Three-dimensional nonlinear displacement-based beam element for members with asymmetric thin-walled sections

• DOI: 10.31224/osf.io/jk8f9
• Publication Date: 2020-12-15T15:35:42Z
• Authors: Xinlong Du; Jerome Hajjar
• Keywords: Tangent stiffness matrix

Asymmetric thin-walled sections such as steel angles and tees are widely used in truss structures transmission towers. To address extreme limit states that these encounter due to events hurricanes earthquakes, it is important capture their response large deformations caused by static or dynamic loading. In the nonlinear deformation regime, members have coupled axial-flexural-torsional so-called Wagner effect noncoincident shear center centroid. A three-dimensional corotational total Lagrangian beam element formulated implemented OpenSees framework account for coupling effects invoking Green-Lagrange strains referenced a basic system. system, forces torque defined with respect center, axial force referred centroid, flexure around section principle axes but planes containing center. The tangent stiffness matrix derived through linearization of governing equation obtained from virtual work. Cubic Hermitian functions transverse displacements linear shape function torsional adopted development. Before conducting transformation, all end transformed act about order remedy membrane locking inextensional bending mode, high terms strain replaced constant effective strain. Cyclic material nonlinearity considered discretizing cross into grid fibers, tracking uniaxial stress-strain constitutive at each fiber, performing numerical integration over obtain matrix. formulation compared against set experimental results validate can model geometric nonlinearities accurately efficiently.