462 IX- DYNAMICS OF DEFORMABLE BODIES. 



The ratio of the tangential stresses on the XZ and YZ planes 

 to the amount of the shear produced , 



is called the sliear modulus of elasticity, or the simple rigidity. 1 ) 

 3. A stretch -squeeze. 



u = ax, v = ~by, w = bz, 

 153) s x = a, s y = s z = l}, <5 = a 26, 



X x = I (a 26) 



Xn = {A (a 26) + 2^#}cos (nx), 

 Y n = {A (a - 26) - 2/^6} cos 



If we choose a and 6 so that 



155 > 6 = 



we have 



X n = 2 11 (a + 6) cos (nx) = ~ a cos (nx). 



If the body is a cylinder, with generators parallel to the X-axis ; 

 bounded by perpendicular ends, experiencing a normal traction p, 

 there is no force on the cylindrical surface, for which cos (nx) = 0, 

 and on the ends 



157) 



The ratio of the tractive force to the -stretch a, 



E=^- 



a 



may be called the stretch or elongation modulus, and is generally 

 known as Young's modulus. 



The ratio of the lateral contraction to the longitudinal extension 



159) r, = l 



1 a 



2 IL 



1) Thomson and Tait use the notation: bulk -modulus =jfe = ^, -[--, simple 



rigidity =w, m = ^-(-/i = -J-^- 



8 



