Material Effects on Tangent Modulus of Steel Square Hollow Section

Document Type : Regular Paper


Department of Civil Engineering, Shahid Rajaee Teacher Training University, Tehran, Iran


The kind of mild steel, the Bauschinger effect because of strain reversal and strain ageing are indicated to affect significantly the tangent modulus of elasticity. Stub column specimens made from a material that has been pre-stretched in tension have a significantly lower tangent modulus of elasticity than those specimens made from as-received material; the reduction is caused by the Bauschinger effect and a resulting reduction in tangent modulus and yield strength. The reduction happens despite increases in material yield strength due to strain ageing after application of the tensile stretching. This paper has shown great reductions of tangent modulus of elasticity when specimens are made from material pre-stretched in tension compared with as-received specimens. Strain ageing has a great influence in minimizing the tangent modulus of elasticity reductions resulting from prior tensile prestretching. The initial tensile pre-strain of stress-relief-annealed specimens does not affect the tangent modulus of elasticity. No reduction was observed in the tangent modulus of elasticity of specimens prestrained in tension and stress-relief-annealed. The FE analysis according to the ABAQUS code was applied to simulate the stress-strain curves. The numerical and the experimental curves were reasonably similar to each other.


Main Subjects

[1]     L. Gardner and T. M. Chan, “Cross-section classification of elliptical hollow sections,” Steel Compos. Struct., vol. 7, no. 3, p. 185, 2007.
[2]     T. M. Chan and L. Gardner, “Compressive resistance of hot-rolled elliptical hollow sections,” Eng. Struct., vol. 30, no. 2, pp. 522–532, 2008.
[3]     T. M. Chan and L. Gardner, “Bending strength of hot-rolled elliptical hollow sections,” J. Constr. Steel Res., vol. 64, no. 9, pp. 971–986, 2008.
[4]     T. M. Chan and L. Gardner, “Flexural buckling of elliptical hollow section columns,” J. Struct. Eng., vol. 135, no. 5, pp. 546–557, 2009.
[5]     T. M. Chan, L. Gardner, and K. H. Law, “Structural design of elliptical hollow sections: A review,” Proc. Inst. Civ. Eng. Struct. Build., vol. 163, no. 6, pp. 391–402, 2010, doi: 10.1680/stbu.2010.163.6.391.
[6]     L. Gardner, T. M. Chan, and M. A. Wadee, “Shear response of elliptical hollow sections,” Proc. Inst. Civ. Eng. Build., vol. 161, no. 6, pp. 301–309, 2008.
[7]     A. Karrech and A. Seibi, “Analytical model for the expansion of tubes under tension,” J. Mater. Process. Technol., vol. 210, no. 2, pp. 356–362, 2010.
[8]     T. Pervez, A. C. Seibi, and A. Karrech, “Simulation of solid tubular expansion in well drilling using finite element method,” Pet. Sci. Technol., vol. 23, no. 7–8, pp. 775–794, 2005.
[9]     P. Barnes, R. Hejazi, and A. Karrech, “Instability of mechanically lined pipelines under large deformation,” Finite Elem. Anal. Des., vol. 146, pp. 62–69, 2018.
[10]   C. Guo, M. Elchalakani, A. Karrech, M. R. Bambach, and B. Yang, “Behaviour and design of cold-formed CHS under static pure bending through finite element analysis,” Thin-Walled Struct., vol. 147, p. 106547, 2020.
[11]   M.-T. Chen and B. Young, “Cross-sectional behavior of cold-formed steel semi-oval hollow sections,” Eng. Struct., vol. 177, pp. 318–330, 2018.
[12]   B. S. EN10210, “2. British Standard: Hot finished structural hollow sections of non-alloy and fine grain steels Part 2: Tolerances, dimensions and sectional properties,” Br. Stand. Inst., 2006.
[13]   S. (Steel C. I. and B. C. S. Association), “Steel building design: Design data in accordance with Eurocodes and the UK national annexes.” SCI London, 2009.
[14]   T. Haque, J. A. Packer, and X.-L. Zhao, “Equivalent RHS approach for the design of EHS in axial compression or bending,” Adv. Struct. Eng., vol. 15, no. 1, pp. 107–120, 2012.
[15]   A. Insausti and L. Gardner, “Analytical modelling of plastic collapse in compressed elliptical hollow sections,” J. Constr. Steel Res., vol. 67, no. 4, pp. 678–689, 2011.
[16]   K. H. Law and L. Gardner, “Lateral instability of elliptical hollow section beams,” Eng. Struct., vol. 37, pp. 152–166, 2012.
[17]   K. H. Law and L. Gardner, “Buckling of elliptical hollow section members under combined compression and uniaxial bending,” J. Constr. Steel Res., vol. 86, pp. 1–16, 2013.
[18]   M. Theofanous, T. M. Chan, and L. Gardner, “Structural response of stainless steel oval hollow section compression members,” Eng. Struct., vol. 31, no. 4, pp. 922–934, 2009.
[19]   M. Theofanous, T. M. Chan, and L. Gardner, “Flexural behaviour of stainless steel oval hollow sections,” Thin-Walled Struct., vol. 47, no. 6–7, pp. 776–787, 2009, doi: 10.1016/j.tws.2009.01.001.
[20]   M.-T. Chen and B. Young, “Material properties and structural behavior of cold-formed steel elliptical hollow section stub columns,” Thin-Walled Struct., vol. 134, pp. 111–126, 2019.
[21]   M. T. Chen and B. Young, “Tests of cold-formed steel elliptical hollow section beams,” 2016.
[22]   M.-T. Chen and B. Young, “Structural performance of cold-formed steel elliptical hollow section pin-ended columns,” Thin-Walled Struct., vol. 136, pp. 267–279, 2019.
[23]   P. Kumar, S. Pandey, and P. R. Maiti, “A Modified Genetic Algorithm in C++ for Optimization of Steel Truss Structures,” J. Soft Comput. Civ. Eng., vol. 5, no. 1, pp. 95–108, 2021.
[24]   R. Abbaschian and R. E. Reed-Hill, Physical Metallurgy Principles-SI Version. Cengage Learning, 2009.
[25]   H. M. Tensi, A. Stich, and G. E. Totten, “Quenching and quenching technology,” Chapter, vol. 4, pp. 157–249, 1997.
[26]   M. Jandera, L. Gardner, and J. Machacek, “Residual stresses in cold-rolled stainless steel hollow sections,” J. Constr. Steel Res., vol. 64, no. 11, pp. 1255–1263, 2008.
[27]   G. Charles, “Salmon, John E. Johnson and Faris A. Malhas-" Steel Structures-Design and Behavior".” Prentice Hall, 2008.
[28]   S. Afshan, B. Rossi, and L. Gardner, “Strength enhancements in cold-formed structural sections—Part I: Material testing,” J. Constr. Steel Res., vol. 83, pp. 177–188, 2013.
[29]   L. Gardner and D. A. Nethercot, “Experiments on stainless steel hollow sections—Part 1: Material and cross-sectional behaviour,” J. Constr. Steel Res., vol. 60, no. 9, pp. 1291–1318, 2004.
[30]   L. Gardner, N. Saari, and F. Wang, “Comparative experimental study of hot-rolled and cold-formed rectangular hollow sections,” Thin-walled Struct., vol. 48, no. 7, pp. 495–507, 2010.
[31]   S.-D. Hu, B. Ye, and L.-X. Li, “Materials properties of thick-wall cold-rolled welded tube with a rectangular or square hollow section,” Constr. Build. Mater., vol. 25, no. 5, pp. 2683–2689, 2011.
[32]   B. Rossi, H. Degée, and F. Pascon, “Enhanced mechanical properties after cold process of fabrication of non-linear metallic profiles,” Thin-walled Struct., vol. 47, no. 12, pp. 1575–1589, 2009.
[33]   M. A. Dabaon, M. H. El-Boghdadi, and M. F. Hassanein, “A comparative experimental study between stiffened and unstiffened stainless steel hollow tubular stub columns,” Thin-walled Struct., vol. 47, no. 1, pp. 73–81, 2009.
[34]   B. Young and W.-M. Lui, “Tests of cold-formed high strength stainless steel compression members,” Thin-Walled Struct., vol. 44, no. 2, pp. 224–234, 2006.
[35]   X.-L. Zhao, “Section capacity of very high strength (VHS) circular tubes under compression,” Thin-Walled Struct., vol. 37, no. 3, pp. 223–240, 2000.
[36]   A. A. S. for T. and Materials, Standard test methods for tension testing of metallic materials. ASTM international, 2009.
[37]   HKS, “ABAQUS/Standard user’s manual.” ABAQUS Inc. Pawtucket, RI, 2005.
[38]   Shekarchi M, Yekrangnia M, Biniaz A, Raftery GM. Effect of elevated temperatures on the compressive behavior of timber filled steel and pultruded GFRP tubes. Compos Struct. 2021;271:114135.