The resisting moment that is caused by a lateral deflection, X1, is found
by assuming rectangular compression stress blocks exist at the supports
(points o and n) and at the center (point m) as shown in Figure 59a. The
bearing width, a, is chosen so that the moment, Mu, is a maximum; that is,
by differentiating Mu with respect to a and setting the derivative equal
to zero. For a solid masonry unit this will will result in:
a = 0.5 (T - X1)
and the corresponding ultimate moment and resistance (Figure 59b) are equal
Mu = 0.25 f'm(T - X1)2
ru = (2/h2)f'm(T -X1)2
When the mid-span deflection is greater than X1 the expression for the
resistance as a function of the displacement is:
r = (2/h2)f'm(T -X)2
As the deflection increases, the resistance is reduced until r is equal to
zero and maximum deflection, Xm, is reached (Figure 59b). Similar
expressions can be derived for hollow masonry units. However, the maximum
value of a cannot exceed the thickness of the flange width.
(2) Non-rigid Supports. For the case where the wall is
supported by elastic supports at the top or bottom or both, the resistance
curve cannot be constructed based on the value of the compression force,
af'm, which is determined solely on geometry of the wall. Instead, the
resistance curve is a function of the stiffness of the supports. Once the
magnitude of the compression force is determined, equations similar to those
derived for the case of the rigid supports can be used.
(3) Simply Supported Walls. If the supports offer no resistance
to vertical motion, the compression in the wall will be limited by the wall
weight above the floor plus any roof load which may be carried by the wall.
If the wall carries no vertical loads, then the wall must be analyzed as a
simply supported beam, the maximum resisting moment being determined by the
modulus of rupture of the mortar.