• University of South Carolina

• EMCH 327

Machine Design (EMCH327 Section 001, Fall 2024) Mid Term Exam 2, 8am, Thursday, Oct. 10, 2024 Name (First/Last): ___________________________________ Score: _______________/100’ 1. Static loading design: A cantilevered hollow tube is subject to the combined loadings. The bending load is 𝐹 = 1.75 kN, the axial tension is 𝑃 = 9 kN, and the torsion is 𝑇 = 72 N ∙ m. Use Ref. h in Appendix Table 15-19 for the relevant cross-sectional properties of the tube, determine the von Mises stress for the point A on the top surface of the tube. Also, for the same point, use the distortion energy theory (DET) to determine the design factor so that the 2014 aluminum alloy with yield strength of 276 MPa can be safely selected as material for the tube. (30’ in total) Solutions: The critical stress element is at point A on the top surface of the tube, where the bending moment is the largest, and the normal and shear stresses induced by the combined loadings are at their maximum values. For point A, this is the plane stress problem (specifically, in xy-plane). For the xyz coordination system established, the 2D plane stress element is shown on the right, with 𝜎𝑥 = 0. Using Ref. h in Appendix Table 15-19, we have following relevant crosssectional properties provided therein: Cross-sectional area 𝐴 = 515.2 mm2 = 515.2 × 10−6 m2 Bending section modulus 𝑆 = 4857 mm3 = 4857 × 10−9 m3 Polar section modulus 𝑍𝑝 = 9715 mm3 = 9715 × 10−9 m3 Since the normal stresses induced by both axial tension and bending moment are along the y-axis, they are additive, giving