Tests for the determination of the moduli of elasticity of con cretes vary considerably in results, and indicate that the modulus depends upon the quality of the concrete, being approximately proportional to the compressive strength. The modulus also varies with the age of the concrete, increasing with age more rapidly than does the strength of the concrete.
The Joint Committee makes the following recommendation 1 concerning the modulus of elasticity: The value of the modulus of elasticity of concrete has a wide range, depending on the materials used, the age. the range of stresses between which it is considered, as well as other conditions. It is recommended that in computations for the position of the neutral axis, and for the resisting moment of beams and for com pression of concrete in columns, it be assumed as: (a) One-fortieth that of steel, when the strength of the concrete is taken as not more than S00 pounds per square inch.
(b) One-fifteenth that of steel, when the strength of the concrete is taken as greater than S00 pounds per square inch and less than 2200 pounds per square inch.
(c) One-twelfth that of steel, when the strength of the concrete is taken as greater than 2200 pounds per square inch and less than 2900 pounds per square inch and (d) One-tenth that of steel, when the strength o. the concrete is taken as greater than 2900 pounds per square inch.
Although not rigorously accurate, these assumptions will give safe results. For the deflection of beams which are free to move longitudinally at the supports, in using formulas for deflection which do not take into account the tensile strength developed in the concrete, a modulus of one-eighth of that of steel is recommended.
104. Reinforced Concrete in Tension.—When reinforced con
crete is subjected to tensile stresses, the two materials act together, each carrying unit stresses in proportion to its modulus of elasticity, so long as the stresses do not exceed the strength of the concrete. When, the steel is stressed to a fair working load, the stress upon .the concrete will have passed its breaking strength, and it can no longer be considered as carrying stress—a condition which usually exists in reinforced concrete beams when carrying normal working loads. The steel in such beams is designed to carry all the tensions, the concrete on the tension side merely holding the steel in place.
In the earlier studies of reinforced beams, it was supposed that the concrete when reinforced became capable of carrying greater tensions than plain concrete, and beam formulas were proposed in which it was assumed that the concrete carried part of the tension. Later investigations, how-ever, showed that this was erroneous and these formulas are no longer used in design.
Observations upon beams under tests have shown that minute cracks, invisible to the naked eye, frequently exist in the concrete surface on the tension side while the beam is carrying only a safe load—a discovery made in testing clamp beams with the tension side uppermost at the University of Wisconsin. Dark, wet lines appeared upon the surface at about the time that the ultimate strength of the concrete was reached, and these later developed into fine cracks. Experience with this type of construction indicates that, when the materials are properly used, no injury results from this overstressing of the concrete, and that the steel is fully pro tected by the concrete.