Page 366 - Aircraft Stuctures for Engineering Student

Problems 347

direct stress due to bending of the beam and show diagrammatically the distribution
of the stress at the section where the maximum occurs.
The thickness t is to be taken as small in comparison with the other cross-sectional
dimensions in calculating the section properties Ixx, Iyy and Ixy.

Ans. uZ-;- = uz,3 = 13w12/384a2t, ui:l = w12/96a2t,
uzT2 =-w12/48a2t

P.9.5 A thin-walled cantilever with walls of constant thickness t has the cross-
section shown in Fig. P.9.5. It is loaded by a vertical force W at the tip and a
horizontal force 2W at the mid-section, both forces acting through the shear
centre. Determine and sketch the distribution of direct stress, according to the
basic theory of bending, along the length of the beam for the points 1 and 2 of the
cross-section.
The wall thickness t can be taken as very small in comparison with d in calculating
the sectional properties I,,, Ixy etc.

Ans. ui:] (mid-point) = -0.05 WZ/td2, uz,l (built-in end) = -1.85 Wl/td2
uiF2 (mid-point) = -0.63 Wl/td2, (built-in end) = 0.1 Wl/td2

Fig. P.9.5

P.9.6 A uniform cantilever of arbitrary cross-section and length I has section
properties, JYX, Iyy and lYy with respect to the centroidal axes shown in Fig. P.9.6.
It is loaded in the vertical (yz) plane with a uniformly distributed load of intensity
wlunit length. The tip of the beam is hinged to a horizontal link which constrains
it to move in the vertical direction only (provided that the actual deflections
are small). Assuming that the link is rigid, and that there are no twisting effects:
calculate:
(a) the force in the link;
(b) the deflection of the tip of the beam.
Ans. (a) 3wZIxy/81xx; (b) wf/8EIxx.