Q3. (a) A prismatic circular rod with one end fixed is acted on by the specified loadings as shown below. Discretise the rod with two equally long linear truss finite elements and calculate: (i) the global/system stiffness matrix and load vector, and (ii) the nodal displacements and element stresses. (b) The theoretically exact displacement, u(x), at any generic material point a distance x from the fixed end is given by the differential eqn. EA du(x) dx =1,(5 0≤x≤L, with the boundary coditions, when x = 0, u(0) = 0, and when x = L, EA EA du(L)= =P, and where dx E=30x10, A=2.0, L=60.0, ts(x) = 20.0/unit length, P = 50.0 Plot the variation of displacements of points along the length of the rod and critically compare these with your finite element results you have obtained in part (a). ts(x) +u(x) Ans. 475x10 (0)=√(175) (475) 650×10-6 Q4. Solve Q3 when f(x) = 10(1+x)/unit length. Also, find the reaction force at the fixed end and hence assess the validity of your finite element solution.

Q3. (a) A prismatic circular rod with one end fixed is acted on by the specified loadings as shown below. Discretise the rod with two equally long linear truss finite elements and calculate: (i) the global/system stiffness matrix and load vector, and (ii) the nodal displacements and element stresses. (b) The theoretically exact displacement, u(x), at any generic material point a distance x from the fixed end is given by the differential eqn. EA du(x) dx =1,(5 0≤x≤L, with the boundary coditions, when x = 0, u(0) = 0, and when x = L, EA EA du(L)= =P, and where dx E=30x10, A=2.0, L=60.0, ts(x) = 20.0/unit length, P = 50.0 Plot the variation of displacements of points along the length of the rod and critically compare these with your finite element results you have obtained in part (a). ts(x) +u(x) Ans. 475x10 (0)=√(175) (475) 650×10-6 Q4. Solve Q3 when f(x) = 10(1+x)/unit length. Also, find the reaction force at the fixed end and hence assess the validity of your finite element solution.

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter1: Tension, Compression, And Shear

Section: Chapter Questions

Problem 1.6.7P: A wine of length L = 4 ft and diameter d = 0.125 in. is stretched by tensile forces P = 600 lb. The...

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