Page 449 - Aircraft Stuctures for Engineering Student

430 Stress analysis of aircraft components
Suppose the lamina of Fig. 10.66 is subjected to stresses 01, at and qt acting
simultaneously. From Eqs (1.42) and (1.46)

at
et = - - qt- (10.54)
Et
71t
7lt = -
Glt
Solving the first two of Eqs (10.54), we obtain

(10.55)

Also 71t = Gltylt I
Equations (10.55) may be written in matrix form as

(10.56)

in which

c21 = (= CI2, see Eq. (10.52))
1 - YPtI
Et
c22 =
1 - YPtl
c33 = Gt
Suppose now that the longitudinal and transverse directions coincide with the x and y
axes respectively of the plates in Chapter 5. Equations (10.56) then become

(10.57)

From Eqs (1.27), (1.28) and the derivation of Eq. (5.13) we see that

a'w . a2W a'W
E, = -z-, EY = -z-, rxy = -2z-
ax2 aY2 axay