Page 464 - Design of Reinforced Masonry Structures

7.26 CHAPTER SEVEN

Calculate deflections of piers 2 and 3 assuming each as fixed-ended.

−4
∆ = (1.184) (10 ) in. (calculated for Method A)
2
−4
∆ = (5.738) (10 ) in. (calculated for Method A)
3
Calculate the deflection of combined Pier 2-3:

∆ = 1 = 1 = (. 9 8418 )(10 −4 )in.
+
23 1 + 1 1 + 1
∆ 2 ∆ 3 (. )( 4 − ( . )( 4 − )
5 738 10 )
1 184 10 )
Calculate the net deflection of the wall.
−5
∆ = ∆ gross − ∆ strip + ∆ piers = (12.6707 − 6.1155 + 9.8148) (10 ) in.
net
−5
= (16.3699) (10 ) in.
R = 1 = 1 = 6109 kips/in.
∆ net (. )(
wall −5
16 3699 10 )
The rigidity of the wall is 6109 kips/in.
3. Method C: Calculate the rigidity of Pier 1 assuming it as a cantilever.
h 8
= = 0 182
.
d 44
3
⎛
h ⎞
h ⎞
∆ = 1 ⎡ ⎢ 4 ⎛ ⎜ ⎟ + ⎜ ⎟ ⎥ ⎤ = 1 [( . 3 + 3 0 182)]
4 0 182)
( .
3
1 ⎝ d ⎠ ⎝ d ⎠
m ⎣
Et ⎦ ⎦ ( 1800 7 625)
)( .
5 −
= 415338 10( )in.
.
p
,
R = 1 = 1 = 24 074 kips/in.
1
∆ 1 (. ) ( 5 −
4 1538 10 )
Calculate the rigidities of piers 2 and 3, assuming each one as fixed-ended. These
were calculated for Method A. Thus,
R = 8446 kips/in.
2
R = 1743 kips/in.
3
Calculate the rigidity of Pier 2-3 combined. Piers 2 and 3 are in parallel. Therefore,
the rigidity of Pier 2-3 is taken as the sum of their individual rigidities.
R 2+3 = R + R = 8446 + 1743 = 10,189 kips/in.
2
3
Pier 1 and Pier 2-3 (combined) are in series. Therefore, the reciprocal of the
rigidity of Pier 1-2-3 equals the sum of the reciprocals of rigidities of Pier 1 and
Pier 2-3. Thus,