**Q1. Axial Loading of Stepped Rod (30 Marks)**

A stepped rod ABCD consisting of solid circular segments is subjected to three axial forces, as shown in Figure Q1. Solve the problem using both analytical solutions and finite element analysis. Use the Excel sheet provided to determine the dimensions of the stepped rod and applied forces.

**(A) **Develop Finite Element (FE) Models to determine the stresses and displacements in each of the segments of the loaded stepped rod. Use 3 mesh sizes, coarse, medium and fine, in your analysis (size of fine mesh should not be greater than 10mm).

**(B)** Determine the stresses and displacements in each of the segments of the loaded stepped rod using analytical solutions. Include the axial load diagram.

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**Q2. ****Torsion of Cantilevered Shaft (25 Marks)**

Using the geometry developed in Q1, apply torsional loads to the geometry as shown in Figure Q2. Solve the problem using both analytical solutions and finite element analysis. Use the Excel sheet provided to determine the applied torque

**(A)** Develop Finite Element (FE) Models to determine the shear stress in each of the segments of the loaded stepped rod. Use 3 mesh sizes, coarse, medium and fine, in your analysis. (size of fine mesh should not be greater than 10mm)

**(B)** Determine the shear stress in each of the segments of the loaded stepped rod using analytical solutions (Include the torque diagram). Compare your results with the analytical solutions.

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