Proportionate and Nonproportionate Shear Walls

Introduction. A major structural system in today’s tall building structural design is the use of shear walls. Structures that solely rely on shear walls is obviously called a shear wall structure. Shear walls provide a high in-plane stiffness and strength for both lateral and gravity loads, and are ideally suitable for tall buildings, especially those conceived in reinforced concrete. Tall buildings designed to carry the entire lateral loading through shear walls can be economical to heights of around 40-stories. Taller structures than 40 stories usually combine shear walls with other structural systems. Shear walls are continuous from the top of the building down into the foundations, to whom they are rigidly attached. They are thus analyzed as vertical cantilevers. In our previous lecture we saw that the term “shear walls” is a misnomer, because shear walls deform predominantly in flexure.

Shear walls should be located so that they carry both the lateral loads and gravity loading sufficiently to cancel the maximum tensile bending stresses in the bottom of the walls caused by the lateral loads. Obviously, the most effective location of the walls is at the building’s perimeter. However, this conflicts with most architectural desires. The figure at right shows that shear walls (in yellow) can be singular or planar in L-shape, T-shape and Ushape, plus a combination of these. The walls are typically combined in use with the elevator core and the stairwells and other service cores.

This lecture studies the behavior of shear walls linked to the floor slabs. The slabs are assumed to have little or no flexural (bending) resistance, so that they only capable of transmitting horizontal forces into the shear walls. Tall buildings using shear walls will consist of an assembly of walls of different lengths and thicknesses. Linking these walls requires a careful study of how the moments and shears redistribute their loads between the walls and their connecting girders and floor slabs. A common rule-of-thumb used by designers of shear walls (for example, LeMessurier), is that the first iteration for the shear wall would assume a 1” wall thickness for each floor height. Therefore, a 40-story building will set the initial shear wall thickness to 40 inches. Thereafter, the analysis will decrease this thickness to a slightly smaller value (such as, ¾”, ½”, etc per floor for the higher levels). Shear walls can be designed to be either: a) proportionate, or b) non-proportionate system of walls.

In a proportionate wall system, the ratios of the flexural rigidities remain constant throughout their heights. These walls do not incur any re-distribution of shears or moments at the change of levels. This system is statically determinate, and from equilibrium, the external moment and shear is distributed between the walls in proportion to their flexural rigidities.

the moment of inertia changes consistently throughout

In a non-proportionate wall system, the ratios of wall flexural rigidities are not constant up the building’s height. At stories where the rigidities change there will be redistributions of the shears and moments in the walls. This system is statically indeterminate and difficult to analyze by hand. For that reason, they are analyzed using the finite element method or the analogous frame analysis. the moment of inertia does not changes consistently throughout