Building Design and Construction Handbook - Merritt - Ventech!

STRUCTURAL THEORY 5.105
Wall A: 6.6 � 0.7 � 7.3 kips
Wall B: 4.4 � 0.1 � 4.5 kips
Wall C: kips
5.12.3 Deflections of Bents or Shear Walls
When parallel bents or shear walls are connected by rigid diaphragms (Art. 5.12.1)
and horizontal loads are distributed to the vertical resisting elements in proportion
to their relative rigidities, the relative rigidity of the framing depends on the combined
horizontal deflections due to shear and flexure. For the dimensions of lateralforce-resisting
framing used in many high-rise buildings, however, deflections due
to flexure greatly exceed those due to shear. In such cases, only flexural rigidity
need be considered in determination of relative rigidity of the bents and shear walls
(Art. 5.12.5).
Horizontal deflections can be determined by treating the bents and shear walls
as cantilevers. Deflections of braced bents can be calculated by the dummy-unitload
method (Art. 5.10.4) or a matrix method (Art. 5.13.3). Deflections of rigid
frames can be obtained by summing the drifts of the stories, as determined by
moment distribution (Art. 5.11.9) or a matrix method. And deflections of shear
walls can be computed from formulas given in Art. 5.5.15, the dummy-unit-load
method, or a matrix method.
For a shear wall with a solid, rectangular cross section, the flexural deflection
at the top under uniform loading is given by the formula for a cantilever in Fig.
5.39:
4 wH
�c � (5.142)
8EI
where w � uniform lateral load
H � height of the wall
E � modulus of elasticity of the wall material
I � moment of inertia of wall cross section � tL3 /12
t � wall thickness
L � length of wall
The cantilever shear deflection under uniform loading may be computed from
2 0.6wH
�v � (5.143)
EA
where Ev � modulus of rigidity of wall cross section
� E/2(1 � �)
� � Poisson’s ratio for the wall material (0.25 for concrete and masonry)
A � cross-sectional area of the wall � tL
The total deflection then is
3
1.5wH H H
�c � �v � �� � � �
(5.144)
Et L L
For a cantilever wall subjected to a concentrated load P at the top, the flexural
deflection at the top is
v