Tangent moduli of hot-rolled I-shaped axial members considering various residual stress distributions

• The exact tangent moduli of hot-rolled steel I-shaped axial members are derived.
• Linear and parabolic patterns are considered as residual stress distributions.
• The moduli can consider the pattern and maximum value of residual stresses.
• The derived equations are verified by inelastic analyses using shell element models.
• The equations can be easily used for plastic hinge analyses with excellent accuracy.

This paper presents an equation for the effective tangent moduli for steel axial members of hot-rolled I-shaped section subjected to various residual stress distributions. Because of the existence of residual stresses, the cross section yields gradually even when the member is subjected to uniform axial stresses. In the elasto-plastic stage, the structural response can be easily traced using rational tangent modulus of the member. In this study, the equations for rational tangent moduli for hot-rolled I-shaped steel members in the elasto-plastic stage were derived based on the general principle of force-equilibrium. For practical purpose, the equations for the tangent modulus were presented for conventional patterns of the residual stress distribution of hot-rolled I-shaped steel members. Through a series of material nonlinear analyses for steel axial members modeled by shell elements, the derived equations were numerically verified, and the presented equations were compared with the CRC tangent modulus equation, the most frequently used equation so far. The comparative study shows that the presented equations are extremely effective for accurately analyzing elasto-plastic behavior of the axially loaded members in a simple manner without using complex shell element models.