CV3602 Question 5 (20 Marks) a) Derive elements N2, B2 and k22 of the interpolation [N], strain-displacement [B] and sti

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Cv3602 Question 5 20 Marks A Derive Elements N2 B2 And K22 Of The Interpolation N Strain Displacement B And Sti 1 (58.17 KiB) Viewed 15 times

CV3602 Question 5 (20 Marks) a) Derive elements N2, B2 and k22 of the interpolation [N], strain-displacement and stiffness [k] matrices respectively of the 3-node bar element of Figure Q5a, with parabolic shape functions. [6 Marks] EA=constant 3 х L/2 L/2 Figure Q5a b) The bar of Figure Q5b with uniform rigidity EA and length L is fixed at both ends, and carries a linear distributed load q = 20x over its left half only. Furthermore, it carries a point load P = 10L2 applied at a distance L/4 from its right end. Determine the displacement at the middle and the stress field of the bar using the 3-node bar element with parabolic shape functions of Figure Q5a. Comment on the accuracy of the results. (14 Marks] q=20x P= 10L2 2 X EA = constant L/2 L/4 L/4 * Figure Q5b