The permanency of concrete, and particularly reinforced concrete, has caused its adoption in the construction of culverts of all dimensions, from a cross-sectional area of a very few square feet, to that of an arch which might be more properly classified under the more common name masonry arch. The smaller sizes can be constructed more easily, and with less expense for the forms, by giving them a rectangular cross-section. The question of foundations is solved most easily by making a concrete bottom, as well as side walls and top. The structure then becomes literally a box. Its design consists in the determination of the external pressure exerted by the earth, and of the required thickness of the concrete to withstand the pressure on the flat sides considered as slabs. The most uncertain part of the computation lies in the determination of the actual pressure of the earth. Under the heading "Retaining Walls," this uncertainty was discussed.

One very simple method is to assume that the earth pressure is equivalent to that of a liquid having a unit-weight equal to that of the weight of a cubic foot of the earth, which is nearly 100 pounds. Under almost any circumstances, these figures would be sufficiently large, and perhaps very excessive. Calculations on such a basis are therefore certainly safe. If the pressure is computed on this basis, and a factor of safety of 2 is used, it is equivalent to an actual pressure of only one-half the amount (which is more probable), having a factor of 4. If the depth of the earth is quite large compared with the dimensions of the culvert, we may consider that the upward pressure on the bottom, as well as the lateral pressure on the sides, is practically the same as the downward pressure on the top. If the bottom of the culvert is laid on rock, or on soil which is practically unyielding, there will be no necessity of considering that there is any upward pressure on the bottom slab tending to burst that slab upward. The softer the soil, the greater will be the tendency to transverse bending in the bottom slab.

Since the design of rectangular box culverts is purely an application of the equations for transverse bending, after the external pressures have been determined, no numerical example will here be given. These structures are not only reinforced with bars, considering the sides as slabs, but should also have bars placed across the corners, which will withstand a tendency of the section to collapse in case the pressure on opposite sides is unequal. They must also be reinforced with bars running longitudinally with the culvert. As in the other cases of longitudinal reinforcement, no definite design can be made for its amount. A typical cross-section for such a culvert is shown in Fig. 115. The longitudinal bars are indicated in this figure. They are used to prevent cracks owing to expansion or contraction, and also to resist any tendency to rupture which might be caused by a settling or washing-out of the subsoil for any considerable distance under the length of the culvert.

Fig. 115. Rectangular Box Culvert.

## 308. Arch Culverts

The general subject of arches, and especially the application of reinforced concrete to arch construction, are taken up in Part V, and therefore will not be further discussed here.