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 𝜎1
[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:
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 𝑀𝑃𝑎
Ultimate strength: 𝑆𝑢 = 400 𝑀𝑃𝑎
Completely adjusted endurance limit: 𝑆e = 200 𝑀𝑃𝑎
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
𝜎𝑚𝑖𝑛 = 140 MPa to 𝜎𝑚𝑎𝑥 = 420 MPa repeated 50,000 times. In the second cycle, stress varies from
𝜎𝑚𝑖𝑛 = −200 MPa to 𝜎𝑚𝑎𝑥 = 350 MPa. The material of the part has ultimate tensile strength 𝑆𝑢𝑡 =
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.
[15]
3.2 Estimate, using Miner’s rule, the number of load repetitions that the part will endure in the second
cycle.
[3]
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