GATE ME 2020 Set 2 — Question 31
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Machine Design → Static & Dynamic Loading → Fatigue, S-N Diagram & Endurance
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Question
A machine member is subjected to fluctuating stress . The endurance limit of the material is 350 MPa. If the factor of safety used in the design is 3.5 then the maximum allowable value of is __________ MPa
(round off to 2 decimal places).
(round off to 2 decimal places).
Correct answer
99.98 to 100.02
Solution
The given fluctuating stress is .The maximum stress is (when ).
The minimum stress is (when ).The mean stress, , is calculated as:The stress amplitude, , is calculated as:Since the mean stress is zero, this is a case of completely reversed stress cycle. For design against fatigue under such conditions, the stress amplitude is compared with the endurance limit ().The factor of safety (FOS) is given by:Given values are:
Endurance limit, MPa
Factor of safety, Substituting the values into the formula:Since , we have:Solving for the maximum allowable value of :Rounding off to 2 decimal places, the value is 100.00 MPa.
The minimum stress is (when ).The mean stress, , is calculated as:The stress amplitude, , is calculated as:Since the mean stress is zero, this is a case of completely reversed stress cycle. For design against fatigue under such conditions, the stress amplitude is compared with the endurance limit ().The factor of safety (FOS) is given by:Given values are:
Endurance limit, MPa
Factor of safety, Substituting the values into the formula:Since , we have:Solving for the maximum allowable value of :Rounding off to 2 decimal places, the value is 100.00 MPa.
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