488 



X. STATICS OF DEFORMABLE BODIES. 



We thus obtain 



u**fl9*, v= -fxs, w 



The curves of equal longitudinal 

 displacement, or contour-lines of 

 the buckled sections, are equi- 

 lateral hyperbolas (Fig. 153). The 

 stresses are, by 112), 



Fig. 153. 



The twisting couple is 



f* f* f* r* 



120) N= I I (xY z - yX,) dS = - ^t. / / (a* y * + tftf) dx dy> 



In a similar we may deal with an equilateral triangular prism. 

 If a be the radius of the inscribed circle, the equation of the boundary 

 may be written, 



(x -d)(x- i//3 + 2 a) (x + y V 3 + 2 a) = 0, 



or 



The function J.(.^ 3 ~3^ 2 ) is 

 a circular harmonic, and 



is constant on the boundary if 

 we take 



Fig. 154. 



The curves of equal distortion 

 are shown in Fig. 154. 



For any contour we have 

 for the couple, from 112) 



121) N 



(xY 2 - 



