Modeling partially yielded regions of W-Shapes using a second-order stiffness reduction over the element length

Stiffness reduction occurs due to yielding of the cross-section of W-Shapes under certain conditions of residual stress, moment, and axial load. This paper investigates the development and performance of a new closed-form stiffness matrix for a beam element that assumes a second-order stiffness reduction over the partially yielded regions of W-Shapes. Even though it is well known the stiffness reduction is nonlinear when the moments vary over the partially yielded regions, it is common to use a stiffness matrix that is based on an assumed linear stiffness reduction. To evaluate the performance of the new stiffness matrix, two beams and three unbraced frames were analyzed using MASTAN2 considering five load increment sizes and nine element conditions. Discussion and recommendations are provided regarding the parameters that influence the modeling results and the ability of the new stiffness matrix to provide better results than the current stiffness matrix that assumes a linear stiffness reduction.

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