We shall assume that the arch carries a filling of earth or cinders weighing 100 pounds per cubic foot, that the top of this filling is level, and that it has a thickness of one foot above the crown. ' Since concrete weighs about 150 pounds per cubic foot, we shall assume this weight of 150 pounds as the unit of measurement, and therefore reduce the ordinates of earthwork to the load line for the top of the earth, as shown in Fig. 232. We shall assume as an additional dead load a pavement weighing 80 pounds per square foot, and shall therefore lay off an ordinate of 80/150 of a foot above the ordinates for the earth-filling load. For this particular problem, we shall only investigate a live load of 200 pounds per square foot, extending over one-half of the span from the abutment to the center. From our previous work in arches, we know that such a loading will test the arch more severely than a similar unit live load extending over the entire arch; and therefore, if the arch proves safe for this eccentric load, we may certainly assume that it will be safe for a full load. These load lines are laid off similarly to the method elaborated in Article 409. The arch has already been laid off in equal horizontal sections, each having a width of 3.07 feet. The two end sections are slightly longer if we consider the entire load which is vertically over the extreme ends of the extrados of the arch. The 18 sections lying between the end sections, have a width of 3.07 feet, and a variable height which may be considered as extending from the top of the load line down to the intrados. We may therefore multiply the widths of these sections by their various heights, and by 150, and obtain the number of pounds weight on each section, and we find the loads as follows:

No. of Section

Loading

1

6,860

2

4,589

3

3,860

4

3,070

5

2,526

6

2,102

7

1,757

8

1,481

9

1,343

10

1,275

No. of Section

Loading

11

1,889

12

1,957

13

2,095

14

2,173

15

2,716

16

3,140

17

3,684

18

4,474

19

5,203

20

7,620

The sum total of this loading, which represents the total dead and live load on a section of the arch one foot wide (in the direction of the axis of the arch), is 63,814 pounds. We lay off these various loads on the right-hand side of the drawing in a vertical line, using a scale of 5,000 pounds per inch. Selecting a pole o1 at random, we draw rays to the various points in the load line.