Hollow Spandrels - arch, line, load, center and ring

HOLLOW SPANDRELS. Since the roadway must not deviate greatly from a horizontal line, a considerable quantity of material is required above the backing to bring the roadway level. Ordinarily this space is filled with earth, gravel, broken stone, cinders, etc. Sometimes, to save filling and also to lighten the load upon the arch, small arches are built over the haunches of the main arch, as shown in Fig. 214. The interior longitudinal walls may be strengthened by transverse walls between them. To dis tribute the pressure uniformly, the feet of these walls should be expanded by foot ings where they rest upon the back of the arch.

1281.

When the load is entirely sta tionary—as in an aqueduct or canal bridge —or nearly so—as in a long span arch under a high railroad embankment—the materials of the spandrel filling and the size and position of the empty spaces may be such as to cause the line of resistance to co incide, at least very nearly, with the center of the arch ring.

For example, ABCD, Fig. 215, represents a semi-arch for which it is required to find a disposition of the load that will cause the line of resistance to coincide with the center line of the arch ring. Divide the arch into any convenient number of voussoirs, and also divide the load into a corresponding number of divisions by vertical lines as shown. From P draw radiating lines parallel to the tangents of the center line of the arch ring at a, b, c, etc.; and then at such a distance from P that 01 shall represent, to any convenient scale, the load on the first section of the arch ring (including its own weight), draw a vertical line through 0; and then the interecpts etc., represent, to scale, the loads which the several divisions

must have to cause the line of resistance to coincide with the center of the arch ring. Lay off the distances etc., at the centers of the respective sections vertically upwards from the center line of the arch ring, and trace a curve through their upper ends. The line thus formed—EF, Fig. 210, page 656—shows the required amount of homogeneous load; i.e., EF is the contour of the homogeneous load that will cause the line of resistance to pass approximately through the center of each joint.

Hence, by choosing. the material of the spandrel filling and arranging the empty spaces so that the actual load shall be equivalent in intensity and distribution to the reduced load obtained as above, the voussoirs can be made of moderate depth.

For three different methods of lightening the haunches, see Fig. 217, page 662, Fig. 219, page 664, and Fig. 220, page 665.

1282. Notice that the lines radiating successively from P, Fig. 215, will intercept increasing lengths on the load-line; and that, there fore, the load which will keep a circular arch in equilibrium must increase in intensity per horizontal foot, from the crown towards the springing, and must become infinite at the springing of a semi circular arch. Hence it follows that it is not practicable to load a circular arch, beyond a certain distance from the crown, so that the line of resistance shall coincide with the center line of the arch ring.