Civil Engineering Reference
In-Depth Information
Example 4.1 presents the calculation of factored loads for a reinforced concrete col-
umn using the ACI load combinations. The largest value obtained is referred to as the criti-
cal or governing load combination and is the value to be used in design.
Notice that the
values of the wind and seismic loads can be different depending on the direction of those
forces, and it may be possible for the sign of those loads to be different (that is, compres-
sion or tension).
This is the situation assumed to exist in the column of this example. These
rather tedious calculations can be easily handled with the enclosed computer program.
EXAMPLE 4.1
The axial loads for a building column have been estimated with the following results:
D
150k,
live load from roof
L
r
60k, live loads from floors
L
300k, compression wind
W
70k, tensile
wind W
60k, seismic compression load
50k, and tensile seismic load
40k. Determine the
critical design load using the ACI load combinations.
SOLUTION
(9-1)
(9-2)
(9-3)(a)
(b)
(c)
(9-4)(a)
(b)
(9-5)(a)
(b)
(9-6)(a)
U
(1.4)(150
0)
210k
U
(1.2)(150
0
0)
(1.6)(300
0)
(0.5)(60)
690k
U
(1.2)(150)
(1.6)(60)
(1.0)(300)
576k
U
(1.2)(150)
(1.6)(60)
(0.8)(70)
332k
U
(1.2)(150)
(1.6)(60)
(0.8)(
60)
228k
U
(1.2)(150)
(1.6)(70)
(1.0)(300)
(0.5)(60)
622k
U
(1.2)(150)
(1.6)(
60)
(1.0)(300)
(0.5)(60)
414k
U
(1.2)(150)
(1.0)(50)
(1.0)(300)
(0.2)(0)
530k
U
(1.2)(150)
(1.0)(
40)
(1.0)(300)
(0.2)(0)
440k
U
(0.9)(150)
(1.6)(70)
(1.6)(0)
247k
U
(0.9)(150)
(1.6)(
60)
(1.6)(0)
39k
(9-7)(a)
(b)
U
(0.9)(150)
(1.0)(50)
(1.6)(0)
185k
U
(0.9)(150)
(1.0)(
40)
(1.6)(0)
95k
Answer:
Largest value
690k. Notice that overturning is not a problem.
For most of the example problems presented in this textbook, in the interest of reduc-
ing the number of computations, only dead and live loads are specified. As a result, the
only load factor combination usually applied herein is the one presented by ACI Equation
9-2. Occasionally, when the dead load is quite large compared to the live load, it is also
necessary to consider Equation 9-1.
4.2
DESIGN OF RECTANGULAR BEAMS
Before the design of an actual beam is attempted, several miscellaneous topics need to be
discussed. These include the following:
1.
Beam proportions.
Unless architectural or other requirements dictate the propor-
tions of reinforced concrete beams, the most economical beam sections are usually ob-
tained for shorter beams (up to 20 or 25 ft in length), when the ratio of
d
to
b
is in the
