GATE 2018 ME (ME2) – Question 48
A square bar of side a is subjected to a steady load of 60 kN and another load fluctuating from −10 kN to 90 kN. Corrected endurance limit is 150 MPa, yield strength 480 MPa and ultimate strength 600 MPa. For safety factor 2, find a (mm) using modified Goodman’s criterion, to two decimal places.
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Correct answer: 31.60 to 31.65
Explanation
Total load varies from $60-10=50$ to $60+90=150$ kN. Mean load is 100 kN and alternating amplitude 50 kN. Modified Goodman with n = 2 gives $$\frac{50000/A}{150}+\frac{100000/A}{600}=\frac12.$$ Thus A = 1000 mm² and $a=\sqrt A=$ **31.62 mm**. Maximum stress 150 MPa is also below the yield limit with the stated safety factor.