Determination of Average Shearing Stress in Bolts
Calculation of Average Shearing Stress:
Given:
Shearing force = 25 kN = 25,000 N
Bolt diameter = 20 mm
Bolt radius (r) = 10 mm = 0.01 m
Number of bolts = 4 (2 bolts per channel shape)
Channel shape = C100 x 8
Plate dimension = 250 mm x 15 mm
Bolt spacing = 150 mm
Shear Area of One Bolt:
Shear area (A) = πr^2
Plugging in the values: A = π(0.01)^2 = 0.000314 m^2
Total Shear Area:
Total shear area = 4 bolts * 0.000314 m^2 = 0.001256 m^2
Calculation of Average Shearing Stress:
Average shearing stress = force/area
Substitute the values: stress = 25,000 N / 0.001256 m^2 = 19,913.42 N/m^2 or 19.91 MPa
Summary:
Therefore, the average shearing stress in the bolts caused by a shearing force of 25 kN parallel to the y-axis is 19.91 MPa. This calculation was based on the shear area of one bolt, the total shear area considering all bolts, and using the formula stress = force/area.