Materials under Combined Stress. 



123 



elasticity, and to allow several tests to be made on each tube. 

 As in the case of the steel tubes, the yield during each 

 test was kept small. The data obtained from these tests are 

 tabulated below. 



Table C. — Tests of Solid Drawn Copper Tubes. 

 External diameter 0'8812 inch. Internal diameter 0*790 inch. 



Test. 



Bending 

 Moment, 

 lbs. ins. 



Twisting 

 Moment, 

 lbs. ins. 



Tension 



due to 



Bending. 



lbs./s. in. 



Shear 

 Stress 

 due to 



Twisting. 



lbs./s. in. 



Maximum 

 Principal 



Stress, 

 lbs./s. in. 



Minimum 



Principal 



Stress, 

 lbs./s. in. 



Stress 

 Difference | 



=2ce 

 Maximum 



Shear 



Stress. 



A2 







1150 







24200 



24200 



-24200 



48-100 



A3 



300 



1180 



12620 



24800 



31910 



-19290 



51200 



C3 



500 



1100 



21040 



23150 



35920 



-14880 



508(H) 



C2 



800 



910 



33660 



19140 



42330 



- 8670 



51000 



C4 



1000 



730 



42080 



15360 



47080 



- r.ooo 



52080 



B3 



1100 



600 



46300 



12620 



49510 



- 3210 



52720 



B2 



1300 



300 i 



fi4700 



6310 



55450 



- 750 



56200 



r 



1330 







56000 







56000 







56000 



Here again the stress difference is approximately con- 

 stant, and the deviation from this law is opposed to a constant 

 maximum stress, because the stress difference increases 

 steadily with the bending moment. The bending moment 

 and the torque are plotted in fig. 3. 



Deviations from the Shear-Stress Law. 



The stress difference is given in the tables, because it is 

 the difference between the maximum and minimum principal 

 stresses, which it follows. It is now more convenient to 

 deal with the maximum shear stress, which is half the stress 

 difference. The stress difference and maximum shear-stress 

 laws are therefore practically alike, but the former does not 

 indicate the existence of the shearing stress which appears to 

 cause the actual fracture of a ductile material. A ductile 

 material behaves like a viscous fluid after the yield-point, so 

 that it would be expected that the flow is caused by a 

 shearing stress. The stress difference theory indicates a 

 result, but it does not indicate the behaviour of the material. 

 Moreover, the shearing is the stress considered by engineers. 



By referring to the tables it will be seen that the maximum 

 principal stress increases tremendously as the bending 

 moment increases, whereas the maximum shear stress is 



