Question

Dovelop the stiffness matrix (k) for each of the spring assemblages shown below

Answer 1

Obtain the global stiffness matrix [K] of the assemblage shown in Figure P2–1 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. (Hint: Do this problem by writing the nodal equilibrium equations and then making use of the force/displacement relationships for each element as done in the first part of Section 2.4. Then solve the problem by the direct stiffness method.)