Answer Happy

Question 4 Establish the stiffness matrix and the applied load matrix necessary for a finite element solution of the plane structure shown in Figure Q4. The positions A, B, C and D may be considered to denote nodes 4, 1, 3 and 2 of the structure, respectively. Nodal displacements need only be defined at positions B and D. The elements AB and BC are beam members whereas the rest of the elements are bar members, which can sustain axial load only. The member properties are as follows: Flexural rigidity EI of members AB and BC = 10? Nm? Extensional rigidity EA of members AB and BC = 5 x 10'N Extensional rigidity EA of all other members = 2 x 10’N Х The magnitude of bending moment M at the ends of a beam of length L which is built-in at its two ends and subjected to a uniformly distributed load of w/unit length is given by M = wL?/12. [25 marks] 2 m B С ffff 4 kN/m 10 kN 1.6 m D 2.4 m 0.8 m Figure Q4