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If c is the maximum compression at the top of the concrete slab and the stress-strain diagram is rectilinear, as in Fig. 105, then the compression at the bottom of the concrete slab is c ---. The averaged compression = (c + e= (kd - - t). The total compression equals the average compression multiplied by the area b't; or, C= As= bt 238 signed, as in the case of the simple concrete footing, to distribute the weight on each concrete column across the width of the concrete footing, and to transfer the weight to the longitudinal bars. The economy of a retaining concrete wall of reinforced concrete lies in the fact that by .adopting a skeleton form of construction and utilizing the tensional and transverse strength which may be obtained from reinforced concrete, a concrete wall may be built, of which the volume of concrete is, in some cases, not more than one- third the volume of a retaining concrete wall of plain concrete which would answer the same purpose.

Although the cost of reinforced concrete per cubic foot will be somewhat greater than that of plain concrete, it sometimes happens that such concrete walls can be constructed for one-half the cost of plain concrete walls. The general outline of a reinforced concrete retaining wall is similar to the letter L, the base of which is a base-plate made as wide as (and generally a little wider than) the width usually considered, necessary for a plain concrete wall. As a general rule, the width of the base should be about one-half the height. The face of the concrete wall is made of a comparatively thin plate whose thickness is governed by certain principles, as explained later. At intervals of 10 feet, more or less, the base-plate and the face are connected by concrete buttresses. These concrete buttresses are very strongly fastened by tie-bars to both the base-plate and the face-plate. The stress in the concrete buttresses is almost exclusively tension. The pressure of the earth tends to force the face-plate outward; and therefore the faceplate must be designed on the basis of a vertical concrete slab subjected to transverse stresses which are at the bottom and which reduce to zero at the top.

If the concrete wall is "surcharged" (which means that the earth at the top of the concrete wall is not level, but runs back at a slope), then the faceplate will have transverse stresses even at the top. The base-plate is held down by the pressure of the superimposed earth. The concrete buttresses must transmit the bursting pressure on the face of the concrete wall backward and downward to the base-plate. The base-plate must therefore be designed by the same method as a horizontal concrete slab carrying a load equal and opposite to the upward pull in each buttress. If the base-plate extends in front of the face of the concrete wall, thus forming 250 (kd —t) > kd. The center of gravity of the compressive stresses is evidently at the center of gravity of the trapezoid of pressures. The distance x of this center of gravity from the top of the concrete beam is given by the formula: 32kd—t. It has already been shown in Article 264, that: Combining this equation with Equation 32, we may eliminate -, and obtain a value for kd: kd = Ard'+ b't'(34) Ar+b't.

If the percentage of steel is chosen at random, the concrete beam will probably be over reinforced or under reinforced. In general it will therefore be necessary to compute the moment with reference to the steel and also with reference to the concrete, and, as before with plain concrete beams (Equation 29), we shall have a pair of equations: A = C (d—x) = b't\ - (kd - t) (d - x) I    (35) = As (d—x) = pb'ds (d — x) If we place led = t in the equation above Equation 34, and solve for d, we have a relation between d, c, s, r, and t, which holds when the neutral axis is just at the bottom of the concrete slab. The equation becomes: Cr. A combination of dimensions and stresses which would place the neutral axis exactly in this position, is improbable, although readily possible; but Equation 36 is very useful to determine whether a given numerical problem belongs to Case 1 or Case 3.

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