CIVIL ENGINEERING FORMULAS

220 CHAPTER NINE

where Awweb area, in^2 (mm^2 )
Afarea of compression flange, in^2 (mm^2 )
0.6Fyw/Fb1.0
Fywminimum specified yield stress, ksi, (MPa), of web steel

In a hybrid girder, where the flange steel has a higher yield strength than the
web, the preceding equation protects against excessive yielding of the lower
strength web in the vicinity of the higher strength flanges. For nonhybrid gird-
ers,Re1.0.

LOAD DISTRIBUTION TO BENTS AND SHEAR WALLS

Provision should be made for all structures to transmit lateralloads, such as
those from wind, earthquakes, and traction and braking of vehicles, to foun-
dations and their supports that have high resistance to displacement. For this
purpose, various types of bracing may be used, including struts, tension ties,
diaphragms, trusses, and shear walls.

Deflections of Bents and Shear Walls

Horizontal deflections in the planes of bents and shear walls can be computed
on the assumption that they act as cantilevers. Deflections of braced bents can
be calculated by the dummy-unit-load method or a matrix method. Deflections
of rigid frames can be computed by adding the drifts of the stories, as deter-
mined by moment distribution or a matrix method.
For a shear wall (Fig. 9.3), the deflection in its plane induced by a load in its
plane is the sum of the flexural deflection as a cantilever and the deflection due
to shear. Thus, for a wall with solid rectangular cross section, the deflection at
the top due to uniform load is

(9.49)

wherewuniform lateral load
Hheight of the wall
Emodulus of elasticity of the wall material
twall thickness
Llength of wall

For a shear wall with a concentrated load Pat the top, the deflection at the top is

(9.50)

If the wall is fixed against rotation at the top, however, the deflection is

f P (9.51)

Et

H

L

3

 3

H

L

c

4 P

Et

H

L

3

0.75

H

L



1.5wH

Et 

H

L

3



H

L