of maximum SCF component loading condition SCF K1 P1 K2 P2 K3 P3 K4 P4 K5 P5 K6 P6 brace 1 SCFb,ax 22.8 β -20.7 β² 1.84 2γ 2γref -3.18 τ -0.45 R/b1 0.14 t1/tb chord 1 SCFch,ax 12.9 β -15.5 β² -2.4 2γ 2γref 3.25 τ 0.69 g' 0.11 tb/t0 2 SCFch,ch 13.3 β -11.4 β² -0.8 2γ 2γref -1.95 τ 0.82 lb/lA -0.15 t0/tb 4.3 Benefit analysis To evaluate the benefit of the gusset plate reinforcement for different joint configurations a further parametric study was performed. Therefore, to reduce the number of variables, certain geometry parameters were fixed, see Figure 4. To determine the benefit, the SCF was calculated both for the non-reinforced joint – defined as SCFCidect - using the formulae from [5] and for the reinforced joint using the regression formula (1). The resulting benefit is calculated using formula (2). 𝑏𝑒𝑛𝑒𝑓𝑖𝑡 =(𝑆𝐶𝐹𝐶𝑖𝑑𝑒𝑐𝑡 −𝑆𝐶𝐹𝑝𝑙𝑎𝑡𝑒) 𝑆𝐶𝐹𝐶𝑖𝑑𝑒𝑐𝑡 (2) The benefit was calculated for the investigated parameter range, see Figure 4, and is plotted as a surface graph for different components, load conditions and geometric parameters, see Figure 5 to Figure 7. For the brace and chord members in load condition 1 good benefits can be achieved especially 2γ ≥20 – up to +43% for SCFb,ax and +68% for SCFch,ax. For 2γ = 15 and low β -ratios the benefit for SCFb,ax is around -1%. For 2γ = 15 and low βand τ -ratios the benefit SCFch,ax is around -25%. For load condition 2 benefits of up to +25% for SCFch,ch can be achieved for high βand τ -ratios. However, for low βand τ -ratios the SCFch,ch of reinforced joints are up to 40% higher than without gusset plate. Figure 5: benefit for braces in load condition 1 – SCFb,ax b1 t1 tB gusset plate thickness E A aB hB lB e g t0 b0 R aried input parameters for benefit analysis mm mm 2mm i ed input parameters for benefit analysis: = = 2 = 2 = Dependent parameters: = Figure 6: benefit for the chord in load condition 1 – SCFch,ax Figure 7: benefit for the chord in load condition 2 – SCFch,ch 5 RECOMMENDATION & OUTLOOK To exploit the full potential of a gusset plate reinforcement of a K-joint made from RHS, the geometry parameters and load condition have to be considered. The highest benefit can be achieved for high βand τ -ratios for braces and chord members in load condition 1. Therefore, the strengthening method is suited for brace and chord members at the supports of a single span truss girder where brace forces are maximum and the chord forces are minimal, see Figure 8. The maximum SCF can simply be calculated using formula (1). The resulting number of endurable load cycles can then be determined using the structural S-N curves from [5]. Since the fatigue strength for load condition 2 is reduced by the strengthening method in most cases, the successor project FOSTA P 1735 [8] investigates optimized weld seam designs to improve the fatigue strength and therefore extend the area of application of the gusset plate reinforcement to joints under load condition 2. Figure 8: Suitable location for gusset plate strengthening in a single span truss girder ACKNOWLEDGEMENTS The research project FOSTA P1442 [4] from the Research Association for Steel Application (FOSTA) is supported by the Foundation for Steel Application Research. The project is carried out at the CCTH and the University of Applied Sciences Munich. The authors would like to thank the project committee and the supporting companies for providing material and fabricating specimens. REFERENCES [1] ‘EN 1993-1-9:2009, Eurocode 3: Design of steel structures - Part 1-9: atigue; German version EN 1993-1-9:2005 + AC:2009’, Beuth erlag GmbH, 2009. doi: 10.31030 1 22 0. [2] U. Kuhlmann and . Gölz, ‘Pra isgerechte Gestaltung von Diagonalrohr‐Anschlüssen im Stahl‐ und erbundbrückenbau’, 2022, doi: 10.1002 stab.20220002 . [3] S. Herion, O. leischer, and D. Koenig, ‘Comparison of Different Configurations of Thick-walled K-joints with Gap made of RHS and CHS’, International Ocean and Polar Engineering Conference, Busan, Korea, 201 . [ ] S. Herion, A. Dürr, P. adendorf, and M. Winkler, ‘ inal report: Increase of fatigue strength of hollow section joints made of high strength steels by shape-optimized gusset plates, OSTA P1 2 32 2019 S 002 10258 19’. 2023. [5] X.- . Zhao, Ed., Design guide for circular and rectangular hollow section welded joints under fatigue loading - CIDECT 8, 2002. [ ] M. Winkler, A. Dürr, S. Herion, and P. adendorf, ‘ atigue tests on connections of hollow sections made of high‐ strength steel with shape‐optimized gusset plates’, 2023, doi: 10.1002 cepa.2309. [ ] P. adendorf, S. Herion, M. Winkler, and A. Dürr, ‘Investigation of the atigue Strength of Shape Optimized Gusset Plates in Rectangular and Circular Hollow Section K-Joints’, doi: 10.101 j.prostr.202 .03.0 5. [8] S. Herion, A. Dürr, P. adendorf, and M. Winkler, ‘ inal report: Optimized weld seam design of tubular connections through gusset plates for an increase in fatigue strength, OSTA P 1 35 25 2023 S 002 10281 23’. e pected 202 . brace chord support gusset plate