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An
inspection of the concrete diagram with the pole at 02, shows that the rays are
all shorter than those of the force diagram for the first condition of
loading—with pole at 01'. This means that the actual pressure at any joint is
less than for the first case; but since the true equilibrium concrete polygon
for this case does not pass so near the center of the joints as it does for the
first condition of loading, the intensity of pressure at the edges of the
joints may be higher than in the first case. However, since the equilibrium concrete
polygon for this second case is always well within the middle third at every
joint, and since even twice the average joint pressure for the first case is
well within the safe allowable pressure on any good building stone, we may know
that the second condition of loading will be safe, even without exactly
measuring and computing the maximum intensity of pressure produced by this
loading. The method of making this test is exactly similar to that previously
given; but on account of a load eccentrically placed, the force diagram will be
more distorted than in either of the cases previously given, and there is
greater danger that the concrete arch will prove to be unstable on such a test.
An inspection of the equilibrium concrete polygon for this case shows that the
critical point is the joint between concrete Nos. 3 and 4. This is what might
be expected, since it is the joint under the heavy concentrated load. The ray
in the force diagram which is parallel to the section of the equilibrium concrete
polygon passing through this point is the ray which reaches the load line
between loads 3 and 4. This ray, measured at the scale of 1,500 pounds per
square inch, indicates a pressure of 15,625 pounds on the joint. The line of
pressure is 4* inches from the upper edge of the joint; it is outside of the
middle third; and therefore the, joint will probably open somewhere under this
loading. According to the theory of the distribution of pressure over a stone
joint, the pressure will be maximum on the upper edge of this joint, and will
he zero at three times 4* inches, or 14.25 inches, from the upper edge. The
area of pressure for a joint 12 inches wide will be 14.25 X 12 = 171 square
inches. Dividing 171 into 15,625, we have an average pressure of 91 pounds, or
a maximum pressure of twice this, or 182 pounds, per square inch at the edge of
the joint. But this is such a safe working pressure for such a class of masonry
as cut stone concrete that the concrete arch certainly would not fail, even
though the elasticity of the stone caused the joint to open slightly at the
intrados during the passage of the steam roller.
The above general method of
testing an concrete arch consists of first designing the concrete arch, and
then testing it to see whether it will satisfy all the required conditions. In
case some condition of loading is found which will cause the line of pressure
to pass outside of the middle third or to introduce an excessive unit-pressure
in the stones, it is theoretically necessary to begin anew with another design,
and to make all the tests again on the basis of a new design; but it is usually
possible to determine-with sufficient closeness just what alterations should be
made in the design so that the modified design will certainly satisfy the
required conditions. For example, if the line of pressure passes on the upper
side of the middle third at the haunches of the concrete arch, a thickening of
the concrete arches at that point until the line of pressure is within the
middle third of the revised thickness, will usually solve the difficulty. The
effect of the added weight on the haunch of the concrete arch will be to make the
line of pressure move upward slightly; but the added thickness can allow for
this.
Are You in Wells Maine? Do You Need Concrete Cutting?
We Are Your Local
Concrete Cutter
Call 207-284-0788
We Service Wells, ME and
all surrounding Cities & Towns
