Page 455 - Design of Reinforced Masonry Structures

SHEAR WALLS 7.17

Alternatively, we can determine the relative rigidity of a fixed-ended shear wall
from Eq. (7.16) if its rigidity is known a priori:
R 9418
R = f = = 0 686.
r )
Et (1800 7 625(. )
m
For a shear wall with an h/d ratio of 0.4545, the relative rigidity is 0.686.
Commentary: The relative rigidity of a fixed-ended shear wall can also be determined
from Table A.27. For an h/d ratio of 0.4545, the value obtained from Table A.27 is
6.86 (by interpolation). As explained earlier, this value represents 10 times the actual
value of relative rigidity, so that the relative rigidity is 0.686.

7.4.4 A Comparison of Flexural and Shear Deflections in Shear Walls
The forgoing discussion shows that the deflection of a shear due to lateral loads consists
of two components: deflection due to flexure and deflection due to shear. A perusal of
Eq. (7.7) and (7.13) shows that for walls with large aspect ratios, the flexural component of
the total deflection will predominate, whereas for squat walls (i.e., walls with small aspect
ratios), the shear component of the total deflection will predominate. For very squat walls,
say, with aspect ratio ≤ 0.25, the flexural deflection component is very small, roughly
8 percent and 2 percent, respectively, for cantilever and fixed-ended walls. Relative rigidities
of such walls can be determined with reasonable accuracy based solely on their shear rigid-
ity. For walls with aspect ratios in the range of 0.25 to 4, both shear and flexural deflection
components contribute significantly to total deflection, and so both should be determined.
Relative contribution of shear deflection as a fraction of total component can be determined
from equations derived earlier. Dividing Eq. (7.2) by Eq. (7.3) and simplifying yields
Cantilever walls:
⎡ 1 ⎤
∆ shear = ⎢ ⎥ ∆ total (7.19)
.
⎣ 1 333(hd 2 + ⎦ 1
/ )
Similarly, dividing Eq. (7.2) by Eq. (7.13) and simplifying yields
Fixed-ended walls:

⎡ 1 ⎤
∆ = ∆ (7.20)
shear ⎢ (hd 2 ⎥ total
⎣ 0 333. / ) + ⎦ 1

Values of shear deflection component as a fraction of total deflection for cantilever and
fixed-ended walls [determined, respectively, from Eqs. (7.19) and (7.20)] for various aspect
ratios are shown in Table 7.1. It is noted that relationships given by Eqs. (7.19) and (7.20)
are valid for rectangular walls with lateral loads applied at the top of the walls. For other
load configurations and end conditions, these relationships would be different.

7.5 RIGIDITY OF A SHEAR WALL WITH OPENINGS

It was pointed out earlier that openings are often provided in shear walls for functional pur-
poses, for example, for providing doors and windows. Walls with openings are sometimes
referred to as perforated walls. The presence of an opening in a wall increases its deflection