a. Compute the total stiffness matrix [K] of the assemblage shown in Figure P3-1 by superimposing the stiffness matrices of the individual bars. Note that [K] should be in terms of A1, A2, A3, E1, E2, E3, L1, L2, and L3. Here A, E, and L are generic symbols used for cross-sectional area, modulus of elasticity, and length, respectively.

Figure P3-1

b. Now let A1 = A2 = A3 = A, E1 = E2 = E3 = E, and L1 = L2 = L3 = L. If nodes 1 and 4 are fixed and a force P acts at node 3 in the positive x direction, find expressions for the displacement of nodes 2 and 3 in terms of A, E, L, and P.
c. Now let A = 1 in2, E = 10 × 106 psi, L = 10 in., and P = 2000 lb.
i. Determine the numerical values of the displacements of nodes 2 and 3.
ii. Determine the numerical values of the reactions at nodes 1 and 4.
iii. Determine the stresses in elements 1-3?

Transcribed Image Text:

2 (3 A, Ej, L A2, E, L A3. E). Ly