Page 510 - Aircraft Stuctures for Engineering Student

Problems 491

The root of the cantilever is built-in, warping being completely suppressed there,
and a shearing force S is applied at the tip in the position indicated.
Derive an expression for the resultant end load in a corner longeron. Also calculate
the resultant deflection of the tip, including the effects of both direct and shear strains.
Ans. P = --

where p2 = 4Gr/3dBE (top right hand) (origin for z at free end)

P.11.10 An axially symmetric beam has the thin-walled cross-section shown in
Fig. P. 11.10. If the thickness t is constant throughout and making the usual assump-
tions for a thin-walled cross-section, show that the torsion bending constant rR
calculated about the shear centre S is
TfE

-+

4-
3

Fig. P.11.10

P.ll.ll A uniform beam has the point-symmetric cross-section shown in
Fig. P. 1 1.1 1. Making the usual assumptions for a thin-walled cross-section, show

_-

Fig. P.ll.ll