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# hw5solutions - Homework 5 Solutions 1 The solid model of...

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Homework 5 Solutions 1. The solid model of the shaft shown to the right was created in class using CUBIT. The shaft has R = 3 cm, L = 5 cm, and h = r = 0.5 cm, and is subjected to torque T of 1000 N-m. Create an ANSYS model from the CUBIT geometry using SOLID45 elements. Compute the maximum torsional stress in the fillet and compare with the textbook values. Ignore large stresses near the applied loads and boundary conditions, and make use of ANSYS cylindrical coordinate system to facilitate load application and results interpretation. Use E = 200 GPa and ν = 0.3. r h R L L Solution: Preliminary Analysis : The preliminary analysis shown here is applicable for both problems 1 and 2. An expression for the stress concentration for a shaft with a fillet is given in Table 17, Case 17c on page 791 of Roark. The stress concentration is written as a multiple of the stress on the smaller area: 3 4 2 3 2 1 2 nom nom max ) 2 ( ) 2 ( ) 2 ( and ) 2 ( 16 where D h C D h C D h C C K h D T K t t + + + = = = π σ In this case σ nom is the shear stress τ r-z at the outer diameter of the smaller shaft. For h / r = 1, the coefficients C 1 through C 4 are C 1 = 1.580, C 2 = -1.796, C 3 = 2.000 and C 4 = -0.784. For 2 h / D = 0.1667, this produces a K t of 1.333. For the dimensions given here, the nominal stress is 40.7 MPa, and the maximum shear stress is expected to be 54.3 MPa. Finite Element Model : The finite element mesh generated in CUBIT was imported into ANSYS. I changed the coordinate system for all the nodes to the global cylindrical frame to facilitate load application. I fixed the nodes on the bottom surface in the Z and Theta directions, and applied a load of 1000 N in the theta (Y) direction to each node on the outer diameter to provide the proper torque. The stress of interest in a shaft in torsion is the shear stress τ θ− z , and I selected only the elements near the fillet for output display in order to ignore the stress concentrations near the load application points. The maximum shear stress was found to be 52.6 MPa, a difference of 3.2 % from the predicted value. See more discussion of the results in problem 2. In this example, the torsional shear stress, τ θ− z, is the most important figure to consider because it is the basis for the stress concentration and also is critical

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from a failure standpoint. In a case of pure shear, if we remember Mohr’s circle, the principle stresses will be equal to the maximum shear, but the yield stress in shear is about 0.577 times the yield stress in tension. 2. Create the same model in ANSYS using TET92 elements. To allow for use of the cylindrical coordinate system, use the Z-axis as the axis of rotation. The model can be constructed by creating the cross-section in the X_Z plane and rotating the area around the axis using the Preprocessor>Operate>Extrude>Areas>About Axis and selecting first the area and then two keypoints which define the axis. I suggest meshing first with an edge length of 0.5 cm and then doing a refinement around the
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hw5solutions - Homework 5 Solutions 1 The solid model of...

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