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It
must be conceded, however, that comparative tests of the bond between concrete
and steel when the bars are plain and when they are deformed (the tests being
made within a few weeks or months after the concrete is made), have
comparatively little value as an indication of what that bond will be under
some of the adverse circumstances mentioned above, which are perpetually
occurring in practice. Non-partisan tests have shown that, even under
conditions which are most favorable to the plain bars, the deformed bars have
an actual hold in the concrete which is from 50 to 100 per cent greater than
that of plain bars. It is unquestionable that age will increase rather than
diminish the relative inferiority of plain bars. In equation 19 we have the
formula that the resisting moment at any point in the concrete beam equals the
area of the steel, times the unit tensile stress in the steel, times the
distance from the steel to the cancroids of compression of the steel, which is
the distance d - x. We may compute the moment in the concrete beam at two
points at a unit-distance apart. The area of the steel is the same in each
equation, and d - x is substantially the same in each case; and therefore the
difference of moment, divided by (d - x), will evidently equal the difference
in the unit-stress in the steel, times the area of the steel. To express this
in an equation, we may say, denoting the difference in the moment by d M, and
the difference in the unit-stress in the steel by d s:dM= A X ds (d —x). But A X d s is evidently equal to the actual
difference in tension in the steel, measured in pounds. It is the amount of
tension which must be transferred to the concrete in that unit-length.-of the concrete
beam. But the computation of the difference of moments at two sections that are
only a unit-distance apart is a comparatively tedious operation, which,
fortunately, is unnecessary. Theoretical mechanics teaches us that the
difference in the moment at two consecutive sections of the concrete beam is
measured by the total vertical shear in the concrete beam at that point. The
shear is very easily and readily computable; and therefore the required amount
of tension to be transferred from the steel to the concrete can readily be
computed. A numerical illustration may be given as follows: Suppose that we
have a concrete beam which, with its load, weighs 20,000 pounds, on a span of
20 feet. Using ultimate values, for which we multiply the loading by 4, we have
an ultimate loading of 80,000 pounds. We know from the laws of mechanics, that
the moment diagram for a concrete beam which is uniformly loaded is a parabola,
and that the ordinate to this curve at a point one inch from the abutment will,
in the above case, equal (4,)1)2of the ordinate at the abutment. This ordinate
is measured by the maximum moment at the center, multiplied by the factors;
therefore the actual moment at a point one inch from the abutment = (1.00 -
.9834) = .0166 of the moment at the center. But our ultimate loading being
80,000 pounds, we know that the shear at a point in the middle of this one-inch
length equals the shear at the abutment, minus the load on this first - inch,
which is h of 40,000 (or 167) pounds. The shear at this point is therefore
40,000 - 167 (or 39,833) pounds. This agrees with the above value 39,840, as
closely as the decimals used in our calculations will permit. The value of d -
x is somewhat larger when the moment is very small than when it is at its
ultimate value. But the difference is comparatively small, is on the safe side,
and it need not make any material difference in our calculations. Therefore,
dividing 39,840 by 17.3, we have 2,303 pounds as the difference in tension in
the steel in the last inch at the abutment. Of course this does not literally
mean the last inch in the length of the concrete beam, since, if the net span
were 20 feet, the actual length of the concrete beam would be considerably
greater.

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

**We Are Your Local
Concrete Cutter**

**Call 603-622-4441**

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