Page 155 - Aircraft Stuctures for Engineering Student

5.4 Combined bending and in-plane loading 139

Y

Fig. 5.13 Component of shear loads in the z direction.
z direction due to the Nxy shear loads only is

or
a2 w aNxy aw
Nxy axay sxsy + - - axsy
ax ay
neglecting terms of a lower order. Similarly, the contribution of N,,x is
d2W dN aw
Nyx axay sxsy + -25 - sxsy
ay ax
The components arising from the direct forces per unit length are readily obtained
from Fig. 5.12, namely

or

a2W aN, dw
N, - SXSY + - - 6x6~
ax2 ax ax
and similarly

The total force in the z direction is found from the summation of these expressions
and is

+ SxSy + 2Nxy - + - - Sxby
8Nxy aw
d2W
SxSy
ax ay aXaE' ay ax