80 



ueoessai-y to have nnifonu materials of good quality. The elements of the 

 strength of the materials entering into the beams were determined first 

 of all ; namely, the compressive and tensional sti'ength of the concrete, to- 

 gether with the niodnlns of elasticity of the concrete, both in tension and 

 compression ; the adhesion bet\^een the cement and the steel ; the elastic 

 limit of the steel ; a mechanical analysis made of the materials. Since 

 the beams were long in span compared to their height, and, therefore, the 

 shearing stresses were not important, rods of smooth steel were used. 

 Having determined all the elements entering into the strength of the 

 beam, and then the tested strength of the beam itself, it next became neces- 

 sary to formulate a mechanical analysis of the combination of steel and 

 concrete in flexure, and, with the experience of the tests of the beams in 

 hand, to derive equations for design and calculation. The truth of these 

 equations and the Aalidity of the process of the analysis could then be 

 checked by reference to the tested strength of the l)eams. These equations 

 were derived and have been used very largely by engineers throughout the 

 country in designing reinforced concrete structures. 



Engineers as a rule have found it necessary to review their knowl- 

 edge of mechanics in dealing with reinforced concrete, not that there is 

 any new principle invohed. but the number of factors in the equations of 

 flexure is greater, and an account nmst be taken of the relative moduli 

 of elasticity of the two materials, steel and concrete. Furthermore, the 

 lack of perfect elasticity of the concrete leads to an assumption of some 

 other than a rectilinear relation between stress and strain. 



Again the neutral axis of the cross section must be determined. Its 

 location is not simply fixed by the center of gravity of the cross section, 

 but is controlled by the amount of steel present, the relative moduli of 

 elasticity of the steel and concrete, and by the position of the steel. The 

 writer's equations have followed the usual assumptions of flexure, with the 

 following special assiniiptions : 



1. That the modulus of elasticity of concrete in tension and com- 

 pression is the same. 



2. That there is a parabolic relation between stress and strain in the 

 concrete. 



3. That in the earlier stages of the loading of the beam the concrete 

 cariies stress in tension, but later, at higher loads, this tensile strength 

 may be disregarded. 



The equations are somewhat cumbersome, but have been reduced to 



