Q4. A compound bar as shown in Figure Q4 carries the axial nodal forces of 10 kN at node 2 and 30 kN at node 3. Node 1 is a rigid support and node 2 is a rigid joint. The cross-sectional area (A) of members at the nodes and the length (L) and modulus of elasticity (E) of the members are shown in the figure. Analyze the compound bar using Finite Element Method by employing two-noded line element for each member, (a) calculate the displacement at node 2 and node 3, and (b) determine the axial stress in the members.
$A_1 = 1255 \, mm^2$
$L = 1000 \, mm$
$E = 200 \, kN/mm^2$
$A_2 = 784 \, mm^2$
$L = 800 \, mm$
$E = 28 \, kN/mm^2$
$A_3 = 784 \, mm^2$
Figure Q4