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Although
this is probably a safe shearing stress, many engineers would consider it
advisable to use special V-shaped stirrups (see a, Fig. 108) to strengthen the concrete
beam against such stress. If the angle of these stirrups with the vertical is,
say, 45°, then the stress in the bars on each side will be .707 of the total
load, assuming that these bars were to take all the stress. This would mean
that these bars would have a stress of about 26,406 pounds, and at 16,000
pounds per square inch would require a total area of 1.65 square inches. Three
'-inch bars would therefore more than provide the necessary area, even assuming
that these stirrups took the entire load, and disregarding the stirrups such as
would ordinarily be placed in the concrete beam,, and also disregarding the
shearing strength of the concrete. If, therefore, these stirrups are made of
1-inch bars instead of 2-inch bars, the shearing stresses in the concrete due
to the concrete beam will be amply provided for.
A complete detailed drawing will
show all of the bars required for a panel between four of these concrete columns.
The student should study this drawing (see Fig. 109) in connection with the
foregoing demonstrations of the dimensions of the bars and of the concrete. When
a definite load, such as a weight carried by a concrete column, is to be
supported on subsoil whose bearing power has been estimated at some definite
figure, the required area of the concrete footing becomes a perfectly definite
quantity, regardless of the method of construction of the concrete footing. But
with the area of the concrete footing once determined, it is possible to effect
considerable economy in the construction of the concrete footing, by the use of
reinforced concrete. An ordinary concrete footing of masonry is usually made in
a pyramidal form, although the sides will be stepped off instead of being made
sloping. It may be approximately stated that the depth of the concrete footing
below the base of the concrete column, when ordinary masonry is used, must be
practically equal to the width of the concrete footing. The offsets in the
masonry cannot ordinarily be made any greater than the heights of the various
steps. Such a plan requires an excessive amount of masonry.
A concrete footing
of reinforced concrete consists essentially of a concrete slab, which is placed
no deeper in the ground than is necessary to obtain a proper pressure from the
subsoil. In the simplest case, the concrete column is placed in the middle of
the concrete footing, and thus acts as a concentrated load in the middle of the
plate (Fig. 110). The mechanics of such a problem are somewhat similar to those
of a concrete slab supported on four sides and carrying a concentrated load in
the center, with the very important exception, that the resistance, instead of
being applied merely at the edges of the concrete slab, is uniformly
distributed over the entire surface. Since the concrete column has a
considerable area, and the concrete slab merely overlaps the concrete column on
all sides, the common method is to consider the overlapping on each side to be
an inverted cantilever carrying a uniformly distributed load, which is in this
case an upward pressure evidently, occurs immediately below each vertical face
of the concrete column. At the extreme outer edge of the concrete slab the
moment is evidently zero, and the thickness of the concrete slab may therefore
be reduced considerably at the outer edge. The depth of the concrete slab, and
the amount of reinforcement, which is of course placed near the bottom, can be
determined according to the usual rules for obtaining a moment. This can best
be illustrated numerically. Assume that a load of 252,000 pounds is to be
carried by a concrete column, on a soil which consists of hard, firm gravel.
Such soil will ordinarily safely carry a load of 7,000 pounds per square foot.
Are You in Weare New
Hampshire? Do You Need Concrete Cutting?
We Are Your Local
Concrete Cutter
Call 603-622-4441
We Service Weare NH and all surrounding Cities & Towns
