540 Dr. J. Prescott on the lorsion of 



one of the three strips is 



Q = \ht £t z ds 



and the total torque is the sum of the torques due to the 

 three strips separately. 



Again consider the box section with projecting pieces 

 shown in fig. 9. The shear lines in the projecting pieces 



Fig. 9. 



^ 



go and return along the same strip, whereas all the lines 

 that run along A'A also run along AC. Thus the torque in 

 the part ACC'A' may be obtained from the rules for a closed 

 tube, whereas the torque in the projecting pieces must be 

 obtained from the rules for open tubes. Suppose the width 

 of the strip is constant everywhere and has the value t, and 

 suppose AA' = a, AC = c + £, A / B = 6, and let all the other 

 projecting pieces have a length b. Then the torque in the 

 closed tube is, by (35), 



Qi=] 



imaVt 

 2(a + fi)' 



(65) 



(66) 



and the torque in the four projections is 



Q 2 = $nTtV, 



The total torque is therefore 



Q=Qi + Q 2 



2nra 2 c 2 t . Q7 



= -^J7 + * nTtb W 



It is obvious that the torque due to the projections is 

 negligible compared with that due to the tube. In fact 

 Q 2 is itself of the same order as quantities neglected in 



