Observe the following general rules. (9) The best-shaped beam is one in which the breadth is from one-half to three-fourths of the effective depth. (10) The breadth should not be less than 1/24 of the span. (11) Stirrups must be amply provided especially when the depth is greater than 1/10 of the span. (12) The breadth must be sufficient for the spacing of the bars. A minimum clear spacing of at least 1 1/2 diameters should be provided, with an equal distance between the outside rod and the surface of the beam. (13) Sufficient rods should be employed; so that the diameter of each will not exceed 1/200 of the span. (14) The length of rod on each side of the centre of the beam should be at least 80 diameters for plain and 50 diameters for deformed bars. (15) Compare the computed weight with the estimated weight of the beam, and revise the design if the difference exceeds 10 per cent. How to Design a Reinforced Concrete Column.-This consists in determining proper dimensions for the post or column, and the steel required for its reinforcement. The following order of computations should be observed. (1) Compute the load, P, to be supported by the column. (2) Estimate the weight, W', of the column itself. (3) Determine the load per sq. in. of sectional area which the concrete can be designed to carry, also the ratio between the moduli of concrete and steel. (4) Choose the percentage of vertical reinforcement. In general this should be between 1 and 21⁄2 per cent. (5) If spiral wrappings are to be used, choose the sectional area, and spacing of the bands. (6) Compute the sectional area required for the column by the following formula, and check its weight. A, the sectional area of the vertical reinforcement. A the effective area of the column. A= the sectional area of the hooping. P W' h = = the load to be supported. the estimated weight of the column itself. C = the safe compressive stress for concrete. р the percentage of vertical steel reinforcement. r = the ratio between the modulus of elasticity of steel and that of concrete in compression. Where bands are used, the section of the column contained within the spirals may be designed to carry 50 per cent more stress than the column without bands, providing: (a) The wrapping is circular in form. (b) A thickness of two inches of concrete is placed outside of the bands, for protection, but not considered as taking any part of the load. (c) The bands are of sufficient size so that their sectional area, An, divided by the pitch, s, or distance between spirals is not less than the diameter of the spiral, D, divided by 500, or (7) The length of the column must not exceed more than 12 times its least lateral dimension. (8) The vertical steel must be as straight as possible, and rest upon bed plates at the bottom. When the bars are spliced, the bars must not be lapped and wired, but the end of the upper bar must rest on the top of the lower one, and be held in place by sleeves made of pipe. The sleeves should be 24 diameters long and the joints should also be stiffened by a half-inch bar about four times as long as the sleeve, which is set alongside of but not in contact with the reinforcement. (9) In all large columns the steel should be protected by at least two inches of concrete, and in small columns by not less than one inch. (10) The percentage of steel which can carry the entire load when stiffened by the concrete can be found by dividing the load to be supported in pounds by 16,000. In general this will run from 4 to 6 per cent. (11) The load on the column must be symmetrically placed, so that the centre of the load coincides with the centre of the column. If the load bears more on one side of the column than it does on the other, it is called an eccentric load; and it requires a larger column to carry an eccentric than it does to carry a symmetrical load. An eccentrically loaded column cannot be designed by the methods explained in this chapter. Example.-Design a square reinforced concrete post, 10 feet long, which will support a load of 20 tons without spiral wrappings. Solution.-(1) P = 20 X 2,000 (2) Estimate W' at 1,500 lbs. = 40,000 lbs. (3) A safe load for concrete in compression is 350 lbs. per sq. in., and a safe value of the ratio, r, is 12. (4) Employ 1.7 per cent of vertical reinforcement. If 4 square bars are used the area of each will be: 1.70 4.43 sq. ins. or 4-11/16 in. square bars are required. (6) The least lateral dimension is 10 inches. 10 inches X 12 = IO feet. As the length of the post is 10 feet or equal to the above value, the design is permissible. Summarying the results of the design, we have, External load, 20 tons. Weight of column, 1,000 lbs. Dimensions, 10 ins. x 10 ins. X 10 feet. Vertical reinforcement, 4-11/16 inch square bars. Example 2.-Design a circular reinforced concrete column with spiral wrappings 12 feet long which will support a load of 59 tons. Solution. (1) P = 59 X 2,000 = 118,000 lbs. (2) Estimate W' at 4,000 lbs. (3) Take C at 350 and r at 12. (4) Take p at 1.5 per cent. (5) For hooping, use 5/16-inch round steel or oval bars having the same sectional area of .076 sq. ins. and let the spirals be spaced apart or have a pitch of 2 inches. With 2 inches of concrete outside of the hooping, the diameter of the post will be 4 + 16 20 inches, and will weigh = .7854 X 20/12 X 20/12 X 12 X 144 = 3,770 lbs., which is less than the estimated weight and is therefore safe. per cent of steel is 3 sq. ins., which is equivalent to 6 square rods. 1.5 3/4 inch 16 500 ; or since .038 is greater than .032 the hooping is in conformity with the condition. (7) The least lateral dimension is 20 inches. 20 inches X 12 = 20 feet. As this is greater than the length of the post, the design easily satisfies the condition as to the ratio of length to least lateral dimension. Summarizing the results of the design, we have for the circular column External load, 59 tons. Weight of column, 3,770 pounds. Diameter of column, 20 inches. Diameter within hooping, 16 inches. Length of column, 12 feet. Vertical reinforcement, 6-3/4 inch square rods. Hooping, 5/16 inch round or oval bars with spirals spaced 2 inches apart. TABLE XX.-TABLE FOR DESIGNING REINFORCED CONCRETE BEAMS AND SLABS+ Medium Heavy Floor Loading-125 Pounds per Square Foot. 1. Bend, diagonally upward, one rod in three, or two rods in four from points in beam to top of beam and over supports. 2. Stirrups are made U-shaped with bent ends. 3. Slab reinforcement is placed at right angles to supporting beams. Cross reinforcement of slightly smaller rods or same rods farther apart is also placed in slabs parallel to beams. 4. Wire fabric or expanded metal mesh may be substituted for rods in the slabs, provided the area of section of metal is kept the same as the rods. + From "Concrete in Factory Construction," published by the Atlas Portland Cement Co. * Place first stirrup in every case 6 inches from support. |