Paul Chapman, Assoc. M. Am. Soc. C. E. (by letter).—Mr. Godfrey has pointed out, in a forcible manner, several bad features of text-book design of reinforced concrete beams and retaining walls. The practical engineer, however, has never used such methods of construction. Mr. Godfrey proposes certain rules for the calculation of stresses, but there are no data of experiments, or theoretical demonstrations, to justify their use.
It is also of the utmost importance to consider the elastic behavior of structures, whether of steel or concrete. To illustrate this, the writer will cite a case which recently came to his attention. A roof was supported by a horizontal 18-in. I-beam, 33 ft. long, the flanges of which were coped at both ends, and two 6 by 4-in. angles, 15 ft. long, supporting the same, were securely riveted to the web, thereby forming a frame to resist lateral wind pressure. Although the 18-in. I-beam was not loaded to its full capacity, its deflection caused an outward flexure of 3/4 in. and consequent dangerous stresses in the 6 by 4-in. angle struts. The frame should have been designed as a structure fixed at the base of the struts. The importance of the elastic behavior of a structure is forcibly illustrated by comparing the contract drawings for a great cantilever bridge which spans the East River with the expert reports on the same. Due to the neglect of the elastic behavior of the structure in the contract drawings, and another cause, the average error in the stresses of 290 members was 18-1/2%, with a maximum of 94 per cent.
Mr. Godfrey calls attention to the fact that stringers in railroad bridges are considered as simple beams; this is theoretically proper because the angle knees at their ends can transfer practically no flange stress. It is also to be noted that when stringers are in the plane of a tension chord, they are milled to exact lengths, and when in the plane of a compression chord, they are given a slight clearance in order to prevent arch action.
The action of shearing stresses in concrete beams may be illustrated by reference to the diagrams in [Fig. 3], where the beams are loaded with a weight, W. The portion of W traveling to the left support, moves in diagonal lines, varying from many sets of almost vertical lines to a single diagonal. The maximum intensity of stress probably would be in planes inclined about 45°, since, considered independently, they produce the least deflection. While the load, W, remains relatively small, producing but moderate stresses in the steel in the bottom flange, the concrete will carry a considerable portion of the bottom flange tension; when the load W is largely increased, the coefficient of elasticity of the concrete in tension becomes small, or zero, if small fissures appear, and the concrete is unable to transfer the tension in diagonal planes, and failure results. For a beam loaded with a single load, W, the failure would probably be in a diagonal line near the point of application, while in a uniformly loaded beam, it would probably occur in a diagonal line near the support, where the shear is greatest.
It is evident that the introduction of vertical stirrups, as at b, or the more rational inclined stirrups, as at c, influences the action of the shearing forces as indicated, the intensity of stress at the point of connection of the stirrups being high. It is advisable to space the stirrups moderately close, in order to reduce this intensity to reasonable limits. If the assumption is made that the diagonal compression in the concrete acts in a plane inclined at 45°, then the tension in the vertical stirrups will be the vertical shear times the horizontal spacing of the stirrups divided by the distance, center to center, of the top and bottom flanges of the beam. If the stirrups are inclined at 45°, the stress in them would be 0.7 the stress in vertical stirrups with the same spacing. Bending up bottom rods sharply, in order to dispense with suspenders, is bad practice; the writer has observed diagonal cracks in the beams of a well-known building in New York City, which are due to this cause.
In several structures which the writer has recently designed, he has been able to dispense with stirrups, and, at the same time, effect a saving in concrete, by bending some of the bottom reinforcing rods and placing a bar between them and those which remain horizontal. A typical detail is shown in [Fig. 4]. The bend occurs at a point where the vertical component of the stress in the bent bars equals the vertical shear, and sufficient bearing is provided by the short cross-bar. The bars which remain horizontal throughout the beam, are deflected at the center of the beam in order to obtain the maximum effective depth. There being no shear at the center, the bars are spaced as closely as possible, and still provide sufficient room for the concrete to flow to the soffit of the beam. Two or more adjacent beams are readily made continuous by extending the bars bent up from each span, a distance along the top flanges. By this system of construction one avoids stopping a bar where the live load unit stress in adjoining bars is high, as their continual lengthening and shortening under stress would cause severe shearing stresses in the concrete surrounding the end of the short bar.
