WORKING STRESS FOR BEAMS. Impact of Live Load. It is well known that the live load, owing to its motion or impact, pro duces greater stresses than the same load at rest; but the amount of this increased effect is largely a matter of judgment. The effect of the live load will depend chiefly upon the relative live-load and dead-load stresses on the member under consideration. In comput ing the stresses in certain parts of railroad bridges, the impact effect of the live load is assumed to add 100 per cent to the stresses; but in reinforced concrete work, the effect of impact is likely to be much less than this. In fixing safe unit working stresses it will be assumed that the live load has been increased by some per cent of itself to reduce it to an equivalent static load.
The Joint Committee on Reinforced Concrete of four national engineering societies recommend that " the tensile stress in the steel shall not exceed 16,000 lb. per sq. in."t _. _. Bond Stress. The ultimate bond strength of plain round soft steel bars is about 250 to 400 lb. per sq. in. of surface of contact, and the usual working stress is 75 lb. per sq. in. Assuming a bond stress of 75 and a tensile stress of 15,000, the length a round rod must be embedded if it is to develop its full working stress is (15,000 X }d') (75 X d) = 50 diameters. For a large rod and a short beam it might be impossible to secure an embedment that would develop the entire strength of the rod, in which case the end of the rod should be anchored by bending a short piece at the end at right angles to the body of the bar or better by passing the rod through a steel plate, or a deformed bar should be used. Tt.e bending of the rod to make it act as web reinforcement also increases its bond resistance.
The Joint Committee recommend: "The bond stress be tween concrete and plain reinforcing bars may be assumed at 4 per cent of the compressive strength at 28 days, or 80 lb. per sq. in. for 2000-lb. concrete; and in the case of drawn wire, 2 per cent or 40 lb. per sq. in. for 2000-lb. concrete." Compression in Concrete. The safe working stress on the extreme fiber of the concrete at a month is usually assumed at 500 or 600 lb. per sq. in., and occhsionally at 700 lb. per sq. in. Numerous tests of beams failing by compression in the concrete show a com pressive strength greater than that usually obtained with cubes. On the other hand, the strength of concrete for a repeated load is less than for a once-applied load. Of course, the concrete grows stronger with age; but if the reinforcement is designed to develop the full strength of the concrete at a month, the safe strength of the steel limits the safe strength of the beam, and hence the strength of the beam does not increase with age. Apparently this relation is some
times overlooked.
The recommendation of the Joint Committee is: "The extreme fiber stress of a beam, calculated on the assumption of a constant modulus of elasticity for concrete under working stresses, may be allowed to reach 32.5 per cent of the compressive strength at 28 days, or 650 lb. per sq. in. for 2000-lb. concrete. Adjacent to the support of continuous beams. stresses 15 per cent higher may be used." Shear in Concrete. If a beam has no web reinforcement, the unit vertical shear should be kept low to prevent failure by diagonal tension; but if the beam has web reinforcement, the unit vertical shear may be considerably larger. For the first case the unit vertical shear, as computed by equation 16, page 232, may be taken at 40 lb. per sq. in.; and for the second case at 100 lb. per sq. in.
The Joint Committee recommend: "Where pure shearing stress occurs, that is, uncombined with compression normal to the shearing surface, and with all tension normal to the shearing plane provided for by reinforcement, a shearing stress of 6 per cent of the compressive strength at 28 days, or 120 lb. per sq. in. on 2000-lb. concrete, may be allowed. In calculations of beams in which diagonal tension is considered to ue taken by the concrete, the vertical shearing stresses should not exceed 2 per cent of the com pressive strength at 28 days, or 40 lb. per sq. in. for 2000-lb. concrete." Coefficient of Elasticity of Concrete. Table 41, page 207, shows the values of the coefficient of elasticity as obtained from compression tests of 12-inch cubes. These results are given to show the effect of age and composition upon the coefficient; but they are not as suitable for use in beam formulas as results deduced from experiments upon beams, since the restraint upon the concrete in the two cases is quite different, and also since the coefficient deduced from beam experiments has been employed in adjusting the constants in the formulas for the strength of beams to make the computed results agree with those obtained by experiments.
Numerous beam experiments by Professor Talbot * show that for a 1 : 3 : 6 limestone concrete about 60 days old and the straight line stress-deformation relation, the coefficient should be taken at not more than 2,000,000 lb. per sq. in. Turneaure and Maurer recommend 2,000,000 as a minimum (apparently for a 1 concrete) and 3,000,000 as a maximum (apparently for a 1 : 2 : 4 concrete). It is usual to consider the coefficient = 2,000,000, i.e., to consider E,, - = 15.