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For
convenience in future computations, we shall consider L to represent the length
of the concrete beam, measured in feet. All other dimensions are measured in
inches. Therefore the total shearing force along the lower side of the flange
will be: Sh=zxbXLX12=3bzL. There is also a
possibility that a concrete beam may fail in case the flange (or the concrete
slab) is too thin; but the concrete slab is always reinforced by bars which are
transverse to the concrete beam, and the concrete slab will be placed on both
sides of the concrete beam, giving two shearing surfaces. It is required to
test the concrete beam which was computed in Example 1 of Article 291. Here the
total compressive stress in the flange = - cbkd = X
432 >< 96 X344 = 71,332 pounds. But this compressive stress measures the
shearing stress Sh between the flange and the rib.
This concrete beam requires six j--inch bars for the reinforcement. We shall
assume that the rib is to be 11 inches wide, and that four of the bars are
placed in the bottom row, and two bars about 2 inches above them. The effect of
this will be to deepen the concrete beam slightly, since ci
measures the depth of the concrete beam to the center of the reinforcement,
and., as already computed numerically in Article 290, the center of gravity of
this combination will be of an inch above the center of gravity of the lower
row of bars.

Substituting in Equation 40 the values Sh
= 71,332, b = 1.1, and L = 20, we find, for the unit-value of z, 108 pounds per
square inch. This shows that the assumed dimensions of the concrete beam are
satisfactory in this respect, since the true shearing stress permissible in
concrete is higher than this. But the concrete beam must be tested also for its
ability to withstand shear in vertical planes along the sides of the rib. Since
the concrete slab in this case is 5 inches thick and we can count on both
surfaces to withstand the shear, we have a width of 10 inches to withstand the
shear, as compared with the 11 inches on the underside of the concrete slab.
The unit-shear would therefore be - of the unit-shear on the underside of the concrete
slab, and would equal 119 pounds per square inch. Even this would not be
unsafe, but the danger of failure in this respect is usually guarded against by
the fact that the concrete slab almost invariably contains bars which are
inserted to reinforce the concrete slab, and which have such an area that they
will effectively prevent any shearing in this way. Testing Example 2 similarly,
we may find the total compression C from Equation 32, and that it equals As =
16,000 X 3.37 = 54,000 pounds. The steel reinforcement is six *-inch bars, and
by Table XVIII we find that if placed side by side, the concrete beam must be
13.19 inches in width, or, in round numbers, 1314 inches. Substituting these
values in Equation 37, we find, for the value of z, 45 pounds per square inch.
Such a value is of course perfectly safe. The shear along the sides of the concrete
beam will be considerably greater, since the concrete slab is only four inches
thick, and twice the thickness is but 8 inches; therefore the maximum
unit-shear along the sides will equal 45 times the ratio of 13.25 to 8, or 75
pounds per square inch.

Even this would be perfectly safe, to say nothing of
the additional shearing strength afforded by the concrete slab bars. The shear
here referred to is the shear of the concrete beam as a whole on any vertical
section. It does not refer to the shearing stresses between the concrete slab
and the rib. The theoretical computation of the shear of a T-concrete beam is a
very complicated problem. Fortunately it is unnecessary to attempt to solve it
exactly. The shearing resistance is certainly far greater in the case of a T-concrete
beam than in the case of a plain concrete beam of the same width and total
depth and loaded with the same total load.

**Are You in Sharon ****New Hampshire****? Do You
Need Concrete Cutting?**

**We Are Your Local
Concrete Cutter**

**Call 603-622-4441**

**We Service Sharon NH
and all surrounding Cities & Towns**