Page 215 - Civil Engineering Formulas

150 CHAPTER FIVE

where A bearing area of anchor plate, and A b maximum area of portion
b
of anchorage surface geometrically similar to and concentric with area of
anchor plate.
A more refined analysis may be applied in the design of the end-anchorage
regions of prestressed members to develop the ultimate strength of the tendons.
should be taken as 0.90 for the concrete.

CONCRETE GRAVITY RETAINING WALLS

Forces acting on gravity walls include the weight of the wall, weight of the earth
on the sloping back and heel, lateral earth pressure, and resultant soil pressure on
the base. It is advisable to include a force at the top of the wall to account for
frost action, perhaps 700 lb/linear ft (1042 kg/m). A wall, consequently, may fail
by overturning or sliding, overstressing of the concrete or settlement due to
crushing of the soil.
Design usually starts with selection of a trial shape and dimensions, and this
configuration is checked for stability. For convenience, when the wall is of con-
stant height, a 1-ft (0.305-m) long section may be analyzed. Moments are taken
about the toe. The sum of the righting moments should be at least 1.5 times the
sum of the overturning moments. To prevent sliding,

R v 1.5P h (5.118)
where coefficient of sliding friction
R total downward force on soil, lb (N)
v
P horizontal component of earth thrust, lb (N)
h
Next, the location of the vertical resultant R should be found at various sec-
v
tions of the wall by taking moments about the toe and dividing the sum by R .
v
The resultant should act within the middle third of each section if there is to be
no tension in the wall.
Finally, the pressure exerted by the base on the soil should be computed to
ensure that the allowable pressure is not exceeded. When the resultant is with-
2
in the middle third, the pressures, lb/ft (Pa), under the ends of the base are
given by
Mc 6e
R v R v
p 1 (5.119)
A I A L
2
2
where A area of base, ft (m )
L width of base, ft (m)
e distance, parallel to L, from centroid of base to R , ft (m)
v
Figure 5.4(b) shows the pressure distribution under a 1-ft (0.305-m) strip of
wall for e L/2 a, where a is the distance of R from the toe. When R is
v
v
exactly L/3 from the toe, the pressure at the heel becomes zero. When R v