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Slab and Beam Design

beams, spans, moments, continuous, support, moment and span

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SLAB AND BEAM DESIGN Bending Moments and Shears.—Structural forms in which slabs of concrete are supported by T-beams are very common in rein forced concrete structures. In this type of construction, the slab is commonly made continuous over the T-bcam and forms the flange of the 'f-beam (see Fig. 53), being built with the beam and a part of it. In determining the bending moments and shears in such con struction, the loads may usually be taken as uniform, and the slabs and beams as fully or partly continuous, depending upon the method of support.

Fully Continuous Reams.—Tf a slab which passes over one or more cross-beam, is firmly held at the ends by being built into and tied by reinforcement to a wall or heavy beam, it may be considered as fully continuous, and when uniformly loaded, the positive moments of the middle of the spans are and the negative moments at supports 'Ll . The shear at each end of span in such a beam is tri. If the movable load covers some of the spans leaving others unloaded, these moments may be somewhat increased. For slabs of this type, it is conservative practice to use for both positive and negative bending moments and for maximum vertical shear.

Supported ends of continuous beams, resting upon side walls or end columns, cannot he considered as fixed, and are to he taken as simply supported. Such a beam, or a slab the ends of which are not fixed, has greater positive moments in the end spans and greater negative moments at the first supports from the ends than fully continuous beams. These moments are usually taken as for beams of more than two spans. The shear in the end span next the first support may be greater than one-half the load on the span and should be taken as .6 wl. For beams of two spans, the nega tive moment at the middle support is taken as and the positive moment as The moments for continuous beams of unequal spans, or with concentrated and uneven loading should be carefully determined for each individual case.

The Joint Committee makes the following recommendations in its 1916 report: (a) For floor slabs the bending moments at center and at support should he taken at xcd- for both dead and line loads, where w represents the 13 load per linear unit and 1 the span length.

(b) For beams the bending moment at center and at support for interior spans should be taken at and for end spans it should be taken at 10 for center and interior support, for both dead and live loads.

(c) In the case of beams and slabs continuous for two spans only, with their ends restrained, the bending moment both at the central support and near the middle of the span should he taken at 102 .

(d) At the ends of continuous beams the amount of negative moment which will he developed in the beam will depend on the condition of restraint or fixedness, and this will depend on the form of construction used. In the ordinary cases a moment of 16 may be taken; for small beams running into heavy columns this should be increased, wl' but not to exceed 12 For spans of unusual length, or for spans of materially unequal length, more exact calculations should be made. Special consideration is also required in the case of concentrated loads.

Even if the center of the span is designed for a greater bending moment than is called for by (a) or (b), the negative moment at the support should not be taken as less than the values there given.

117. Loading of Slabs, Beams and Girders.

Slabs are commonly used as continuous beams passing over a number of T-beams, of which the slab forms the flange as shown in Fig. 53.

They are reinforced for tension in one direction, perpendicular to the T-beams,and in computation are considered as rectangular beams one foot in width. The T-beams supporting such slabs frequently rest upon girders, which are used to widen the interval between columns, and permit the T-beams to be spaced close enough for economical design of slab. The load upon a T-beam in such a system is uniformly distributed and consists of the weight of a half span of the slab and its load, on each side of the beam. The loads upon the girders are con centrated at the points where the T-beams cross, but may usually be taken as uniformly distributed without material error.

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