The New York Rapid-transit Subway

110 DISCUSSION ON NEW YORK SUBWAY. [Minutes of Mr. Haigh, principle in a permanent structure to allow the tensional side of the concrete to fracture. The subways being designed, as stated in the Paper, with an allowance of 12,000 lbs. per square inch on the steel, long before that stress was reached tensional cracks would occur in the concrete, oxidation of the steel might commence, and when the load came the rods might not be in a condition to bear it. They could be designed to bear the load with the depths adopted in the Subway and yet have the bottom concrete limited to a tensional stress whicli was under the normal breaking-stress. It was not necessary to allow a safe tensional stress, because reliance was not placed on the concrete but on the steel bars. The ratio of the moduli of elasticity was about 20 to 1 before the concrete fractured. Although there were records now available of numerous tests of concrete beams, and the use of that type of construction was rapidly extending on the basis of such tests, it was well to recognize that the element of permanency of reinforced concrete had not yet received the proof it needed. In the meantime an absolutely safe procedure for important engineering structures involving the use of reinforced- concrete beams could be adopted by limiting the compressive stress on the concrete to a safe limit, and reinforcing with steel the lower tensional portion to such a degree that fracturing strain might be presumed not to occur before the required maximum loading was passed. Up to a limit very near to the tensile fracture-strain of concrete, its modulus of elasticity altered very slightly. In order to examine what such a procedure meant in comparison with the flat reinforced-concrete cover adopted for New York, he would take the Author’s limiting compressive stress on the concrete, (500 lbs. per square inch) and ratio (20 to 1) between the moduli of elasticity, and, in addition, he would use a limiting tensile stress of 300 lbs. per square incli:— Let M be the bending moment of maximum external loading on 12 inches breadth of beam ; c » the maximum compressive stress of the upper surface of the beam ; t„ the maximum tensile stress of the concrete at the under- surface of the beam; d „ the depth of beam; A „ tlie cross-sectional area of steel reinforcement; the units being inches and pounds. Then, equating forces and moments in the usual way for the middle of the beam, and assuming the metal to be buried 2 inches—