Unformatted text preview: MECH 325 Machine Elements
Tutorial 9 – Static Analysis of Shafts 1. Adapted from Shigley, Problem 5‐23 (8th Ed.) (To be demonstrated by the TA) The figure shows a shaft mounted in bearings at A and D. There are pulleys at B and C. The forces shown acting on the pulley surfaces represent the belt tensions. The shaft is to be made of ANSI 1035 steel (Sy = 81 ksi) using a design factor nd = 2.8. a. Draw the shear, bending moment, and torque beam diagrams for the shaft (you may need to draw separate sets of diagrams for the x‐y and x‐z plane) b. Find the net bending moment and torque at A, B, C, and D; use this to determine the location which governs the shaft design c. Determine the stresses as a function of shaft diameter at the governing location (one of A, B, C, or D from above) d. Apply the Distortion‐Energy Failure Criteria to determine the required shaft diameter based on static analysis 2. Adapted from Shigley, Problem 5‐25 (8th Ed.) (To be done by students.) The gear forces shown act in planes parallel to the y‐z plane. The force on Gear A is 300 lbf and the shaft is turning at constant speed. Consider the bearings at O and B to be simple supports. Consider a static analysis, a factor of safety of 3.5, and a yield strength of 60 ksi for the material. Use the distortion‐energy theory to determine the minimum safe diameter of the shaft. Use the same approach as in question 1 (note that the distortion energy theory does require principle stresses to be determined, although doing so will still yield the correct answer). Comments on This Tutorial
This tutorial focuses on static analysis of shafts, and forms the foundation for the upcoming material on dynamic effects and fatigue. Remember: the static analysis is not the whole picture. In addition, this tutorial uses one particular method of predicting failure in materials (the Distortion‐Energy Failure Theory). The details and limitations of this theory are outlined below; many other theories exist for other situations (see Sections 5‐3 to 5‐10). Distortion-Energy Failure Theory
See Section 5‐5. The Distortion‐Energy failure theory estimates the stress at which failure will occur in a ductile material. It is appropriate when the yield strength in tension is approximately equal to the yield strength in compression. The estimate is less conservative than some other approaches (such as the Maximum Shear Stress method). Failure is assumed to occur when the Von Mises stress, σ´, equals or exceeds the yield strength, Sy, with a factor of safety, n σ′ = Sy n For the case of plane stress, the Von Mises stress is computed as σ ′ = σ x 2 − σ xσ y + σ y 2 + 3τ xy 2 For three‐dimensional stress (no longer plane stress) the computation of the Von Mises stress is different, but the approach is the same. See equation 5‐12. ...
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- Fall '10
- Statics, TA, static analysis, Von Mises stress