Birla Institute of Technology & Science, Pilani Work Integrated Learning Programmes Division AY 2021-2022 S2 EC-1: Assignment 1 Course No. Course Title Weightage Submission due date Date assigned No. of pages in this document Instructions: : AE ZG633 : Advances in vehicle body structures : 10% of course score : 03 MAR 2022 11:30 PM : 4 FEB 2022 :2 1. This assignment is for 50 points, and your EC-1 score will be scaled down to 12.5 points. 2. Upload your submissions through the Taxila system as per the deadline noted above. Your submission must be a single pdf file (multiple files or other file formats are not allowed). Submissions outside the Taxila system (such e-mails, Whatsapp etc.) will not be considered. 3. Plan for unexpected down times and submit early – the system will not accept late submissions. 1. For the state of plane stress with x-y axes as shown, do the following: 1.1 draw the Mohr’s circle using the sign convention discussed in class [4] 1.2 determine the principal normal stresses and the angle from the x-axis to π1 [4] 1.3 draw the state of stress on an element rotated 30° clockwise from the x-axis [4] 2. The varying stresses produced at a certain point in a component subjected to combined axial loading, bending and twisting are as follows (assume that the varying stresses are in phase with each other): (i) (ii) (iii) Axial loading: Constant stress of 20 MPa Bending: Completely reversed load causing 60 MPa maximum stress Twisting: Repeated load causing maximum stress of 50 MPa The fatigue stress concentration factors due to the presence of a hole in the component are: πΎπ for axial loading = 1.1, πΎπ for bending = 1.4, Page 1 of 2 πΎπ for twisting load = 2.0 The material properties of the component are provided below: Yield strength: ππ¦ = 300 πππ Ultimate strength: ππ’ = 400 πππ Completely adjusted endurance limit: πe = 200 πππ Use the modified Goodman criterion for fatigue failure. Answer the following in light of the above: 2.1 Determine if the part has finite or infinite life. [10] 2.2 Calculate the factory of safety guarding against fatigue failure assuming infinite life. [4] 2.3 Calculate the factory of safety guarding against yielding. [6] 3. A machine part is subjected to fluctuating stress over two cycles. In the first cycle, stress varies from ππππ = 140 MPa to ππππ₯ = 420 MPa repeated 50,000 times. In the second cycle, stress varies from ππππ = −200 MPa to ππππ₯ = 350 MPa. The material of the part has ultimate tensile strength ππ’π‘ = 590 MPa, yield strength ππ¦ = 490 MPa, and corrected endurance strength ππ = 200 MPa. Assume π = 0.9. Use the modified Goodman criterion for fatigue failure. 3.1 Calculate the life of the part in each cycle. [15] 3.2 Estimate, using Miner’s rule, the number of load repetitions that the part will endure in the second cycle. [3] -§§§§§- Page 2 of 2