[ANSWERED] a. Compute the total stiffness matrix ½K of the assemblage shown in Figure P3–1 by superimposing the

a. Compute the total stiffness matrix ½K of the assemblage
shown in Figure P3–1 by superimposing the stiffness matrices of the individual
bars. Note that ½K should be in terms of A
1
; A
2
; A
3
;
E
1
; E
2
; E
3
; L
1
; L
2
, and
L
3
. Here A; E, and L are generic symbols used for cross-sectional
area, modulus of elasticity, and length, respectively.
b. Now let A
1
= A
2
= A
3
=
A; E
1
= E
2
= E
3
= E, and L
1
= L
2
= L
3
= 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 in
2
, E = 10 10
6
psi,
L = 10 in., and P = 1000 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.