Page 553 - Aircraft Stuctures for Engineering Student

534 Matrix methods of structural analysis

Ans. v1 = -PL/.\/ZAE, v3 = -0.293PL/AE, SI2 = P/2 = SI4

S23 = -0.207P = S43, 5'13 = 0.293P
Fx,2 = -Fxq4 = 0.207P, Fy,2 = Fy,4 = P/2
P.12.2 Use the stiffness method to find the ratio HIP for which the displacement
of node 4 of the plane pin-jointed frame shown loaded in Fig. P.12.2 is zero, and for
that case give the displacements of nodes 2 and 3.
All members have equal axial rigidity EA.

Ans. HIP =0.449, v2 = -4P1/(9 + 2A)AE
v3 = - 6PL/(9 + 2a)AE

I'

1
Fig. P.12.2

P.12.3 Form the matrices required to solve completely the plane truss shown in Fig.
P.12.3 and determine the force in member 24.41 members have equal axial rigidity.
Ans. S24 = 0.

Fig. P.12.3