Page 129 - Aircraft Stuctures for Engineering Student

Problems 113

Under some system of loading, member 14 carries a tensile stress of 0.7N/mm2.
Calculate the change in temperature which, if applied to member 14 only, would
reduce the stress in that member to zero. Take the coefficient of linear expansion as
Q: = 24 x 10-6/"C and Young's modulus E = 70 000 N/mmz.
Ans. 5.6"C.

P.4.9 The plane, pin-jointed rectangular framework shown in Fig. P.4.9(a) has
one member (24) which is loosely attached at joint 2: so that relative movement
between the end of the member and the joint may occur when the framework is
loaded. This movement is a maximum of 0.25mm and takes place only in the
direction 24. Figure P.4.9(b) shows joint 2 in detail when the framework is
unloaded. Find the value of the load P at which member 24 just becomes an effective
part of the structure and also the loads in all the members when P is 10 000 N. All
bars are of the same material (E = 70000N/mm2) and have a cross-sectional area
of 300mm2.
Ans. P = 2947N: F12 = 2481.6N(T), F23 = 1861.2N(T), F34 = 2481.6N(T),
F41 = 5638.9N(C), F1, = 9398.1N(T), F24 = 3102.ON(C).

/0.25mrn
600 mm

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I-
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Fig. P,4.9

P.4.10 The plane frame ABCD of Fig. P.4.10 consists of three straight members
with rigid joints at B and C, freely hinged to rigid supports at A and D. The flexural
rigidity of AB and CD is twice that of BC. A distributed load is applied to AB, varying
linearly in intensity from zero at A to w per unit length at B.
Determine the distribution of bending moment in the frame, illustrating your
results with a sketch showing the principal values.
Ans. MB = 7w12/45, Mc = 8w12/45. Cubic distribution on AB, linear on BC
and CD.