[4 points (see breakdown below)] The figure shows a truss, where the horizontal and vertical displacements at node 2 (pin support) and the vertical displacement at node 3 (roller support) are fixed to zero. The nodal forces are: H1=0 and V1= -1000 lb at node 1, H3=0 (node 3) and V3, H2, V2 are unknown reaction forces. Obtain the member forces F1, F2, F3 following the procedure described below. It is not necessary to determine the nodal displacements.

(a) [ 2 points] Get the nodal equilibrium equation AF=P by setting up the equilibrium equations at nodes, where F and P are the member force and the nodal force vectors. You need to determine all components Aij of the matrix A, substitute the given values of the nodal forces in P while leaving the reaction forces as

unknowns. (Read la #3 Pr. 8 for the general process of setting up the equilibrium equations like above.) (b) [1 point] This is a system of 6 equations for 3 unknowns. We need only 3 equations to determine the 3 member forces F1, F2, F3. Select three appropriate equations from the above 6 equations and solve for the member forces. (c) [1 point] Now that the member forces are known, determine the reaction forces V3, H2 and V2 with the help of the 3 equations which were not used in (b).

1000 lb 90 F. H2 230 V2