What is the factor of safety for a steel hanger with an ultimate strength of 70,000 N/cm² supporting a load of 87,500 N with a cross-sectional area of 5 cm²?

To determine the factor of safety for the steel hanger, it is essential to understand the relationship between the ultimate strength of the material and the actual stress experienced due to the applied load.

The factor of safety (FS) is calculated using the formula:

[

\text{FS} = \frac{\text{Ultimate Strength}}{\text{Actual Stress}}

]

First, we need to find the actual stress the hanger experiences. This is calculated by dividing the load by the cross-sectional area:

[

\text{Actual Stress} = \frac{\text{Load}}{\text{Cross-Sectional Area}} = \frac{87,500 \text{ N}}{5 \text{ cm}^2} = 17,500 \text{ N/cm}^2

]

Next, with the ultimate strength given as 70,000 N/cm², we now can substitute these values into the factor of safety formula:

[

\text{FS} = \frac{70,000 \text{ N/cm}²}{17,500 \text{ N/cm}²} = 4

]

This calculation shows that the factor of safety for the steel hanger is 4. A factor of safety