A tie bar is made of a material having a tensile strength of 231MPa and has to carry a load of 225kN. What is the diameter of the bar if a factor of safety of 7 is applied?
Where do I begin?
To determine the diameter of the bar, we need to consider two factors: the material's tensile strength and the applied load, taking into account the factor of safety.
Here's how you can approach this problem:
1. Understand the terminologies:
- Tensile strength: It is the maximum amount of tensile stress a material can withstand before failure.
- Load: It is the force applied to an object, in this case, the tie bar.
- Factor of safety: It is a design parameter that accounts for uncertainties and potential variations in the load or material properties. It ensures that the structure or component can handle the applied load without failure.
2. Calculate the allowable stress:
The allowable stress is the maximum stress the tie bar can handle while considering the factor of safety. It is obtained by dividing the tensile strength by the factor of safety:
Allowable stress = Tensile strength / Factor of safety
In this case, the tensile strength is 231 MPa, and the factor of safety is 7. So, the allowable stress would be:
Allowable stress = 231 MPa / 7
3. Calculate the stress due to the load:
The stress due to the load can be calculated by dividing the load by the cross-sectional area of the tie bar:
Stress = Load / Cross-sectional area
4. Determine the cross-sectional area:
The cross-sectional area of a circular bar can be calculated using the formula:
Cross-sectional area = (π * Diameter^2) / 4
5. Rearrange the formula and solve for the diameter:
Combine steps 3 and 4 to get:
Allowable stress = Load / ((π * Diameter^2) / 4)
Rearrange the formula to solve for the diameter:
Diameter = sqrt((4 * Load) / (π * Allowable stress))
6. Substitute the values and calculate the diameter:
Substitute the values: Load = 225 kN (converted to N), Allowable stress = 231 MPa / 7, and π ≈ 3.14159.
Diameter = sqrt((4 * 225,000 N) / (3.14159 * (231 MPa / 7)))
Calculate the diameter using a calculator, and ensure that the final unit is appropriate for the problem.
Following these steps should help you determine the diameter of the tie bar.