Effect of Initial Out-of-Straightness Imperfection on Second-Order Elastic Behavior of Planar Frames

Geometrical imperfections usually occur during fabrication and erection. Initial out-of-straightness is one of the most common types of these flaws. In this paper, the elastic tangent stiffness matrix of an initially curved beam-column element subjected to nodal forces and transverse member loads is derived. Second-order analysis of planar frames is carried out afterwards. The proposed method introduces a new function for explicit modeling of out-of-straightness imperfection and incorporates it directly into the element's stiffness matrix. In addition, the proposed technique uses only one element for each member and presents a single formulation for both tensile and compressive members. The obtained load-deflection curve is compared with those predicted by other methods and the effect of initial out-of-straightness imperfection is also discussed. Results of numerical examples indicate that initial out-of-straightness imperfection is less important if the stability of frame is controlled by second-order P-Δ effect. On the other hand, it can have a considerable effect on the behavior of structure when second-order P-δ effect is dominant.