Page 206 - Aircraft Stuctures for Engineering Student

190 Structural instability

Fig. 6.25 Determination of flange forces.
in the web, together with direct loads FT and FB in the top and bottom flanges
respectively. FT and FB are produced by a combination of the bending moment Wz
at the section plus the compressive action (a,) of the diagonal tension. Taking
moments about the bottom flange
aztd2
WZ = FTd - -
2
Hence, substituting for a- from Eq. (6.97) and rearranging
wz w
F==-+- (6.98)
d 2tana
Now resolving forces horizontally
FB - FT + aztd = O
which gives, on substituting for nz and FT from Eqs (6.97) and (6.98)
wz w
FB=--- (6.99)
d 2tana
The diagonal tension stress a, induces a direct stress a,, on horizontal planes at any
point in the web. Thus, on a horizontal plane HC in the element ABCD of Fig. 6.24
there is a direct stress a,, and a complementary shear stress 7, as shown in Fig. 6.26.

B

Fig. 6.26 Stress system on a horizontal plane in the beam web.