Equation - dm2_080231

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(b) For any further lateral motion of point m, compressive
forces will occur at points m and o. These compressive forces form a couple
that produces a resistance to the lateral load equal to:
EQUATION:
ru = 8Mu/h2
(135)
where all symbols have previously been defined.
(c) When point m deflects laterally to a line n-o (Figure 58c),
the moment arm of the resisting couple will be reduced to zero and the wall
with no further resistance to deflection.  In this position the diagonals om
and mn will be shortened by an amount equal to L - h'/2
The unit strain in the wall caused by the shortening will be:
EQUATION:
[epsilon]m = (L - h'/2)/L
(136)
where,
[epsilon]m = unit strain in the mortar, in/in
All the shortening is assumed to occur in the mortar joints; therefore:
EQUATION:
fm = Em[epsilon]m
(137)
where,
Em = modulus of elasticity of the mortar, psi
fm = compressive stress corresponding to the strain s[epsilon]m,
psi
In most cases fm will be greater than the ultimate compressive strength of
the mortar fm, and therefore cannot exist.  Since for walls of normal
height and thickness each half of the wall undergoes a small rotation to
obtain the position shown in Figure 58c, the shortening of the diagonals om
and mn can be considered a linear function of the lateral displacement of
point m. The deflection at maximum resistance, X1, at which a compressive
stress, fm, exists at points m, n, and o can therefore be found from the
following:
X1 - Xc = f'm = f'm
EQUATIONS:
(138a)
T  - Xc
fm
Em[epsilon]m
or
(T - Xc)f'm
X1 =
+ Xc
(138b)
(Em[epsilon]m)
2.08-214