The above ratios are applied to the use of Ransome twisted bars, which have a high elastic limit and give a factor of safety of about 4.
In the above problem, the total compression is 19,500 lbs.; this, divided by 500 lbs., gives a required area in the upper third of the beam of 39 square inches. 39x3=117 square inches; total area of beam, 117 square inches, divided by inches depth assumed, gives / ', 100 inches width of beam. A width of inches may be used.
Ransome's Formula. Ransome's formula for a simple beam uniformly loaded. is: wi ---...
7d in which, W. Total dead and live load, in tons.
When the beam is not uniformly loaded, the formula becomes: X 8 7d in which BM equals the maximum bending moment in inch-tons.
In order that the compressive stress per linear foot of width resulting from a chosen value of d shall not exceed the safe compressive strength of the concrete, there must be 16 square inches of concrete above the bars for each ton of stress.
16S 12d, from which, Substituting this value of S in the above formula, we have: W1 Id d • 21 --W1 Having obtained d, the total stress in tons, S = d.
Example. Assume a flat floor slab, having a span of 12 feet carrying a live load of 150 lbs. per square foot.
It is necessary to assume the dead weight of the floor. Let this be taken as 75 lbs. per sq. ft., making a total load of 225 lb. per sq. ft. The total load W in tons on a strip of floor 1 ft. wide would be: 12 X 225 2,000 tons, and we have for d, The total stress in the bars would equal X tons. Assuming an allowable working stress on the metal of 8 tons per sq. in., there will be sq. in. of metal required—or four rods % in. square—in each foot width of slab. When rods are used, the distance from center of rod to bottom should be at least in.; and in. for in. square rods. For %-in. rod reinforcement, we will have a total thickness of inches.
given by the formula. This condition prevents the concrete in the top of the slab from being strained beyond its safe compressive strength.
In the design of an ordinary beam which is to rest freely upon a support at each end, we have only to consider tension as occurring in the material on the under side of the beam. This is not the condition generally found in reinforced structures. The beams, girders, and floors, commonly form a continuous mass, thereby fixing the beams and girders more or less firmly at the ends. This condition prevents the ends of the beams and girders from inclining, as the bending occurs in the cen ter, thereby causing the top surface of the beam to come into tension over the supporting walls or columns. Reinforcing rods must be placed near the top surface of such beams and girders, and anchored firmly, just as they are placed near the bottom surface in the middle of the span.
In floor construction where some form of wire fabric is used as a reinforcing agent, the sag of the fabric as it is stretched continuously across several spans brings it toward the lower surface of the floor slab in the center, thereby giving it reinforcement in the proper place; and the fabric slants upward again toward the ends of the span in order to pass over the beams into the next span. This upward slope of the ma terial again places strength where it is needed.
When the ends of rods are to be joined in a continuous construction, unless they are joined by some form of connection, practice shows that they should overlap in the concrete for about fifty diameters.
In the case of of reinforced con crete, the assumption upon which calculations are often based is that we may substitute for the actual T-section the area of the rectangle found by extending the sides of the flange section downward until they meet a horizontal line passing through the center of gravity of the end sections of the reinforcing rods in the lower part of the web, and we may then figure as in the case of beams of rectangular section. There is claimed to be but small error in this assumption.