288. Case 3. 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 led_ which is less than t. The center of compression is at the height from the base, or = s led. Equa tions 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 slab, and not to the width of the stem or rib.
2S9. Width of Flange. The width (b') of the flange is usually considered to be equal to the width between adjacent 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 beams are very far apart, they must have corresponding strength to carry such a floor load, and the shearing stresses between the rib and the 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 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 slab which is due to the T beam is confined to a strip which is (say) fifteen or twenty times the thickness of the slab. If the compression is computed for two cases, both of which have the same size of rib, same steel, same thickness of slab, but different slab widths, it is found, as might be expected, that for the narrower 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 slab beyond which no com pression would he developed by the transverse stress in a T-beam rib under it. It is probably safe to assume that it extends for seven to ten times the thickness of the slab on each side of the rib. If the beam as a whole is safe on this basis, then it is still safer for any addi tional width to which the compression may extend.
290. Width of Rib. Since it is assumed that all of the com pression occurs in the slab, the only work done by the concrete in the rib is to transfer the tension in the steel to the 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 T-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. Although it would be difficult to develop any rule for the proper spacing between bars without making assumptions which are perhaps doubtful, the following empirical rule is frequently adopted by designers: The spacing between bars, center to center, should be two and a-quarter times the diameter of the bars. Fire insurance and municipal specifications usually require that there shall be two inches clear outside of the steel. This means that the beam shall be four inches wider than the net width from out to out of the extreme bars. The data given in Table XVIII will therefore be found very convenient, since, when it is desired to use a certain number of bars of given size, a glance at the table will show immediately whether it is possible to space them in one row; and, if this is not possible, the necessary arrangement can be very readily designed. For example, assume that six '-inch bars are to be used in i beam. The table shows immediately that the re quired width of the beam (following the rule) will be 14.72 inches; but if, for any reason, a beam 11 inches wide is considered preferable, the table shows that four '--inch bars may be placed side by side, leaving two bars to be placed in an upper row. Following the same rule regarding the spacing of the bars in vertical rows, the distance from center to center of the two rows should be 2.25 X .S75 = 1.97 inches, showing that the rows should be, say, two inches apart center to center. It should also be noted that the plane of the center of gravity of this steel is at two-fifths of the distance between the bars above the lower row, or that it is eight-tenths of an inch above the center of the lower row.