Question

1. Derive the global stiffness matrix for the following two-spring system $k_1$ 3 $k_2$ www 1 ? 2 x 2. a. Obtain the global stiffness matrix $[K]$ of the assemblage shown in Figure 1 by superimposing the stiffness matrices of the individual springs. Here $k_1$, $k_2$, and $k_3$ are the stiffnesses of the springs as shown. b. If nodes 1 and 2 are fixed and a force $P$ acts on node 4 in the positive x direction, find an expression for the displacements of nodes 3 and 4. c. Determine the reaction forces at nodes 1 and 2. $k_1$ $k_2$ P Figure 1 $k_3$ 2 x 3. For the spring assemblages shown in Figure 2, determine the nodal displacements, the forces in each element, and the reactions. Use the direct stiffness method. k=50 lb/in k=100 lb/in k=50 lb/in

          1. Derive the global stiffness matrix for the following two-spring system
$k_1$
3
$k_2$
www
1
?
2
x
2. a. Obtain the global stiffness matrix $[K]$ of the assemblage shown in Figure 1 by
superimposing the stiffness matrices of the individual springs. Here $k_1$, $k_2$, and $k_3$ are the stiffnesses
of the springs as shown.
b. If nodes 1 and 2 are fixed and a force $P$ acts on node 4 in the positive x direction, find
an expression for the displacements of nodes 3 and 4.
c. Determine the reaction forces at nodes 1 and 2.
$k_1$
$k_2$
P
Figure 1
$k_3$
2
x
3. For the spring assemblages shown in Figure 2, determine the nodal displacements, the forces
in each element, and the reactions. Use the direct stiffness method.
k=50 lb/in k=100 lb/in
k=50 lb/in

1. Derive the global stiffness matrix for the following two-spring system
k1
3
k2
www
1
?
2
x
2. a. Obtain the global stiffness matrix [K] of the assemblage shown in Figure 1 by
superimposing the stiffness matrices of the individual springs. Here k1, k2, and k3 are the stiffnesses
of the springs as shown.
b. If nodes 1 and 2 are fixed and a force P acts on node 4 in the positive x direction, find
an expression for the displacements of nodes 3 and 4.
c. Determine the reaction forces at nodes 1 and 2.
k1
k2
P
Figure 1
k3
2
x
3. For the spring assemblages shown in Figure 2, determine the nodal displacements, the forces
in each element, and the reactions. Use the direct stiffness method.
k=50 lb/in k=100 lb/in
k=50 lb/in

Added by Richard D.

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