Page 136 - Aircraft Stuctures for Engineering Student

120 Energy methods of structural analysis

P.4.23 Figure P.4.23 shows a frame pinned to its support at A and B. The frame
centre-line is a circular arc and the section is uniform, of bending stiffness EI and
depth d. Find an expression for the maximum stress produced by a uniform tempera-
ture gradient through the depth, the temperatures on the outer and inner surfaces
being respectively raised and lowered by amount T. The points A and B are unaltered
in position.
Ans. 1.30ETa.

Fig. P.4.23

P.4.24 A uniform, semi-circular fuselage frame is pin-jointed to a rigid portion of
the structure and is subjected to a given temperature distribution on the inside as
shown in Fig. P.4.24. The temperature falls linearly across the section of the frame
to zero on the outer surface. Find the values of the reactions at the pin-joints and
show that the distribution of the bending moment in the frame is
0.59EIaOo COS ?/J
M=
h
given that:
(a) the temperature distribution is
<
9 = 80cos2?/J for - ~/4 ?/J < ~/4
>
8=0 for - ~/4 II, > n/4

Fig. P.4.24