Page 131 - Aircraft Stuctures for Engineering Student

Problems 115

obey a non-linear elastic stress-strain law given by
E=T[l+ (31

E

where r is the stress corresponding to strain E. Bars 15,45 and 23 each have a cross-
sectional area A, and each of the remainder has an area of Ala. The length of
member 12 is equal to the length of member 34 = 2L.
If a vertical load Po is applied at joint 5 as shown, show that the force in the member
23, i.e. FZ3, is given by the equation
any'+' + 3.5~ + 0.8 = 0

where
x = F23/Po and (Y = Po/Ar0

Fig. P.4.12

P.4.13 Figure P.4.13 shows a plan view of two beams, AB 9150mm long and DE
6100mm long. The simply supported beam AB carries a vertical load of 100000N
applied at F, a distance one-third of the span from B. This beam is supported at C
on the encastrk beam DE. The beams are of uniform cross-section and have the
same second moment of area 83.5 x lo6 mm4. E = 200 000 N/mm2. Calculate the
deflection of C.
Am. 5.6mm.

Fig. P.4.13