An iron bolt is used to connect two iron plates together. The bolt
must withstand shear forces up to about 3300 N. Calculate the
minimum diameter for the bolt, based on a safety factor of 7.0
To calculate the minimum diameter of the bolt, we need to use the formula for shear stress and the given safety factor.
The formula for shear stress is:
Shear Stress = Force / Area
In this case, the force is the maximum shear force the bolt must withstand, which is 3300 N.
The safety factor is the ratio of the maximum allowable stress to the actual stress on the bolt. In this case, the safety factor is 7.0.
To find the minimum diameter of the bolt, we need to rearrange the formula for shear stress and solve for the area.
Area = Force / Shear Stress
Since the safety factor is the ratio of maximum allowable stress to actual stress, we can express the actual stress as:
Shear Stress = Maximum Allowable Stress / Safety Factor
Now we can substitute this expression into the equation for area:
Area = Force / (Maximum Allowable Stress / Safety Factor)
To calculate the minimum diameter, we can use the formula for the area of a circle:
Area = π * (Diameter/2)^2
So, the equation becomes:
π * (Diameter/2)^2 = Force / (Maximum Allowable Stress / Safety Factor)
Let's solve for the diameter:
Diameter = √((Force / (Maximum Allowable Stress / Safety Factor)) * (4 / π))
Now we can substitute the values into the formula:
Diameter = √((3300 N / (Maximum Allowable Stress / 7.0)) * (4 / π))
Please note that the value for the maximum allowable stress must be provided in order to obtain the final calculation for the minimum diameter of the bolt.