Brittle Materials under Combined Stress. 911 



Calculation of the Stresses. 



The maximum stress due to bending was calculated from 

 the formula 



in which 



p is the maximum stress. 



y is the greatest distance from the neutral line of the 



section = ~ . 



M is the maximum bending moment acting on the beam. 

 I is the moment of the inertia of the section about its 



neutral line = -prr • 



d is the diameter of the bar. 



The maximum shearing stress due to the torque was given 



q 16T 



S is the maximum shearing stress. 

 T is the torque. 



The maximum principal stress P x was ~ +\/'t- -fS 2 , and 



ihe minimum principal stress P* was - —\ /¥- -fS 2 . The 



/v 2 2 V 4 



stress difference was 2\ / *_ -f S 2 , and the maximum shear 

 /~2 v 4 



stress \/ P £ -fS 2 . 



If the maximum principal stress be represented by P 1? 

 and the least principal stress at the same point by P 3 , then 

 the maximum stress law states that Pi = constant; the maxi- 

 mum strain theory is represented by Pi — ??P 3 = constant, 

 since in these tests the second principal stress, P 2 , is zero ; 

 and the shear stress being constant corresponds to 

 l 3 ! — P 3 = constant. 



Data from the Tests. 



Stress-strain diagrams for a pure torsion test and a simple 

 bending test have been plotted in fig. 2. The diagram shows 



