BOND BETWEEN STEEL AND CONCRETE. In order that the re inforcement and the concrete may act in unison, it is necessary that there be adhesion or bond between the steel and the concrete. Ob viously, for a beam uniformly loaded the tension on the steel is a maximum at the center of the beam and decreases each way toward the end, the difference in the tension between any two points being transmitted to the concrete by the bond between the steel and the concrete. This increment (or decrement) of the tension in the steel is finally transferred to the compression area of the concrete, and becomes an increment (or decrement) to the compressive stress in the concrete above the neutral axis.
To find a formula for the bond stress proceed as follows: Let V = the total vertical shear at any section, that is, the reaction at the end support minus the load between the support and the section; and z = distance along the beam.
substituting V and transposing • dT is the rate of change in the total tensile stress in the reinforcement dx at the section under consideration, and is for a unit of length of the beam; and measures the force that is transmitted to the concrete by the bond or adhesion. If B = the bond per unit of area of the surface of the bar, m = the number of reinforcing bars, s = the surface of a bar per unit of length, then V can be determined when the condition of loading is known, and jd can be found by equation 4, page 227, or really by equation 3, page 227; and therefore the bond stress required per unit of surface of the reinforcing rods can be determined by equation 15 above. It should be noticed that the bond stress depends upon j, which in turn depends upon the steel ratio and upon the ratio of the coefficient of elasticity of the steel to that of the concrete.
Equation 15 is for horizontal reinforcement, and if the reinforcing bars are inclined or bent up from the horizontal, the above differ entiation is no longer true, since jd then becomes a variable. How ever,. for reasons that will appear in the next section, this limitation is not important.
The bond is due to the adhesions of the cement and also to the gripping action of the concrete in setting; and may be deter mined either by applying a direct pull or push to a bar embedded in concrete, or by applying the preceding formula to the results obtained by testing a reinforced concrete beam. The following conclusions concerning bond are the results of experiments.* Dif ference in the size of the reinforcing rods makes little or no difference in the bond resistance. Flat bars give considerably less resistance than round ones; and bars having a surface as they come from the rolls give about twice the resistance of those having a polished surface. The bond resistance is greater for wet than for dry concrete, and is greater for rich than for lean mixtures; and increases with the age of the concrete. Since concrete setting in air contracts while that
setting in water expands, it is probable that the bond is greater for concrete setting in air than in water; but this has not been proved by experiment. A small amount of rust on the steel increases the bond resistance; but if the rust is thick enough to fort scales, it greatly decreases the bond. After the bond has been broken, plain rods give a frictional resistance of about two thirds of the original bond resistance.
The bond stress for plain round mild steel rods in beams failing by tension of the steel varied from 70 to 193 lb. per sq. in.; while applying a direct pull to similar bars embedded in similar concrete gave bond resistances from 200 to 500 lb. per sq. in.* Other experi menters get results for the direct tests running as high as 750 lb. per sq. in. for plain round rods, while the results for deformed bars (§ 465) are still higher. Only a few experiments have been made to determine the bond resistance developed in a beam under stress, but apparently the value thus determined is only about 70 per cent of that obtained by direct experiment. However, it is safe to conclude that a beam reinforced with plain round steel bars is ordinarily in no danger of failing through insufficient bond between the steel and the concrete; in other words, at the time when a beam fails by tension in the steel, the factor of safety of the bond resistance is 21 to 4 for ordinary structural steel, and 11 to 21 for steel having an elastic limit of 55,000 lb. per sq. in.t Before the laws of flexure of reinforced concrete were clearly understood, there were introduced a number of special or deformed bars whose surface has such a shape as to increase the bond stress considerably. Several of the more common of these bars are shown in Fig. 28, page 236. Since plain bars ordinarily give more than enough bond resistance to develop the elastic limit of the steel, it is clear that generally there is no advantage in these special forms, the only exception being for short, heavily loaded beams in which there is not space for sufficient embedment of the rods to develop the required bond stress with plain steel rods (see 4 472). Some con structors employ deformed bars where the concrete is to set under water (see 4 456).
A misinterpretation of the cause of failures of reinforced concrete beams seemed to show that the failure was due to the slipping of the reinforcing rod in the concrete; but the true interpretation probably is that the slipping was the result and not the cause of the failure, i.e., the slipping took place after failure due to some other cause.