Civil Engineering Reference
In-Depth Information
Figure 2.9
Computing Stresses
f
c
(12)(110,000)(9.32)
10,887
1130 psi
(8)
(12)(110,000)(13.68)
10,887
f
s
13,269 psi
Example 2.5 illustrates the analysis of a doubly reinforced concrete beam—that is,
one that has compression steel as well as tensile steel. Compression steel is generally
thought to be uneconomical, but occasionally its use is quite advantageous.
Compression steel will permit the use of appreciably smaller beams than those that
make use of tensile steel only. Reduced sizes can be very important where space or archi-
tectural requirements limit the sizes of beams. Compression steel is quite helpful in reduc-
ing long-term deflections, and such steel is useful for positioning stirrups or shear
reinforcing, a subject to be discussed in Chapter 8. A detailed discussion of doubly rein-
forced beams is presented in Chapter 5.
The creep or plastic flow of concrete was described in Section 1.11. Should the com-
pression side of a beam be reinforced, the long-term stresses in that reinforcing will be
greatly affected by the creep in the concrete. As time goes by, the compression concrete
will compact more tightly, leaving the reinforcing bars (which themselves have negligible
creep) to carry more and more of the load.
As a consequence of this creep in the concrete, the stresses in the compression bars com-
puted by the transformed-area method are assumed to double as time goes by. In Example 2.5
the transformed area of the compression bars is assumed to equal 2
n
times their area
On the subject of “hair splitting,” it will be noted in the example that the compression
steel area is really multiplied by 2
n
s
.
A
1. The transformed area of the compression side
equals the gross compression area of the concrete plus minus the area of the holes in
the concrete which theoretically should not have been included in the concrete part.
This equals the compression concrete area plus
s
2
nA
s
),
(1
A
s
.
1 is used in
the moment of inertia calculations. The stresses in the compression bars are determined
(2
n
1)
A
Similarly, 2
n
