Stiffness of Materials

The example wall shown below is part of the previous single family structure.  I've exploded it for easier viewing. You will remember from our discussion of the Modulus of Elasticity that each material its own range of strengths in which it functions. Of the three materials shown below, the cement stucco (concrete) is the strongest as well as the thickest.  The plywood is second in strength but equivalent in thickness to the third place gypboard.

If this wall is subjected to lateral loads, the strongest material (stucco) will be the first to resist the load.  If the force exceeds the capacity of the stucco, the remaining materials will be called on to resist the load. At first, the plywood and gypboard will act together.  But over repetitive cycles, the fasteners in the gypboard will lose some of their strength due to hole enlargement.  In the end, the plywood - the material we consider to resist lateral loads - will finally receive the whole design load.

Example Wall
If we consider each of the materials alone as if they were cantilevered
beams, their strength would be proportional to their thickness (b) as in
(b)(d*d)/6 and to their Modulus of Elasticity (48*E*If)/(P)(L*L*L).

Note: Stiffness is the inverse of deflection.  Thus the standard formula for
deflection is inverted.

The interaction of materials is an important consideration when designing or remodelling a structure. A similar set of circumstances occurs when materials like the ones in the example above are separated in the structure. Some examples will be presented later on when we look at shear walls in the field.