18 



SHEARING. 



sets of stresses, one in tension and one in compression, at 

 right angles to the diagonals of the square, and of e<|ii;il 

 intensity to the shearing stresses. 



In tne case of tension and compression the strain is 

 reckoned as the amount the bar is elongated or shortened ; 

 in shearing the strain is the angle of distortion, as, for 



e B A b or D c. 

 is such that 



1 AA O LAV 14 J. A AAil UJ-JLV kJUJ- LVL A_A Xk7 VA.XV/ tUJ_lii . 



instance, in Fig. 7, the strain is th 



E is the modulus of direct elasticity, am 



e am 



E = 



In a somewhat similar sense there is a modulus of trans- 

 verse elasticity or modulus of rigidity, G, such that 



G= (VI.) 



where is the angle of distortion. 



FIG. 7. 



The relation which exists between the modulus of 

 direct elasticity E and the modulus of rigidity G may be 

 shown in the following \vay : 



Let the angle of distortion be small, say 0. It has been 

 shown that when there are four equal shearing stresses 

 acting along the sides of the square, they are equivalent in 

 their effects to those of two direct stresses at right angles to 

 one another acting along the diagonals of the square, 

 and equal to one another in intensity and also to the 

 shearing stresses. Thus, if S is the shearing siress, f t and 

 / the two stresses along the diagonals, one of which is 

 tensile and the other compressive, then 

 S = ft = fc 



