By drawing a portion of the adjoining arch, we find that its extrados intersects the extrados of the arch considered at a point about 7 feet 6 inches above the pier. By drawing a line from this point toward the center for joints, which is about midway between the center for the extrados and the center for the intrados, we have the line for the joint which is virtually the skewback joint and the abut ment of the arch.
The center of the pier is precisely 17 feet from the center of the arch. We shall assume that the arch is overlaid with a filling of earth or cinders which is 18 inches thick at the crown, and that it is level. Drawing a horizontal line to represent the top of this earth filling, we may divide this line into sections which are 2 feet wide, commencing at the vertical line through the center of the pier. Ex tending this similarly to the other side of the arch, we have eight sections of loading on each side of the keystone section. Drawing lines from the points where these verticals between the sections inter sect the extnidos, toward the center for joints, previously determined, we have the various joints of the voussoirs. Assuming, as in the previous numerical problem that the cinder fill weighs 100 pounds per cubic foot, and that the stone weighs 160 pounds per cubic foot, we determine the reduced load line for the top of the earth fill over tile entire arch.
We shall assume that the arch carries a railroad track and a heavy class of traffic. The weight of roadbed and track may be computed as follows: The ties are to be S feet long; the weight of This is the equivalent of 0.58 foot depth of stone, and we therefore add this uniform depth to the reduced load line for the earth.
A 50-ton freight-car, fully loaded, will weigh 134,000 pounds; with a length between bumpers of 37 feet, this will exert a pressure of about 450 pounds per square foot on a strip S feet wide. This is equiv alent to 2.8 feet of masonry. We shall therefore consider this as a requirement for uniform loading over the whole arch.
It would be more precise to consider the actual wheel loads for the end trucks of two such cars which are immediately following each other; but since the effect of this would be even less than that of the calculation for a locomotive, which will be given later, and since the deep cushion of earth filling will largely obliterate the effect of con centrated loads, the method of considering the loading as uniformly distributed will be used. We therefore add the uniform ordinate
equal to 2.8 feet over the whole arch. We shall call this the first condition of loading.
We shall assume for the concentrated loading, a consolidation locomotive with 40,000 pounds on each of the four driving axles, spaced 5 feet apart. This means a wheel base 15 feet long; and we shall assume that this extends over voussoirs 1 to S inclusive, while the loading of 450 pounds per square foot is on the other portion of the arch. A weight of 40,000 pounds on an axle, which is supposed to be distributed over an area 5 feet long and S feet wide, gives a pressure of 1,000 pounds per square foot, or it would add an ordinate of 6.33 feet of stone; these ordinates are added above the load line repre senting the load of •the roadbed and track. We shall call this the second condition of loading.
The load for each voussoir is determined by the method given in Article 417. The direction of the pressure on the voussoir is determined by drawing a line toward the extrados center from the intersection of the vertical through the trapezoid of loading with the extrados. The length of that vertical is laid off below that point of intersection; then a horizontal line drawn from the lower end-of the vertical intersects the line of force at a point which measures the amount of that pressure on the voussoir. The area of the voussoir is determined as described in Article 417; and the resultant of the loading and the weight of the voussoir is obtained. This is indicated as force No. 1 in Fig. 226. In this case, it includes the locomotive loading on the left-hand side of the arch. The forces acting on voussoirs Nos. 2, 3, 4, 5, 6, 7, and S are similarly determined. The forces on voussoirs Nos. 9 to 17 inclusive, on the basis of the uniformly distributed load equal to 450 pounds per square foot, are also similarly determined. The loads on voussoirs Nos. 10 to 17 inclusive will be considered to measure the loads on voussoirs Nos. S to 1 inclusive, for the first condition of loading. The loading with the locomotive over voussoirs Nos. 1 to S, and cars over voussoirs Nos. 9 to 17, con stitutes the second condition of loading.