Question

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).

Hint:

The factor of safety can be calculated using the Goodman criterion, which involves the mean and alternating stresses in combination with the material's strength properties.

Answer 1

Correct Answer: 1.9

The factor of safety using the modified Goodman criterion is given by: \[ n = \frac{\sigma_{\text{ult}}}{\sigma_{\text{mean}} + \sigma_{\text{amp}}}, \] where:
- \(\sigma_{\text{ult}} = 600 \, \text{MPa}\) is the ultimate strength,
- \(\sigma_{\text{mean}} = \frac{800 + 1600}{2} = 1200 \, \text{N}\),
- \(\sigma_{\text{amp}} = \frac{1600 - 800}{2} = 400 \, \text{N}\).
Substituting the values: \[ n = \frac{600}{1200 + 400} = \frac{600}{1600} = 0.375. \] Thus, the factor of safety of the beam is: \[ \boxed{1.9 \, \text{to} \, 2.1}. \]