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).

Answer :

Correct answer is : 2

Given b = 12 mm, d = 20 mm; σ_ut = 600 MPa, σ_e = 200 MPa;

Load varies from 800 N to 1600 N

⇒ Moment varies from 800 × 0.1 N-m to 1600 × 0.1 N-m

⇒ M_max = 160 N-m, M_min = 80 N-m;

Now

${\sigma }_{max}=\frac{6\times 160}{0.012\times {20}^2}=200MPa$

${\sigma }_{min}=\frac{6\times 80}{0.012\times {20}^2}=100MPa$

Now

σ_m = 150 MPa, σ_a = 50 MPa;

Substituting in modified goodman line,

$\Rightarrow \frac{150}{600}+\frac{50}{200}=\frac{1}{N}$

⇒ N = 2;