This section is from the book "Cyclopedia Of Architecture, Carpentry, And Building", by James C. et al. Also available from Amazon: Cyclopedia Of Architecture, Carpentry And Building.
238. The terra culvert is usually applied to a small waterway which passes under an embankment of a railroad or a highway. The term is confined to waterways which are so small that standard plans are prepared which depend only on the assumed area of waterway that is required. Although the term is sometimes applied to arches having a span of 10 or 15 feet, or even more, the fact that the structures are built according to standard plans justifies the use of the term culvert as distinguished from a structure crossing some perennial stream where a special design for the location is made. The term culvert therefore includes the drainage openings which may be needed to drain the hollow on one side of an embankment, even though the culvert is normally dry.
Culverts are variously made of cast iron, wrought iron, and tile pipe, wood, stone blocks with large cover-plates of stone slabs, stone arches, and plain and reinforced concrete; still another variety is made by building two side walls of stone and making a cover-plate of old rails.
240. Culverts made of wood should be considered as temporary, on account of the inevitable decay of the wood in the course of a few years. When wood is used, the area of the opening should be made much larger than that actually required, so that a more permanent culvert of sufficient size may be constructed inside of the wooden culvert before it has decayed. For present purposes, the discussion of the subject of Culverts will be limited to those built of stone and concrete.
The choice of stone as a material for culverts should depend on the possibility of obtaining a good quality of building stone in the immediate neighborhood. Frequently temporary trestles are used when good stone is unobtainable, with the idea that after the railroad is completed, it will be possible to transport a suitable quality of building stone from a distance and build the culvert under the trestle. The engineer should avoid the mistake of using a poor quality of building stone for the construction of even a culvent simply because such a stone is readily obtainable.
DOUBLE-COTTAGE DORMITORIES, PARENTAL SCHOOL, MAYFAIR, ILL.
W. B. Mundie. Architect. Chicago. 111.
SUPERINTENDENT'S COTTAGE, PARENTAL SCHOOL, MAYFAIR, ILL.
W. B. Mundie, Architect, Chicago, 111.
Since a culvert always implies a stream of water which will have a scouring action during floods, it is essential that the side walls of culverts should have an ample foundation, which is sunk to such a depth that there is no danger that it will be undermined. There are cases where a bed of quicksand has been encountered, and where the cost of excavating to a firmer soil would be very large. In such a case, it is generally possible to obtain a sufficient foundation by constructing a platform or grillage of timber which underlies the entire cuivert, beneath the floor of the culvert. Of course, timber should not be used for the foundation, except in cases where it will always be underneath the level of the ground-water and will therefore always be wet. If the soil has a character such that it will be easily scoured, the floor of the culvert between the side walls should be paved with large pebbles, so as to protect it from scouring action. At both ends of the culvert, there should always be built a vertical wall which should run from the floor of the culvert down to a depth that will certainly be below any possible scouring influence, in order that the side walls and the flooring of the culvert cannot possibly be undermined.
The above specifications apply to all forms of stone culverts, and even to arch culverts, except that in the case of the larger arch culverts the precautions in these respects should be correspondingly observed. When stone culverts are built with vertical side walls which are from 2 to 4 feet apart, they are sometimes capped with large flagstones covering the span between the walls. The thickness of the cover-stone is sometimes determined by an assumption as to the transverse strength of the stone, and by applying the ordinary theory of flexure. The application of this theory depends on the assumption that the neutral axis for a rectangular section is at the center of depth of the stone, and that the modulus of elasticity for tension and compression is the same. Although these assumptions are practically true for steel and even wood, they are far from being true for stone. It is therefore improper to apply the theory of flexure to stone slabs, except on the basis of moduli of rupture which have been experimentally determined from specimens having substantially the same thickness as the thickness proposed. Also, on account of the variability of the actual strength of stones though nominally of the same quality, a very large factor of safety over the supposed ultimate strength of the stone should be used.
The maximum moment at the center of a slab one foot wide equals 1/8 Wl, in which W equals the total load on the width of one foot of the slab, and l equals the span of the slab, in feet; but by the principles of Mechanics, this moment equals 1/6 Rh2, in which R equals the modulus of transverse strength, in pounds per square foot; and h equals the thickness of the stone, in feet. Placing these two expressions equal to each other, and solving for h, we find: h2 = 6/8 Wl/R
Assume that a culvert is covered with 6 feet of earth weighing 100 pounds per cubic foot. Assume a live load on top of the embankment equivalent to 500 pounds per square foot, in addition; or that the total load on the top of the slab is equivalent to 1,100 pounds per square foot of slab. Assume that the slab is to have a span (l) of 4 feet. Then the total load W on a section of the slab one foot wide, will be 1,100 X 4 = 4,400 pounds. Assume that the stone is sandstone, with an average ultimate modulus of 525 pounds per square inch (see Table XII), and that the safe value R is assumed to be 55 pounds per square inch, or 144 X 55 pounds per square foot. Substituting these values in the above equation for h, we find that h equals 1.29 feet, or 15.5 inches.
The above problem has been worked out on the basis of the live load which would be found on a railroad. For highways, this could be correspondingly decreased. It should be noted that in the above formula the thickness of the stone h varies as the square root of the span; therefore, for a span of 3 feet (other things being the same as above), the thickness of the stone h equals For a span of 2 feet, the thickness should be 11.0 inches.
Owing to the uncertainty of the true transverse strength of building stone, as has already been discussed in the design of Offsets for Footings (see sections 181-183), no precise calculation is possible; and therefore many box culverts are made according to empirical rules, which dictate that the thickness shall be as follows:
For a 2-foot span, 10 inches; For a 3-foot span, 13 inches; For a 4-foot span, 15 inches.
These values are slightly less than those computed above.
Although a good quality of granite, and especially of bluestone flagging, will stand higher transverse stresses than those given above for sandstone, the rough rules just quoted are more often used, and are, of course, safer. When it is desired to test the safety of stone already cut into slabs of a given thickness, their strength may be computed from Equation 8, using the values for transverse stresses as already given in Table XII.