Page 193 - Civil Engineering Formulas

CONCRETE FORMULAS 129

positive and negative moment should be proportioned for crack control so that
specific limits are satisfied by
3
d
z f s2 c A (5.35)
where f calculated stress, ksi (MPa), in reinforcement at service loads
s
d thickness of concrete cover, in (mm), measured from extreme ten-
c
sion surface to center of bar closest to that surface
2
2
A effective tension area of concrete, in (mm ) per bar. This area should
be taken as that surrounding main tension reinforcement, having the
same centroid as that reinforcement, multiplied by the ratio of the area
of the largest bar used to the total area of tension reinforcement
These limits are z 175 kip/in (30.6 kN/mm) for interior exposures and z
145 kip/in (25.3 kN/mm) for exterior exposures. These correspond to limiting
crack widths of 0.016 to 0.013 in (0.406 to 0.33 mm), respectively, at the
extreme tension edge under service loads. In the equation for z, f should be
s
computed by dividing the bending moment by the product of the steel area and
the internal moment arm, but f may be taken as 60 percent of the steel yield
s
strength without computation.
REQUIRED STRENGTH

For combinations of loads, the ACI Code requires that a structure and its mem-
bers should have the following ultimate strengths (capacities to resist design
loads and their related internal moments and forces):
With wind and earthquake loads not applied,
U 1.4D 1.7L (5.36)

where D effect of basic load consisting of dead load plus volume change
(shrinkage, temperature) and L effect of live load plus impact.
When wind loads are applied, the largest of the preceeding equation and the
two following equations determine the required strength:

U 0.75(1.4D 1.7L 1.7W) (5.37)
U 0.9D 1.3W (5.38)

where W effect of wind load.
If the structure can be subjected to earthquake forces E, substitute 1.1E for
W in the preceding equation.
Where the effects of differential settlement, creep, shrinkage, or temperature
change may be critical to the structure, they should be included with the dead
load D, and the strength should be at least equal to
U 0.75(1.4D 1.7L) 1.4(D T) (5.39)

where T cumulative effects of temperature, creep, shrinkage, and differential
settlement.