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The
discrepancy is due to the dropping of decimals during the computations. From Equation
33, we compute that x = 1.72; then (d - x) = 23.28. Substituting the value of
the moment and of the dimensions in the upper part of Equation 35, we compute c
to be 420 pounds per square inch. Similarly, making substitutions in the lower
part of Equation 35, using the more precise value of (ci
- x) for the lever-arm of the steel, we find s = 16,052 pounds per square inch.
The student should verify in detail all these computations. The total required
area of 5.08 square inches may be divided into; say, 8 round bars - inch in
diameter. These would have an area of 4.81 square inches. The discrepancy is
about five per cent. These bars, placed in two rows, would require that the concrete
beam should be at least 10.78 inches wide. We shall call it 11 inches. The
total depth of the concrete beam will be three inches greater than ci, OT 28 inches. This means 23 inches below the concrete
slab, and the area of concrete below the concrete slab is therefore 11 X 23 =
253 square inches, rather than 12 X 22 square inches, as assumed for trial. The
shearing stresses between the rib and concrete slab of the girder are of
special importance in this case.

The quantity 5h of Article 293 equals the
total compression in the concrete, which equals the total tension in the steel,
which equals, in this case, 16,052 X 5.08 = 81,544 pounds. This equals 3 bzl, in which b = 11, 1 = 16 (feet), and z is to be
determined: z = 81,544 -- (3 x 11 >< 16) 154 pounds per square inch. This
measures the maximum shearing stress under the concrete slab, and is almost
safe, even without the assistance furnished by the stirrups and the bars, which
would come up diagonally through the ends of the concrete beam (where this
maximum shear .occurs) nearly to the top of the concrete slab. The vertical planes
on each side of the rib have a combined width of 10 inches, and therefore the
unit-stress is >< 154 = 169 pounds per square inch. This is a case of
true shear, and a 1:2:4 concrete should stand such a stress with a large factor
of safety. But there are still other shearing stresses in these vertical
planes. Considering a strip of the concrete slab, say, one foot wide, which is
reinforced by concrete slab bars that are parallel to the girder, the
elasticity of such a strip (if disconnected from the girder) would cause it to
sag in the center. This must be prevented by the shearing strength of the
concrete in the vertical plane along each edge of the girder rib. On account of
the combined shearing stresses along these planes, it is usual to specify that
when girders are parallel with the concrete slab bars, bars shall be placed
across the girder and through the top of the concrete slab for the special
purpose of resisting these shearing stresses.

Some of the stresses are
indefinite, and therefore no precise rules can be computed for the amount of
the reinforcement. But since the amount required is evidently very small, no
great percentage of accuracy is important. A recent specification on this point
required--inch bars, 5 feet long, spaced 12 inches apart. The shear of the
girder, taken as a whole, should be computed as for simple concrete beams, as
already discussed in Article 295; and stirrups should be used, as described in
Article 279. Another special form of shear must be considered in this problem. Where
the concrete beams enter the girders, there is a tendency for the concrete
beams to tear their way out through the girder. The total load on the girder by
the two concrete beams on each side, is of course equal to the total load on
one concrete beam, and equals 37,350 pounds. Some of the reinforcing bars of
the concrete beam will be bent up diagonally so that they enter the girder near
its open end. We therefore have 2 X 22 > (11 = 484 square inches, the area
to be sheared out. Dividing this figure into 37,350 will give 77 pounds per
square inch.

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

**We Are Your Local
Concrete Cutter**

**Call 603-622-4441**

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