Out‐of‐Plane Strengths of Steel Beams

Geometrically non-linear approximations on stability and free vibration of composite beams

“…However, second-order finite element models have been used by a number of researchers in the analysis of structures [15][16][17][18][19], due to the fact that these models have sufficient accuracy for the elastic flexural-torsional stability of beams [11].…”

“…However, many of these theories differ in the grade of non-linearity considered in their formulation. For example, second-order displacement field has been used in a formulation of finite element models for 3D non-linear analysis of beam structures [14][15][16][17][18][19]. This approximation presents several advantages because it simplifies the coupling between the displacement and rotations and so the tangent stiffness matrix (used for the non-linear incremental-iterative analysis) can be simplified.…”

Geometric and material nonlinear analyses of elastically restrained arches

“…The values of E, y , E s , n y , n s need to be input from experimental results or using assumed values. The values n y = 11 and n s = 31 can usually be used [14,15]. For steel reinforcement, cold-formed steel section, and deck sheeting, the stress and strain curves display no typical yield characteristics.…”

Dynamics of nonprismatic thin-walled composite members of generic section

“…The rotations and curvatures of the axes x*, y* and z* can be obtained as shown in Love (1944), Trahair and Bild (1990) and Bild et al (1992):…”