Author: admin

1. a. Assemble the stiffness matrix for the assemblage shown in Figure P3–19 by superimposing the stiffness matrices of the springs. Here k is the stiffness of each spring.
b. Find the x and y components of deflection of node 1.
2. For the plane truss structure shown in Figure P3–20, determine the displacement of node 2 using the stiffness method. Also determine the stress in element 1. Let A = 5 in
2
, E = 1 106 psi, and L = 100 in.

1. Find the horizontal and vertical displacements of node 1 for the truss shown in Figure P3–21. Assume AE is the same for each element.
2. For the truss shown in Figure P3–22 solve for the horizontal and vertical components of displacement at node 1 and determine the stress in each element. Also verify force equilibrium at node 1. All elements have A
1
= 1 in
2
and E = 10
6
psi. Let L = 100 in.

1. For the truss shown in Figure P3–23, solve for the horizontal and vertical components of displacement at node 1. Also determine the stress in element 1. Let A = 1 in
2
, E = 10:0 106 psi, and L = -100 in.
2. Determine the nodal displacements and the element forces for the truss shown in Figure P3–24. Assume all elements have the same AE.

1. Now remove the element connecting nodes 2 and 4 in Figure P3–24. Then determine the nodal displacements and element forces.
2. Determine the displacement components at node 3 and the element forces for the plane truss shown in Figure P3–27. Let A = 3 in
2
and E = 30 106 psi for all elements. Verify force equilibrium at node 3.

1. Show that for the transformation matrix [T] of Eq.
(3.4.15), [T]
T
= [T]
1
and
hence Eq. (3.4.21) is indeed correct, thus also illustrating that [k]=[ T]
T
k’
[T] is the expression for the global stiffness matrix for an element.
2. For the plane trusses shown in Figures P3–29 and P3–30,
determine the horizontal and vertical displacements of node 1 and the stresses
in each element. All elements have E = 210 GPa and A ¼ 4:0 10
4
m
2
.

1. Remove element 1 from Figure P3–30 and solve the problem.
Compare the displacements and stresses to the results for Problem 3.30.
2. For the plane truss shown in Figure P3–32, determine the
nodal displacements, the element forces and stresses, and the support
reactions. All elements have E = 70 GPa and A = 3:0 10
4
m
2
.
Verify force equilibrium at nodes 2 and 4. Use symmetry in your model.

1. For the plane trusses supported by the spring at node 1
in Figure P3–33 (a) and (b), determine the nodal displacements and the stresses
in each element. Let E = 210 GPa and A = 5:0 10
4
m
2
for
both truss elements.
2. For the plane truss shown in Figure P3–34, node 2 settles
an amount d = 0:05 in. Determine the forces and stresses in each element due to
this settlement. Let E = 30 10
6
psi and A = 2 in
2
for
each element.

For the symmetric plane truss shown in Figure P3–35,
determine (a) the deflection of node 1 and (b) the stress in element 1. AE=L
for element 3 is twice AE=L for the other elements. Let AE=L = 10
6
lb/in. Then let A = 1 in
2
, L = 10 in., and E = 10 10
6
psi
to obtain numerical results.

For the space truss elements shown in Figures P3–36 and
P3–37, the global displacements at node 1 have been determined to be u
1
= 0:1 in., v
1
= 0:2 in., and w
1
= 0:15 in. Determine the
displacement along the local x’ axis at node 1 of the elements. The
coordinates, in inches, are shown in the figures.

For the space truss elements shown in Figures P3–38 and
P3–39, the global displacements at node 2 have been determined to be u
2
= 5 mm, v
2
= 10 mm, and w
2
= 15 mm. Determine the
displacement along the local x’ axis at node 2 of the elements. The
coordinates, in meters, are shown in the figures.