Page 367 - Aircraft Stuctures for Engineering Student

348 Open and closed, thin-walled beams

Fig. P.9.6
P.9.7 A thin-walled cantilever has a constant cross-section of uniform thickness
with the dimensions shown in Fig. P.9.7. It is subjected to a system of point loads
acting in the planes of the walls of the section in the directions shown.
Calculate the direct stresses according to the basic theory of bending at the points 1 ,
2 and 3 of the cross-section at the built-in end and half-way along the beam. Illustrate
your answer by means of a suitable sketch.
The thickness is to be taken as small in comparison with the other cross-sectional
dimensions in calculating the section properties Ixx, IxY etc.
Ans. At built-in end, u2,] = -11.4N/mm2, uz,2 = -18.9N/mmZ,
a,,3 = 39.1 N/mmz

Half-way, uz,l = -20.3 N/mm2, u2:2 = -1.1 N/mm2,
(T,,~ = 15.4N/mm2

Fig. P.9.7

P.9.8 A uniform thin-walled beam has the open cross-section shown in Fig. P.9.8.
The wall thickness t is constant. Calculate the position of the neutral axis and
the maximum direct stress for a bending moment M, = 3.5Nm applied about the
horizontal axis Cx. Take r = 5 mm, t = 0.64mm.

Ans. a = 51.9", a,,,,, = 101 N/mm2.