A round tie bar in a framework is subjected to a load of 65 kN. If the radius is 15 mm, what is the stress in the tie?

To determine the stress in the tie bar, we can use the formula for stress, which is defined as the force applied per unit area. The stress in the tie bar can be calculated using the equation:

[ \text{Stress} = \frac{\text{Force}}{\text{Area}} ]

In this case, the force applied is 65 kN (or 65,000 N). The area (A) of a circular cross-section can be calculated using the formula:

[ A = \pi r^2 ]

where ( r ) is the radius of the tie bar. Given that the radius is 15 mm, it should be converted to meters for the calculation:

[ r = 15 , \text{mm} = 0.015 , \text{m} ]

Now, substituting the radius into the area formula:

[ A = \pi (0.015)^2 ]

[ A = \pi (0.000225) ]

[ A = 0.00070686 , \text{m}^2 ]

Next, we can calculate the stress:

[ \text{Stress} = \frac{65,000 , \text{