If we assume the load to be uniformly distributed over the top, the moments will he as follows: if the sectional area of the sides be mnacie the same as those of the top and bottom, we have For sizes of culverts commonly used may be considered the limiting value to which the moment may approximate. The moments in top and bottom slabs are decreased and those in the sides increased as the ratio of height t:o width is lessened.
The pressure of earth against the sides of the culvert produces moments in the top, bottom and sides of the culvert of opposite sign to those produced by the load upon top of the culvert, and therefore tend to reduce the effect of the top load upon the culvert. Such pressures always exist to sonic extent, but are not accurately known. It is usual to assume that unit horizontal pressure, when considered, is about one-third the unit vertical pressure. The mo ments caused by the side pressures will always be much less than those clue to the vertical loads and not sufficient to overcome those moments.
If the side pressures be supposed to exist when the vertical loads are not on the culvert, as may be the case with moving loads, the sides will be subject to positive moments and need reinforcing at the inner surfaces.
The existence of side pressures tends to increase the negative moments at the corners, and a box culvert can act as a whole only when the corners are reinforced sufficiently to carry these moments without cracking at the corners.
In case the fill upon the culvert is not sufficient to distribute the load over the whole top of the culvert, the moment will be increased. For a load at the middle of span, the moments will be about double those for the same total load distributed over the span.
In highway culverts which are covered only with the thickness of the road surface, the distribution of the load may be considered as in Art. 41. In such culverts, the live load should be increased 25 per cent to allow for impact.
When, as is sometimes the case, the corners of the culvert are not reinforced for negative moment, the top becomes a simple beam, resting upon the sides but not rigidly attached to them, and the sides carry only the horizontal cart h pressure as simple beams. Such construction is shown in Fig. 99, which represents a standard section for a highway culvert de signed to carry a 20-ton auto truck. The section in Fig. OS is designed for the same loading.
181. Arch Culverts.— For locations where suf ficient headroom is avail able, arch culverts are often preferable to those with flat top. Very pleas ing and artistic effects may frequently be ob tained by careful design of arches for such use. Under fills of considerable height, arch culverts will commonly be more economical to construct than slab top culverts. Fig. 100 shows a section for a standard highway culvert for use under automobile traffic.
The analysis of stresses in arch culverts may be made in the same manner as is given for arch bridges in Chapter X. The horizontal earth pressures on the sides of the arch are usually taken as one-third of the vertical pressures at the same point. These pressures are of greater relative importance than in bridges of longer span. For short spans, plain concrete is com monly employed, while for spans greater than about 8 feet, rein forcement is usually introduced for greater security, although not necessary to carry moments.