Obtain the global stiffness matrix K of the assemblage shown in Figure P2-1 by s

Question

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. 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. 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.) Figure P2-1

Explanation / Answer

we have

tension will remain same in all the spring

thus

X= x1+ x2+ x3

0r T/K= T/K+ T/K2 + T/K3

thus

a)1/K= 1/K1 +1/K2 +1/K3

now

x2=

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