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Although
such concrete is theoretically subject to tension, and does actually contribute
its share of the tension when the stresses in the concrete beam are small, the
proportion of the necessary tension which the concrete can furnish when the concrete
beam is heavily loaded, is so very small that it is usually ignored, especially
since such a policy is on the side of safety, and also since it greatly
simplifies the theoretical calculations and yet makes very little difference in
the final result. We may therefore consider that in a unit-section of the
concrete beam, as in Fig. 92, the concrete above the neutral axis is subject to
compression, and that the tension is furnished entirely by the steel. In
computing the transverse stresses in a wooden concrete beam or steel I-concrete
beam, it is assumed that the modulus of elasticity is uniform for all stresses
within the elastic limit. Experimental tests have shown this to be so nearly
true that it is accepted as a mechanical law. This means that if a force of 1,000
pounds is required to stretch a bar .001 of an inch, it will require 2,000
pounds to stretch it .002 of an inch. Similar tests have been made with
concrete, to determine the law of its elasticity. Unfortunately, concrete is
not as uniform in its behavior as steel. The results of tests are somewhat
contradictory. Many concrete construction engineers have argued that the
elasticity is so nearly uniform that it may be considered to be such within the
limits of practical use. But all experimenters who have tested concrete by
measuring the proportional compression produced by various pressures agree that
the additional shortening produced by an additional pressure, say of 100 pounds
per square inch, is greater at higher pressures than at low pressures. A test
of this sort may be made substantially as follows: A square or circular column
of concrete at least one foot long is placed in a testing machine. A very
delicate micrometer mechanism is fastened to the concrete by pointed screws of
hardened steel. These points are originally at a known distance apart—say 8
inches. When the concrete is compressed, the distance between these points will
be slightly less. A very delicate mechanism will permit this distance to be
measured as closely as the ten-thousandth part of an inch, or to about of the length. Suppose that the various
pressures per square inch, and the proportionate compressions, are as given in
the following tabular form: We may plot these pressures and compressions as in
Fig. 93, using any convenient scale for each. For example, for a pressure of 800
pounds per square inch, we select the vertical line which is at the horizontal
distance from the origin according to the scale adopted. Scaling off on this
vertical line the ordinate .00045, according to the scale adopted for
compressions, we have the position of one point of the curve. The other points
are obtained similarly. Although the points thus obtained from the testing of a
single concrete blocks of concrete would not he considered sufficient to establish
the law of the elasticity of concrete in compression, a study of the curves
which may be drawn through the series of points obtained for each of a large
number of concrete blocks, shows that these curves will average very closely to
parabolas that are tangent to the initial modulus of elasticity, which is here
represented in the diagram by a straight line running diagonally across the
figure. It is generally considered that the axis of the parabola will be a
horizontal line when the curve is plotted according to this method. The
position of the vertex of the parabola cannot be considered as definitely
settled. Professor Talbot has computed the curve as if the vertex were at the
point of the ultimate compression of the concrete, although he conceded that
the vertex might be in an imaginary position corresponding to a compression in
the concrete higher than that which the concrete could really endure.
Are You in Mont Vernon New Hampshire? Do You
Need Concrete Cutting?
We Are Your Local
Concrete Cutter
Call 603-622-4441
We Service Mont
Vernon NH and all surrounding Cities & Towns