IEON AND STEEL 229 



When torsion tests are made, the moment in in. Ib. is read from 

 the machine, and the shearing stress in the outer fiber in lb./in. 2 is 

 computed from the formula, 



p 



where Pa is the twisting moment read from the machine, r the 

 radius of the test piece, and I p the polar moment of inertia of the 

 cross section.* 



The modulus of elasticity in shear is computed from the relation, 



G- (Pa}l , 



~w 



where Pa and I p are defined as above, I is the gauged length in inches, 

 and 6 is the angle of twist in radians. 



The test piece is held in position by a set of adjustable jaws similar 

 to those used in ordinary pipe wrenches. The gauged length should 

 be taken far enough from the ends so that the local stress due to the 

 jaws may not influence the results. 



179. Torsion as a test of shear. Although the torsion test is used 

 to determine the shearing strength of materials, it is not an accurate 

 test, since the shearing stress is a maximum on the outer elements, 

 and zero at the center. For this reason the inner material tends to 

 reenforce the outer, thus giving a higher shearing strength than 

 would otherwise be obtained. A more perfect torsion test would be 

 one made upon a hollow tube of the material, for in this case the 

 inner reenforcing core would not be present. However, the difficulty 

 of obtaining suitable hollow tubes for test pieces makes their use 

 impracticable for ordinary tests. 



A further objection to the torsion test as a test of shearing strength 

 lies in the fact that there is considerable tension in the outer ele- 

 ments of the test piece during the test. Any element of the cylin- 

 drical test piece which is a straight line before the strain becomes a 

 helix during the test. Since the length of the helix is greater than 

 that of the original element, a tensile stress is thus produced in the 

 outer fibers. In fact, in testing wrought iron in torsion the outer 

 fibers often fail in tension along the helix. The slight shortening 



* For a cylinder, I p = 



