Second: Microscopical examination of the surface of steel, and of concrete which has been moulded around the steel, shows that the adhesion depends chiefly on the roughness of the steel, and that the cement actually enters into the microscopical indentations in the surface of the metal. Since a stress in the metal even within the elastic limit necessarily reduces its cross-section somewhat, the so called adhesion will be more and more reduced as the stress in the metal becomes greater. This view of the case has been verified by recent experiments by Professor Talbot, who used bars made of tool steel in many of his tests. These bars were exceptionally smooth; and concrete beams reinforced v ith these bars failed generally on account of the slipping of the bars. Special tests to determine the bond resistance, showed that it was far lower than the bond resistance of ordinary plain bars.
Third: There is evidence to show that long-continued vibration, such as is experienced in many kinds of factory buildings, etc., will destroy the adhesion during a period of rears. Some failures of buildings and structures which were erected several years ago, and which were long considered perfectly satisfactory, can hardly be explained on any other hypothesis. Owing to the fact that there are comparatively few reinforced-concrete structures which have been built for a very long period of years, positive information as to the durability and permanency of adhesion is lacking. It must be con ceded, however, that comparative tests of the bond between concrete and steel when the bars are plain and when they are deformed (the tests being made within a few weeks or months after the concrete is made), have comparatively little value as an indication of what that bond will be under some of the adverse circumstances mentioned above, which are perpetually occurring in practice. Non-partisan tests have shown that, even under conditions which are most favor able to the plain bars, the deformed bars have an actual hold in the concrete which is from 50 to 100 per cent greater than that of plain bars. It is unquestionable that age will increase rather than diminish the relative inferiority of plain bars.
277. Computation of the Bond Required in Bars. From Equation 19 we have the formula that the resisting moment at anv point in the beam equals the area of the steel, times the unit tensile stress in the steel, times the distance from the steel to the ccntroid of compression of the steel, which is the distance d .r. We may com
pute the moment in the beam at two points at a. unit-distance apart. The area of the steel is the same in each equation, and d x is substantially the same in each ease; and therefore the difference of moment, divided by (d x), will evidently equal the difference in the unit-stress in the steel, times the area of the steel. To express this in an equation, we may say, denoting the difference in the moment by d J1, and the difference in the unit-stress in the steel by d s : dm x (d x) But A X d s is evidently equal to the actual difference in tension in the steel, measured in pounds. It is the amount of tension which must be transferred to the concrete in that unit-length of the beam. But the computation of the difference of moments at two sections that are only a unit-distance apart, is a comparatively tedious opera tion, which, fortunately, is unnecessary. Theoretical mechanics teaches us that the difference in the moment at two consecutive sections of the beam is measured by the total vertical shear in the beam at that point. The shear is very easily and readily computable; and therefore the required amount of tension to be transferred from the steel to the concrete can readily be computed. A numerical illus tration may be given as follows: Suppose that we have a beam which, with its load, weighs 20,000 pounds, on a span of 20 feet. Using ultimate values, for which we multiply the loading by 4, we have an ultimate loading of S0,000 pounds. Therefore, 1 80,000 X 240 8 2,400,000.
Using the constants previously chosen for 1 :3: 5 concrete, and there fore utilizing Equation 23, we have this moment equal to 397 b Therefore b = 6,045.
If we assume b = 15 inches; d = 20.1 inches; then d .r = .86c1 = 17.3 inches. The area of steel equals: A = .00S4 b d = 2.53 square inches. We know from the Jaws of mechanics, that the moment diagram for a beam which is uniformly loaded is a parabola, and that the ordinate to this curve at a point one inch from the abutment will, in the above case, equal (-1--A-)' of the ordinate at the abutment. This ordinate is measured by the maximum moment at the center, multiplied by the factor (1:1, 14,161 = .9834 ; therefore the actual moment 14,400 at a point one inch from the abutment = (1.00 .9834) = .0166 of the moment at the center. But .0166 X 2,400,000 = 39,840.