Page 450 - Aircraft Stuctures for Engineering Student

10.6 laminated composite structures 431

so that Eqs (10.57) may be rewritten as

(10.58)

From Section 5.3
M, = J ’ axzdz, M~ = I, 1-112 T,~Z dz
rtl2
tl2
412 ayz dz, Mxy = - J ‘
-t/2
Substituting for a,, cy and rxy from Eqs (10.58) and integrating, we obtain

Writing Cllt3/12 as Dll, C12t3/12 as D12

(10.59)

Similarly

(10.60)

and

(10.61)

For a lamina subjected to a distributed load of intensity q per unit area we see, by
substituting for M,, My and Mxy from Eqs (10.59)-(10.61) into Eq. (5.19), that

(10.62)

Further, for a lamina subjected to in-plane loads in addition to q we obtain, by a
comparison of Eq. (10.62) with Eq. (5.33)

- a2W a2W a2W
-
-+N
-q+Nx-+2N ’ay’ xya~ay (10.63)
ax2
Problems involving laminated plates are solved in a similar manner to those included
in Chapter 5 after the calculation of the modiiied flexural rigidities D1 1, Ol2, DZ2 etc. If
the principal material directions 1 and t do not coincide with the x and y directions in
the above equations, in-plane shear effects are introduced which modify Eqs (10.62)