3 FIGURE 7.7 Stress distributions for the beam described in example 7.2. variation of S across the thickness. edge of ply number 2. k:(GX100(0.02)-10X104k: Kl.5X100/0.02-80x100k: K15X100)(008)-45X108k: variation of (E.)z. (a)Normal stresses 9 10.108X 品 (b)Shear stresses y distribution can then be determined to within a constant K2 by finding the as (T)k=K2S,where s is defined by equation (7.21).The shear stress 2bhEr can be set equal to a constant,K2 and the shear stress can be written and equation (7.21).For a given cross section,however,the ratio 3V/ with an even number of uniform thickness plies is given by equation(7.20) The interlaminar shear stress at the inner surface of the kth ply for a beam outer surface as in a homogeneous isotropic beam but,rather,at the outer figure 7.7(a).It is seen that the maximum normal stress occurs not on the The predicted distribution of o,across the thickness is plotted in For the inner surface of ply number 1 (on the neutral surface),,=0. :/k801X51-)100(0601X5。私1大:1 Fo For the inner surface of ply number 2,,=Ki(5x 106)(0.01)=5x 104K1. Similarly,for the outer surface of ply number 2,the stress is ox= For the inner surface of ply number 3,z=0.02 in and the stress is o,= modulus is (E )a=E2 =1.5 x 106 psi,z=0.03 in and the stress is o,= For the outer surface of ply number 3(the outer transverse ply),the ply be determined to within a constant Ki=M/Eby finding the corresponding Principles of Composite Material Mechanics Fork=3 For k=2 for k=1 distribution is substantial,however,because of the small number of plies. the shear stress at the outer surface is zero.The deviation from the parabolic ness is plotted in figure 7.7(b).As with the shear stress in a homogeneous isotropic beam,the maximum shear stress occurs on the neutral surface and surface must be stress-free The predicted distribution ofacross the thick- the outer surface.This also satisfies the boundary condition that the outer material in this"imaginary ply,"S=0 and the shear stress must be zero on of ply number 3 or the outer surface of the laminate.Since there is no Finally,for k=4,equation(7.20)gives the shear stress at the inner surface of an"imaginary ply"whose inner surface is the same as the outer surface Analysis of Laminates -0.833x100pa1(6.74GRa :2.5X1022647.24GPa 装家 2166x100ps118.a4Gpa) 615((+1.5x10 兰 From equation(7.20)and equation(7.21)