As another condition of loading, we shall assume that the above load extends only across one-half of the arch. We shall probably find that, owing to the eccentricity of this form of loading, the stability of the arch is in much greater danger than when the entire arch is loaded with a maximum load.

The loads on each voussoir are scaled from the reduced load line according to the various conditions of loading. The area between the two verticals over each voussoir is measured with all necessary accuracy by multiplying the horizontal width between the verticals by the scaled length of the perpendicular which is midway between the verticals. The weight of the voussoir itself may be computed as accurately as necessary, by multiplying the radial thickness by the length between the joints as measured on the curve lying half-way between the intrados and the extrados.

For example, the load for full loading of the arch which is over voussoir No. 1, is measured as follows: The width between the perpendiculars is 2.0 feet; the height measured on the middle vertical is 4.05 feet; the area is therefore 8.10 feet, which, multiplied by 160, equals 1,296 pounds, which is the load on this voussoir for every foot of width of the arch parallel with the axis. The radial thickness of voussoir No. 1 is 1.90 feet, and the length is 2.15 feet; this gives an area of 4.085 feet, which, multiplied by 160, equals 653.6 pounds. The weight of the voussoir is therefore almost exactly one-half that of the live and dead loads above it; therefore the resultant of these two weights will be almost precisely one-third of the distance between the center of this stone and the vertical through the center of the loading. By drawing this line, we have the line of action of the resultant of these two forces, and this value is the sum of 1,296 and 654, or 1,950 pounds.

In order to simplify the figure, the arrows representing the lines of force of the loading on the voussoir and the weight of the voussoir have been omitted from the figure, and only their resultant is drawn in. It was of course necessary to draw in these forces in pencil and obtain the position of the resultant, as explained in Fig. 221; and then, for simplicity, only the resultant was inked in.

The loads on the other voussoirs are computed similarly. The numerical values for the loads on the various voussoirs (including the weights of the voussoirs), are tabulated as follows:

 Voussoir No. Load Weight of Voussoir Total 1 and 11 1,296 654 1,950 2 ,, 10 1,135 592 1,727 3 ,, 9 1,010 528 1,538 4 ,, 8 927 483 1,410 5 ,, 7 880 456 1,336 6 867 455 1,322

For this first condition of loading, the total loads for voussoirs Nos. 7, 8, 9, 10, and 11 will be the same as those for voussoirs 5, 4, 3, 2, and 1 respectively.

The loads for the second condition of loading are found by using the same load on the first five voussoirs, but with only half of the live load on voussoir No. 6, which means that the load for the first condition of loading (1,322 pounds) is reduced by 200 pounds, making it 1,122 pounds. Voussoirs Nos. 7 to 11 are each reduced by 400 pounds. The total load for each voussoir is as tabulated below.

The loads for the third condition of loading are found by using the same loads as were employed for the second condition, except that for voussoirs Nos. 3 and 4, 1,600 pounds should be added to each load. These loads are also tabulated below: