Page 512 - Aircraft Stuctures for Engineering Student

Problems 493

P.11.14 An open section beam of length 21, whose ends are free to warp, consists
of two uniform portions of equal length I, as shown in Fig. P. 1 1.14. The cross-sections
of the two halves are identical except that the thickness in one half is t and in the other
2t. If the St. Venant torsion constant and the torsion-bending constant for the portion
of thickness t are J and r respectively, show that when the beam is loaded by a
constant torque T the relative twist between the free ends is given by
TI
9-
2p1( 10 cosh2 pl - 1)
where

p2 = GJ/EI' and G = shear modulus (constant throughout)

Fig. P.lt.14