Elasto-plastic model for analysis of influence of imperfections on stiffness of fully anchored light-frame timber shear walls

In order to stabilize timber-framed buildings against lateral loads, the diaphragm action of roofs, floors and walls is often used. This paper deals with the influence of imperfections such as gaps and uplift on the stiffness and the horizontal displacement of fully anchored shear walls. The significance of analyzing the effects of imperfections is evident when evaluating the stiffness of shear walls; tests of walls show that the horizontal displacement is underestimated in calculations using the stiffness of sheathing-to-framing joints as obtained from experiments. Also, in real structures where hold-downs are used, the influence of gaps and uplift should be included in order to obtain realistic displacements in the serviceability limit state. The analytical model is based on ideal plastic behavior of the mechanical sheathing-to-timber joints with stresses parallel to the perimeter of the frame and on linear elastic behavior for stresses perpendicular to the bottom rail. Using this elasto-plastic model, the equations for the stiffness and the deflection versus the number of segments in the wall are derived. The fully anchored condition for the shear walls is simulated by applying a diagonal load to the shear wall. Three types of imperfections are evaluated: Walls with gaps at all studs, a gap only at the trailing stud, and gaps at all studs, except at the trailing stud. It is shown that the effect of imperfections on the stiffness of the wall in the initial stage is considerable. Depending on the distribution of the gaps and the number of segments included in the shear wall, the displacement of the shear wall is increased several times compared to that of a fully anchored wall diaphragm with no gaps; e.g. for a single segment wall more than four times. However, for walls with more than six segments the effect of imperfections can be neglected. Finally, the theoretical model is experimentally verified.