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A theoretical determination of the amount of such reinforcing steel is practically impossible, since it depends on assumptions which are they themselves very doubtful. It is usually conceded that if there is placed in the concrete an amount of steel whose cross-sectional area equals about of 1 per cent of the area of the concrete, the concrete structure will be proof against such cracks. Fortunately, this amount of steel is so small that any great refinement in its determination is of little importance. Also, since such bars have a value in tying the concrete structure together, and thus adding somewhat to its strength and ability to resist disintegration owing to vibrations, the bars are usually worth what they cost. When concrete beams are laid in conjunction with overlying concrete floor-concrete slabs, the concrete for both the concrete beams and the concrete slabs being laid in one operation, the strength of such concrete beams is very much greater than their strength considered merely as plain concrete beams, even though we compute the depth of the concrete beams to be equal to the total depth from the bottom of the concrete beam to the top of the concrete slab.

An explanation of this added strength may be made as follows: If we were to construct a very wide concrete beam with a cross-section such as is illustrated in Fig. 104, there is no hesitation about calculating such strength as that of a plain concrete beam whose width is b, and whose effective depth to the reinforcement is ci. Our previous study in plain concrete beams has shown us that the steel in the bottom of the concrete beam takes care of practically all the tension; that the neutral axis of the concrete beam is somewhat above the center of s a concrete below the neutral axis is to - b -transfer the stress in the steel to the concrete in the top of the concrete beam; and that even in this work it must be assisted somewhat by stirrups or by bending up the steel bars. If, therefore, we cutout from the lower corners of the concrete beam two rectangles, as shown by the non shaded areas, we are saving a very large part of the concrete, with very little loss in the strength of the concrete beam, provided we can fulfill certain conditions. The steel, instead of being distributed uniformly throughout the bottom of the wide concrete beam, is concentrated into the comparatively narrow portion which we shall hereafter call the rib of the concrete beam. The concentrated tension in the bottom of this rib must be transferred to the compression area at the top of the concrete beam. We must also design the concrete beam so that the shearing stresses in the plane (mn) immediately below the concrete slab shall not exceed the allowable shearing stress in the concrete.

We must also provide that failure shall not occur on account of shearing in the vertical planes (m r and n s) between the sides of the concrete beam and the flanges. These will be computed in accordance with straight-line formulate. There are three possible cases, according as the neutral axis is: (1) below the bottom of the concrete slab (which is the most common case, and which is illustrated in Fig. 105); (2) at the bottom of the concrete slab; or (3) above it. All possible effect of tension in the concrete is ignored. For Case 1, even the compression furnished by the concrete between the neutral axis and the underside of the concrete slab is ignored. Such compression is of course zero at the neutral axis; its maximum value at the bottom of the concrete slab is small; the summation of the compression is evidently small; the lever arm is certainly not more than y; therefore the moment due to such compression is insignificant compared with the resisting moment due to the concrete slab. The computations are much more complicated; the resulting error is a very small percentage of the true figure, and the error is on the side of safety.

Are You in Portsmouth New Hampshire? Do You Need Concrete Cutting?

We Are Your Local Concrete Cutter

Call 603-622-4441

We Service Portsmouth NH and all surrounding Cities & Towns