TESTING OF STRUTS. 287 



prevented from being deflected. At A and B are what are 

 called the points of " contrary flexure," the part between 

 A and B being in exactly the same condition as the pillar 

 in Fig. 147. The length of this portion is one-half the 

 total length of the pillar. The same conditions are 

 attained if the ends are built in or fixed in any other way, 

 so long as movement is prevented. 



The third case is shown in Fig. 149. Here the pillar is 

 fixed at one end and free at the other. The point of 

 contrary flexure is at A, the length A B being two-thirds 

 the total length. 



First consider the case of Fig. 146. Let / c be the 

 uniform compressive stress on a cross section of the pillar 

 due to the pressure caused by the load alone. This 

 will be 



f - P 

 f * A' 



where A is the area of the section in square inches. 



Again, let / b be the maximum stress on the concave 

 or compression side of the pillar. Here 



A _-* 



T " I 



(see "Deflection of Beams," par. 14, p. 34). 

 Or, 



, MY 



But M = P. S, where S is the deflection of the middle of the 

 pillar from the vertical, and 



, M. f 

 >a El 

 So that, substituting, 



, PMP y PP 

 '""^ET'T* El 



in this expression, E, the modulus of elasticity, is con- 

 stant for a given material ; and I, the " moment of 

 inertia " = A Jf, where k is the radius of gyration. So 

 that, if C is a constant only depending on the material 



if the total maximum stress be called/, then 



P P P 



