6-170 



DESIGN OF LAMINATES 



Case 2. Plates with Clamped Edges Under Uniform Loads 



The deflection equation for plates with clamped edges under uniform loads is (18): 



w = As x 



(x - a Jt\ (n-3 ) 

 sin 6 n T) sinh y n (n-3 J 



H n (3) 



sin ^ n (r\-$ J sinh 



Y n n + 



iin \ X + 



V^T 



sin c m (x-a) sinh d n x + sin c,^ sinh d m (x-a) 



sin a m r\ > (6. 61) 



where : 



m = T d -= a mP c m =a n o 



H n (0) = Y n sin6 n 3 + 6 n sinh Y n 3 

 K m (a) = d m sin c n a + c m sinh d m a 



b m = 



So. 



m 



8°m\" A nVnV^ 



83 _ a 



a„ = TT~3 " a 



^aV — E 

 a Zn (c 2 + 



°m d m G m( a ) 



1 Zffi (c 2 ♦ \ 2 + d 2)2 _ Uc 2 x 2 



\ m n m/ ^ m n 



cos 5 n 3 + cosh Yn3 



F n (P) "> 



/_p_\sin6 n 3 + sinh Y n 3 



G m (a) =v 



cos c a + cosh d m a 



(4) 



sin c m a + sinh d m a 



Symbols not defined are as previously noted. 



From this general deflection equation 6.61, the following basic plate moment equations 

 and the equation for the deflection at the center of the plate have been derived: 



1=\ 



Fig. 6-49. Uniformly Loaded 

 Plates with Clamped Edges 



