Calculation of Shear Stress on a Circular Bar

To calculate the shear stress acting on a circular bar, we need to consider the axial load applied on the bar, the diameter of the bar, and the angle at which the load is applied.

Given:
Axial load (F) = 80 kN
Diameter of bar (d) = 40 mm
Angle (θ) = 42.3 degrees

Step 1: Convert the diameter to radius
The diameter of the bar is given as 40 mm. To calculate the shear stress, we need to convert it to radius. The radius (r) can be calculated by dividing the diameter by 2.
r = d/2 = 40 mm/2 = 20 mm

Step 2: Convert the radius to meters
The shear stress is typically calculated in SI units, so we need to convert the radius from millimeters to meters.
r = 20 mm = 20/1000 = 0.02 m

Step 3: Calculate the shear force
To calculate the shear stress, we need to first find the shear force (V). The shear force can be calculated using the axial load (F) and the angle (θ) at which the load is applied.
V = F * sin(θ)
= 80 kN * sin(42.3 degrees)
= 80 kN * 0.676
= 54.08 kN

Step 4: Calculate the shear stress
Finally, we can calculate the shear stress (τ) using the formula:
τ = V / (π * r^2)

Substituting the values, we get:
τ = 54.08 kN / (π * (0.02 m)^2)
= 54.08 kN / (π * 0.0004 m^2)
= 54.08 kN / (0.00126 m^2)
= 43 MPa

Conclusion:
The shear stress acting on the circular bar, subjected to an axial load of 80 kN with a diameter of 40 mm and an angle of 42.3 degrees, is 43 MPa.