Use the minimum number of Euler–Bernoulli beam finite elements to analyze the beam problems shown in Fig. P5.20. In particular, give:

(a) The assembled stiffness matrix and force vector.

(b) The specified global displacements and forces, and the equilibrium conditions.

(c) The condensed matrix equations for the primary unknowns (i.e., generalized forces) separately. Exploit symmetries, if any, in analyzing the problems. The positive convention used for the generalized displacements and forces is the same as that given in Fig. 5.2.2.

Figure P5.20

 

90 Hinge - 2)