586 the bell system technical journal, may 1953 



Appendix 



method for analyzing stresses and strains from photoelastic 

 pictures 



The methods for analyzmg photoelastic pictures are given in detail 

 in a number of books and other publications^ and only a brief summary 

 of the method used here will be given. 



When polarized light is sent normal to a plane of photoelastic material 

 that is strained in the plane, the light is broken up into an ordinary and 

 an extraordinary ray that travel with different velocities. It is shown^ that 

 the birefringence, which is defined as the difference between the two 

 indices of refraction m and 112 (i.e. the index of refraction is the ratio 

 between the velocity of light for one of the rays in a vacuum to the 

 velocity in the medium) is given by 



B = Ml - M2 = CV(Ti - T2y + 4.TI , (19) 



where C is a constant called the relative stress optical constant, Ti is 

 the tensional stress along the X axis, T2 the tensional stress along the 

 Y axis and Te the shearing stress in the XY plane. If we change the 

 direction that we call the X axis until we reach the direction of maxi- 

 mum stress, the relations between this stress and the tensional stress 

 at right angles to it are given by the equations 



T[ = Ti cos'^ + 2 sin (9 cos OT^ + T2 sin' 6, 



(20) 

 T2 = Ti sin'^ - 2 sin ^ cos STq + T2 cos' 6, 



where 



d is the angle between the X axis and the axis of maximum tension. 

 [f is chosen so that Ti is a maximum, we find 



tan 29 = ^.^^ (21) 



and 



r; = ^'' t ^^ - iVcr, - T^f + ATI 



(22) 



' Coker and Filon, Photoclasticity, Cambridge University Press, 1931. M. 

 Hetenyi, Handbook of Kxporimental Stress Analysis, John Wiley and Sons, Chap. 

 17, 1950. R. D. Mindlin, J. Applied l^hysics, April 1939, pp. 222-241 and May 1939, 

 pp. 273-294. W. P. Mason, Eleotrooptic and Photoelectric Effects in Crystals, 

 Bell System Tech. J., 29, pp. 161-188, April, 1950. 



