104 Dr. J. Prescott on the Equations of Equilibrium 



to the distance from the middle surface. The residual 

 tensions are equivalent to couples M 3 , M 2 , per unit length of 



Fig. 3. 



M,A 





>>Q. 



sections perpendicular to dx and dy respectively. The 

 residual shear stresses give rise to equal couples Q per unit 

 length about normals to the same two sections. These 

 couples are represented by vectors in fig. 3, the right-handed 

 screw system of representation being understood. The £-axis 

 points upwards — that is, towards the reader. The expressions 

 for these couples, which are correctly given by Poisson's 

 theory, are 



M 



1 = IS? 



-°a 



M,=C 



9 2 i« . 3 2 «o ) 





o ox oy 



where 



=(1 + «)C 



c _2 EA 3 



~d 2 iv 

 'dx'dy 1 



3 1 



(15) 

 (16) 



(17) 

 (18) 



It should be observed that the vector representing Q is 

 along the outward normal for the pair of faces perpendicular 

 to dx, and along the inward normal for the pair of faces 

 perpendicular to dy. 



