Page 212 - Aircraft Stuctures for Engineering Student

196 Structural instability

Fig. 6.30 Effect of taper on diagonal tension field beam calculations.

field beams since, for the latter case, k = 1 giving the results of Eqs (6.106), (6.107)
and (6.94).
In some cases beams taper along their lengths, in which case the flange loads are no
longer horizontal but have vertical components which reduce the shear load carried
by the web. Thus, in Fig. 6.30 where d is the depth of the beam at the section
considered, we have, resolving forces vertically

w- (~T+Fg)Sin@-at(dCOSa)Sina=O (6.117)
For horizontal equilibrium
(FT - FB) COS /3 - gttd COS' = 0 (6.118)
Taking moments about B
wz - FTd COS @ + $gttd2 Cos2 a = 0 (6.1 19)
Solving Eqs (6.117), (6.118) and (6.119) for q, FT and FB

at = td 2w 2a (1 -$tan@) (6.120)
sin
)]
W
FT=-[z+?( 1 --tan@
d cos @ (6.121)
W
FB=-[z-F( )] (6.122)
d cos @ 1 - -tan@
Equation (6.102) becomes
(6.123)

Also the shear force S at any section of the beam is, from Fig. 6.30
s w - (FT + &j) sinp
or, substituting for FT and FB from Eqs (6.121) and (6.122)
G)
S= W 1 --tan/3 (6.124)