Sensitivity analysis of steel moment frames accounting for geometric and material nonlinearity

Design Optimization of Steel Moment Frames Under Extreme Earthquake Loading

“…These drift distributions are deemed to be nearly uniform and satisfactory for design. It is generally unlikely to obtain an optimal design with f 2 =0 due to the following reasons: 1) the cross sections are discrete variables; 2) the errors in computing sensitivity information are unavoidable [32]; 3) the plastic deflections are extremely sensitive to the change of sectional size (a plastic deflection is usually two orders of magnitude more sensitive than an elastic deflection [31] For member plastification taken as a measure of damage, it is observed from Figures 6 and 7 that damage is somewhat uniformly distributed over all stories of the structures where the frames undergo nearly uniform interstory drift (i.e., as desired, there is no significant concentration of plastic deformation). This phenomenon illustrates the close correlation between the inelastic interstory drift and the structural plastic state.…”

“…/∂A j = 0 if k≠j [32] and expanding Eq. (46) in terms of plasticity factors, the sensitivity of displacement μ l is then derived from Eqs.…”

“…(2) for element j at end n (n=1 or 2); ∂R jn P /∂A j is the derivative of rotational stiffness of the plastic hinge for element j at end n; and supercript (m-1) is load step index. See [32] for detailed derivation of Eq. (47).…”

“…Gong et al [31,32] derived sensitivity analysis formulations for the pushover analysis procedure described in Section 2. For the completeness of this paper, the sensitivity formulations are given briefly in the following.…”

“…where: ∂C sk /∂A j and ∂C gk /∂A j are the derivatives of correction matrices C sk and C gk , respectively [32]; ∂S k /∂A j and ∂G k /∂A j are the derivative of elastic stiffness matrix S k and geometric stiffness matrix G k , respectively.…”