228 



STRENGTH OF MATERIALS 



the radius, and having its plane at right angles to the axis of the 

 bar; the other arm carries a pointer so arranged as to move over 

 the scale when the bar is twisted. The arc of the scale is called the 

 troptometer arc and the arm supporting it the troptometer arm. The 

 angular distortion at the center of the bar for the given gauge length 

 is then obtained by dividing the reading on the troptometer arc by 

 the length of the troptometer arm plus the radius of the specimen, 

 or, expressed as a formula, 



reading- on troptometer arc 

 An ^ le ( = troptometer arm + radius of specimen ' 



where is the angle of twist (see Article 92). 



Problem 172. A steel rod with a gauged length of 10 in. and .85 in. in diam- 

 eter, when tested in torsion, gave the data tabulated below. Draw the strain 

 diagram, plotting the stress in lb./in. 2 on the outer fiber as ordinates, and the cor- 

 responding angle of twist as abscissas. Also locate the elastic limit, compute the 

 modulus of elasticity of shear, and the modulus of elastic resilience. 



TORSION TEST OF STEEL 



178. Form of torsion test specimen. Specimens for torsion tests 

 are made cylindrical, and usually long enough to get a gauged length 

 of 10 in. The cylindrical form has been adopted because its cross 

 sections remain plane during torsion, whereas hi other forms a cross 

 section which is plane before torsion is deformed into a warped 

 surface by the strain, and therefore does not give a simple shearing 

 stress (see Article 98). The torsion test is used to determine the 

 shearing strength of materials, that is, the resistance offered by the 

 material to one cross section slipping over another (see Article 67). 



