Figure shows a conical frustum shaped rod fixed between rigid walls. A distributed axial load of...

 

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Figure shows a conical frustum shaped rod fixed between rigid walls. A distributed axial load of 10kN/m intensity is acting on the rod and there is a temperature increase from 20 °C to 50 °C. The diameter of cross section at left end is 0.2m, the diameter at right end is 0.1m and the length of the rod is 1.2m. The rod material is A-36 steel with E=200 GPa and a=11.7x10-6 (°C) ¹. a) Calculate support reactions and the maximum magnitude of stress (compressive or tensile) throughout the rod. Check convergence of results by increasing the number of elements in your FE model (Calculate for reaction forces and max stress and stop iterations if |E₂|<1% for all unknowns). Present your results in a table. b) Obtain the governing differential equation and boundary conditions by the principle of virtual work. Solve this equation by one of the weighted residual methods of your choice. Compare results of FEM and this method for the axial displacement and normal stress in a table or figure. du Hint: Use polynomial trial functions and take o = E dx account for the thermal effects. aAT in virtual strain energy to 0.2 m 1.2 m- 10kN/m 0.1 m Figure shows a conical frustum shaped rod fixed between rigid walls. A distributed axial load of 10kN/m intensity is acting on the rod and there is a temperature increase from 20 °C to 50 °C. The diameter of cross section at left end is 0.2m, the diameter at right end is 0.1m and the length of the rod is 1.2m. The rod material is A-36 steel with E=200 GPa and a=11.7x10-6 (°C) ¹. a) Calculate support reactions and the maximum magnitude of stress (compressive or tensile) throughout the rod. Check convergence of results by increasing the number of elements in your FE model (Calculate for reaction forces and max stress and stop iterations if |E₂|<1% for all unknowns). Present your results in a table. b) Obtain the governing differential equation and boundary conditions by the principle of virtual work. Solve this equation by one of the weighted residual methods of your choice. Compare results of FEM and this method for the axial displacement and normal stress in a table or figure. du Hint: Use polynomial trial functions and take o = E dx account for the thermal effects. aAT in virtual strain energy to 0.2 m 1.2 m- 10kN/m 0.1 m

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Part a Support Reactions and Maximum Stress Model and convergence To calculate the support reactions and maximum stress we can use the finite element ... View the full answer