GATE 2021 ME (ME1) – Question 64

Machine Design · Fatigue strength and S-N diagram · 2 marks · Numerical answer

A machine part in the form of cantilever beam is subjected to fluctuating load as shown in the figure. The load varies from 800 N to 1600 N. The modified endurance, yield and ultimate strengths of the material are 200 MPa, 500 MPa and 600 MPa, respectively. The factor of safety of the beam using modified Goodman criterion is _____ (round off to one decimal place).

100 mm cantilever with 12 mm by 20 mm section and downward tip load ranging from 800 to 1600 N. See the attached source image.

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Correct answer: 1.99 to 2.01

Explanation

Mean and alternating loads are 1200 and 400 N. Section modulus $Z=12(20)^2/6=800$ mm³ gives mean stress 150 MPa and alternating stress 50 MPa.

Modified Goodman gives $1/n=\sigma_a/S_e+\sigma_m/S_{ut}=50/200+150/600=0.5$. Hence **n=2.0**. Maximum stress 200 MPa is below the 500 MPa yield strength.