﻿544 Mr. W. A. Scoble on the Strength and Behaviour 



12. A Formula for Combined Bending and Twisting. 

 The corresponding bending and twisting moments required 

 to cause yield are plotted in fig. 5. The curves are an ellipse 

 Fig-. 5. — Twisting and Bending Moments at Yield. 



IOOO 1500 



Sending Moment i 



through the points representing the limiting cases with load of 

 one kind only, a circle with the smaller moment as radius, and a 

 curve representing the common formula T e = M+ VM 2 + T 2 , 

 T e being the equivalent twisting moment, M the actual bend- 

 ing moment, T the actual twisting moment. The last is 

 ridiculously wrong, and it is difficult to understand why it 

 has found so much favour. Putting T = 0, T e = 2M e . This is 

 only true i£ the tensile and torsional shear strengths are equal, 

 whereas all experimental results indicate that this is far from 

 correct. The ellipse fits the results best, but the circle is 

 recommended on account of an explanation of the difference 

 between the limiting bending and twisting moments which is 

 given later. Thus the formula for combined bending and 

 twisting becomes T e =M e = yMVF + T 2 . 



T e = the equivalent twisting moment. 



M e = „ „ bending # „ 



T = the actual torque to which the shaft is subjected. 



M = „ bending moment to which the shaft 



is subjected. 



