Q1 FINITE ELEMENT ANALYSIS Consider the following continuous beam, shown in figure Q1, under the action of horizontal lo

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Q1 Finite Element Analysis Consider The Following Continuous Beam Shown In Figure Q1 Under The Action Of Horizontal Lo 1 (53.82 KiB) Viewed 15 times

Q1 FINITE ELEMENT ANALYSIS Consider the following continuous beam, shown in figure Q1, under the action of horizontal load P (which is applied along the centroidal axis of the beam). The first half of the continuous beam (from node 1 to 2) has a flexural rigidity of 2 El and the second half of the beam (from node 2 to 3) has a flexural rigidity of El. Node 1 is fully restrained, node 2 is only free to rotate and node 3 is only free to rotate and translate horizontally. WO Po 2 EI EI L Z Figure Q1 (a) Derive the system flexural stiffness matrix and the system geometric stiffness matrix. You should use static condensation to reduce the system order. (20 marks) (b) Hence, determine the critical value of P that corresponds to the first linear buckling instability of the system in figure Q1. (10 marks) (©) By completing the solution to the eigenvalue problem in Q1(b) sketch (approximately) the buckling mode shapes for the first and second buckling modes. (10 marks) (d) Discuss qualitatively what should happen in an analysis of this problem if the load P was applied along the lower horizontal edge of element between node (2) and (3). (10 marks)