Page 473 - Design of Reinforced Masonry Structures

SHEAR WALLS 7.35

TABLE E7.7 Relative Rigidities of Piers
Pier h(ft) D(ft) h/d R r Comments
1 6 36 0.167 19.248 Cantilever
2 10 8 1.25 1.753 Fixed
3 6 6.67 0.9 2.916 Fixed
4 6 5.333 1.125 2.084 Fixed
5 4 20 0.2 16.447 Fixed

Piers 3 and 4 are in parallel. Their combined relative rigidity is equal to the sum
of the relative rigidities of individual piers. Thus,

R 3+4 = R + R = 2.916 + 2.084 = 5.0
3
4
Piers 3-4 and 5 are in series. Therefore, the relative rigidity is given by the sum
of the reciprocals:
3 831
R ++ = 1 = .
34 5
.
0 261
1 1 1 1 1
= + = + = .
0 261
R 34 5 R 34 R 5 50 . 16 447
.
+
++
Piers 2 and 3-4-5 are in parallel. Therefore, their combined relative rigidity is
given by the sum of their relative rigidities:
R 2+3+4+5 = R +R 3+4+5 = 1.753 + 3.831 = 5.584
2
Piers 1 and 2-3-4-5 are in series. Therefore, their combined relative rigidity is
given by
1 1 1
= +
R ++ + + R R + + +
1 234 5 1 234 5
= 1 + 1 = 0.2231
19 248 5 584
.
.

R = 1 = .
433
wall
.
0 231
The relative rigidity of the solid wall can be calculated.
⎛ ⎝ h ⎞ solid = 16 = 0 444.
d ⎠
36
R solid = 6.021 – (6.021-5.833)(0.4) = 5.946 (by interpolation from Table A.26)
The relative rigidity of the perforated wall is
⎛ 433 ⎞
.
( 100) ≈ 72 8%of relativerigiditythhesolidwall
.
⎝ 5 946 ⎠
.
This is the same as the result obtained in Example 7.6.