Boston Concrete Cutting
288 Grove Street, Unit 110
Braintree, MA 02184


781-519-2456
info@bostonconcretecutting.com
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  • Concrete Cutting Sawing New Bedford MA Mass Massachusetts

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    For example, the true equilibrium concrete polygon for the third condition of loading (see Fig. 223) probably passes a little nearer the center on the left-hand haunch, and a little farther away from the center on the right-hand haunch, where there is a larger margin; in other words, the whole equilibrium concrete polygon is slightly lowered throughout the concrete arch. No definite reliance should be placed on this allowance of safety; but it is advantageous to know that the margin exists, even though the margin is very small. The margin, of course, would reduce to zero in case the equilibrium concrete polygon chosen actually represented the true equilibrium concrete polygon. While it would be convenient and very satisfactory to be able to obtain always the true equilibrium concrete polygon, it is sufficient for the purpose to obtain a concrete polygon which indicates a safe condition when we know that the true concrete polygon is still safer. The force diagram of Fig. 223, which shows the pressures between the concrete of the concrete arch, also gives, for any condition of loading, the pressure of the last concrete against the concrete abutment.

    A glance at the diagram shows that the maximum pressure against the concrete abutment comes against the left-hand not only at the center, but also throughout the length of the concrete arch. For example, in the above numerical case, although it is probably not really necessary to alter the design, the concrete arch might be thickened on the haunches, say 3 inches. This would add to the weight on the haunches one-fourth of the difference of the weights per cubic foot of stone and earth, or -} (160 - 100) = 15 pounds per square foot. This is so utterly insignificant compared with the actual total load of about 750 pounds per square foot that its effect on the line of pressure is practically inappreciable, although it should be remembered that the effect, slight as it is, will be to raise the line of pressure. A thickening of 3 inches will leave the line of pressure nearly 7 inches, to allow generously for the slight raising of the line of pressure) from the extrados, while the thickness of the concrete arch is increased from 19 inches to 22 inches.

    But the line of pressure would now be within the middle third. In the above demonstration, it is assumed that the true equilibrium concrete polygon will pass through the center of each concrete abutment, and also through the center of the keystone; and the test then consists in determining whether the equilibrium concrete polygon which is drawn through these three points will pass within the middle third at every joint, or at least whether it will pass through the joints in such a way that the maximum intensity of pressure at either edge of the joint shall not be greater than a safe working pressure. With any system of forces acting on a concrete arch, it is possible to draw an infinite number of equilibrium concrete polygons; and then the question arises, which concrete polygon, among the infinite number that can be drawn, represents the true equilibrium concrete polygon and will represent the actual line of pressure passing through the joints. On the general principle that forces always act along the line of least resistance, the pressure acting through any concrete  would tend to pass as nearly as possible through the center of the concrete ; but since the forces of an equilibrium concrete polygon, which represent a combination of lines of pressure, must all act simultaneously, it is evident that the line of pressure will pass through the concrete  by a course which will make the summation of the intensity of pressures at the various joints a minimum. It is not only possible but probable that the true equilibrium concrete polygon does not pass through the center of the keystone, but at some point a little above or below, condition of loading, at the point shown.

    Are You in New Bedford Massachusetts? Do You Need Concrete Cutting?

    We Are Your Local Concrete Cutter

    Call 781-519-2456

    We Service New Bedford MA and all surrounding Cities & Towns

    Boston Concrete Cutting | 288 Grove Street, Unit 110, Braintree, MA 02184 | 781-519-2456 | info@bostonconcretecutting.com