304 Profs. W. E. Ayrton and J. Perry. [Feb. 14, 



From this we see that the greatest shear stress is at the ends of the 

 minor axis, and at the boundary is the least at the ends of the major 

 axis — 



If C is the twisting couple we know that — 



C 



t=_, or 

 A 



t _C qg + ff 

 IS" TraW 



Using these values of t in the above we obtain for the total shear 

 .stress at a point x, y of an elliptic section — 



(5), 



and this at the extremity of the minor axis becomes 



20 



Applying (5) to our case where the twisting couple is Fr cos «, and 

 the bending couple Fr sin a, and recollecting that the direction we 

 have chosen for y on the section is perpendicular to the axis of the 

 spiral, we see that at a point x, y on the section bent about the axis 

 of x, that is, x is perpendicular to the plane in which bending 

 occurs the shear stress q equals — 



2Fr cos a / 



-V&V + ay (6), 



and the tensile or compressive stress p at the point x, y due to bending 

 equals 



-^-JVsin* (7). 



And the resultant tensile, or compressive, stress/ at the point x, y is 



Therefore since 



a* 6 2 



is the equation of the ellipse, the stress at the boundary, 



f=^{v^^+\/y~+^^ 2 -y")) ■ ■ ■ (8). 



