Page 509 - Aircraft Stuctures for Engineering Student

490 Structural constraint

S1 u1 =constant
-.
L
._I
p1,o +

\
u2 = constant
Fig. P.11.8
members vary such that the direct stresses 01 and az in the edge members are
constant.
Assuming that transverse strains are prevented, that the sheet transmits shear stress
only and that each part has suitable end members to take the complementary shear
stresses, derive expressions for the variation of direct stress a3 in the stringer and
for the variation of shear flow in the upper panel in terms of the dimensions given
and the elastic moduli E and G for the material.
sinh pz
[l
Ans. a3 = (T) -coshpz-- (1 - cosh,d) 1
sinh pl
cosh pz
q1 =A(T)p[sinhpz+- sinh pl (1 - coshpl) 1

where
p2 = 2GtlbAE
P.11.9 A uniform cantilever of length 1 has the doubly symmetrical cross-section
shown in Fig. P.11.9. The section shape remains undistorted in its own plane after
loading. Direct stresses on the cross-section are carried only in the concentrated
longeron areas shown, and the wall thickness dimensions given relate only to shearing
effects. All longerons have the same Young’s modulus E and all walls the same
effective shear modulus G.

I

Fig. P.11.9