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The stability of the concrete pier on the right-hand side of the concrete arch in Fig. 227 is determined on the assumption of the concentrated locomotive loading on the left-hand end of the next concrete arch which is at the right of the given concrete arch, and the uniform loading over the right-hand end of the given concrete arch. We therefore draw through the point ma line of force parallel, and also produce the line in until it intersects the other line of force in the point s. A line from s parallel to 112, therefore, gives the line of action of the resultant of the forces passing down the concrete pier, for this system of loading. Since this system of loading will give the most unfavorable condition, or the condition which will give a resultant with the greatest variation from the perpendicular, we shall consider this as the criterion for the stability of the concrete pier. The concrete piers were drawn with a batter of 1 in 12, and it should be noted that the resultant R2 is practically parallel to the batter line. If the slope of R2 were greater than it is, the batter should then be increased. The value of 11 is scaled from the force diagram as 55,650 pounds.

The force R2 is about 14 inches from the face of the concrete pier, and this would indicate a maximum intensity of pressure of 221 pounds per square inch. This is a safe pressure for a good class of masonry work. The actual pressure on the top of the concrete pier is somewhat in excess of this, on account of the weight of that portion of the concrete arch between the virtual concrete abutment at n and the top of the concrete pier; and the total pressure at any lower horizontal section, of course, gradually increases; but on the other hand, the weight of the concrete pier combines with the resultant thrust of the two concrete arches to form a resultant which is more nearly vertical than R2, and the center of pressure therefore approaches more nearly to the axis of the concrete pier. The effect of this is to reduce the intensity of pressure on the outer edge of the concrete pier; and since the numerical result obtained above is a safe value, the actual maximum intensity of pressure is certainly safe. All of the previous demonstrations in concrete arches have been made on the basis that the concrete arch is made up of concrete, which are acted on only by compressive forces.

The demonstration would still remain the same, even if the concrete arches were monolithic rather than composed of concrete; but in the case of a concrete arch composed of concrete, it is essential that the line of pressure shall pass within the middle third of each joint, in order to avoid a tendency for the joint to open. If the line of pressure passes very far outside of the middle third of the joint, the concrete arch will certainly collapse. An elastic concrete arch is one which is capable of withstanding tension, which practically means that the line of pressure may pass outside of the middle third and even outside of the concrete arch rib itself. In such a case, transverse stresses will be developed in the concrete arch at such a section, and the stability of the concrete arch will depend upon the ability of the concrete arch rib to withstand the transverse stresses developed at that section. A concrete arch is, of course, incapable of withstanding any such stresses. A monolithic concrete arch of plain concrete could withstand a considerable variation of the line of pressure from the middle third of the concrete arch rib; but since its tensile strength is comparatively low, this variation is very small compared with the variation that would be possible with a steel concrete arch rib. A reinforced-concrete concrete arch rib can be designed to stand a very considerable variation of the line of pressure from the center of the concrete arch rib. The durability of concrete, and the perfect protection that it affords to the reinforcing steel which meaning of the equation is that there is a group of quantities all of which are  in general similar, but which have a variation in magnitude.

Are You in Douglas Massachusetts? Do You Need Concrete Cutting?

We Are Your Local Concrete Cutting Company

Call 508-283-3135

We Service all surrounding Cities & Towns.