70 STRENGTH OF MATERIALS 



only for different specimens of the material but also for different por- 

 tions of the same specimen. For this reason it is impossible to apply 

 to such materials a general method of analysis with any assurance 

 that the results will approximate the actual behavior of the material. 

 For practical purposes, however, the best method is to calculate the 

 strength of such materials by the formulas deduced above, and 

 then modify the result by a factor of safety so large as to include 

 all probable exceptions. 



The behavior of cast iron is more uncertain than that of any other 

 material of construction, and for this reason its use is to be avoided 

 if possible. If two pieces from the same specimen are subjected 

 to tensile strain and to cross-bending strain respectively, it will be 

 found that the ultimate strength deduced from the cross-bending 

 test is about twice as great as that deduced from the tensile test. 

 The reason for this is that the neutral axis does n<>t pass through 

 the center of gravity of a cross section, lying nearer the compression 

 than the tension side, and also because the stresses increase more 

 slowly than their distances from the neutral axis. If, thru, it becomes 

 necessary to design a cast-iron beam, the ultimate tensile strength 

 used in the calculation should be that deduced from tensile tests. 



For materials such as concrete, stone, and cement, the most rational 

 method of procedure is to introduce a correction coefficient ?; in 

 formula (18) and put 



where it has been found by experiment that for granite rj = .96, f<r 

 sandstone rj = .84, and for concrete rj = .97.* 



* Foppl, Festigkeitslehre, p. 144. 



