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When the stresses s and c in the steel and concrete, the ratio r of the elasticity, and the thickness t of the concrete slab are all determined, then the solution of Equation 36 will give a value of d which would bring the neutral axis at the bottom of the concrete slab. But it should not be forgotten that the compression in the concrete (c) and the tension in the steel will not simultaneously have certain definite values (say c = 500, and s = 16,000) unless the percentage of steel has been so chosen as to give those simultaneous values. When, as is usual, some other percentage of steel is used, the equation is not strictly applicable, and it therefore should not be used to determine a value of d which will place the neutral axis at the bottom of the concrete slab and thus simplify somewhat the numerical calculations. For example, for c = 500, s = 16,000, r = 12, and t = 4 inches, d will equal 14.67 inches. Of course this particular depth may not satisfy the requirements of the problem. If the proper value for d is less than that indicated by Equation 36, the problem belongs to Case 3; if it is more, the problem belongs to Case 1. The diagram of pressure is very similar to that in Fig. 105, except that it is a triangle instead of a trapezoid, the triangle having a base c and a height kcl which is less than i.

The center of compression is at 1- the height from the base, or x = - kd. Equations 25 to 29 are applicable to this case as well as to Case 2, which may be considered merely as the limiting case to Case 3. But it should be remembered that b' refers to the width of the flange or concrete slab, and not to the width of the stem or rib. The width (b') of the flange is usually considered to be equal to the width between adjacent concrete beams, or that it extends from the middle of one panel to the middle of the next. The chief danger in such an assumption lies in the fact that if the concrete beams are very far apart, they must have corresponding strength to carry such a concrete floor load, and the shearing stresses between the rib and the concrete slab will be very great. The method of calculating such shear will be given later. It sometimes happens (as illustrated in Article 296), that the width of concrete slab on each side of the rib is almost indefinite. In such a case we must arbitrarily assume some limit, and say that the compression in the concrete slab which is due to the concrete beam is confined to a strip which is (say) fifteen or twenty times the thickness of the concrete slab. If the compression is computed for two cases, both of which have the same size of rib, same steel, same thickness of concrete slab, but different concrete slab widths, it is found, as might be expected, that for the narrower concrete slab width the unit-compression is greater, the neutral axis is very slightly lower, and even the unit-tension in the steel is slightly greater.

No demonstration has ever been made to determine any limitation of width of concrete slab beyond which no compression would be developed by the transverse stress in a T-concrete beam rib under it. It is probably safe to assume that it extends for seven to ten times the thickness of the concrete slab on each side of the rib. If the concrete beam as a whole is safe on this basis, then it is still safer for any additional width to which the compression may extend. Since it is assumed that all of the compression occurs in the concrete slab, the only work done by the concrete in the rib is to transfer the tension in the steel to the concrete slab, to resist the shearing and web stresses, and to keep the bars in their proper place. The width of the rib is somewhat determined by the amount of reinforcing steel which must be placed in the rib, and whether it is desirable to use two or more rows of bars instead of merely one row. As indicated in Fig. 104, the amount of steel required in the base of a concrete beam is frequently so great that two rows of bars are necessary in order that the bars may have a sufficient spacing between them so that the concrete will not split apart between the bars.

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