EC-1 Assignment 1

Birla Institute of Technology & Science, Pilani
Work Integrated Learning Programmes Division
AY 2021-2022 S2
EC-1: Assignment 1
Course No.
Course Title
Submission due date
Date assigned
No. of pages in this document
: AE ZG633
: Advances in vehicle body structures
: 10% of course score
: 03 MAR 2022 11:30 PM
: 4 FEB 2022
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
1.1 draw the Mohr’s circle using the sign convention discussed in
1.2 determine the principal normal stresses and the angle from
the x-axis to 𝜎1
1.3 draw the state of stress on an element rotated 30° clockwise
from the x-axis
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):
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:
𝐾𝑓 for axial loading = 1.1,
𝐾𝑓 for bending = 1.4,
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𝐾𝑓 for twisting load = 2.0
The material properties of the component are provided below:
Yield strength: 𝑆𝑦 = 300 π‘€π‘ƒπ‘Ž
Ultimate strength: 𝑆𝑒 = 400 π‘€π‘ƒπ‘Ž
Completely adjusted endurance limit: 𝑆e = 200 π‘€π‘ƒπ‘Ž
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.
2.2 Calculate the factory of safety guarding against fatigue failure assuming infinite life.
2.3 Calculate the factory of safety guarding against yielding.
3. A machine part is subjected to fluctuating stress over two cycles. In the first cycle, stress varies from
πœŽπ‘šπ‘–π‘› = 140 MPa to πœŽπ‘šπ‘Žπ‘₯ = 420 MPa repeated 50,000 times. In the second cycle, stress varies from
πœŽπ‘šπ‘–π‘› = −200 MPa to πœŽπ‘šπ‘Žπ‘₯ = 350 MPa. The material of the part has ultimate tensile strength 𝑆𝑒𝑑 =
590 MPa, yield strength 𝑆𝑦 = 490 MPa, and corrected endurance strength 𝑆𝑒 = 200 MPa. Assume
𝑓 = 0.9. Use the modified Goodman criterion for fatigue failure.
3.1 Calculate the life of the part in each cycle.
3.2 Estimate, using Miner’s rule, the number of load repetitions that the part will endure in the second
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