A 20mm diameter rivet is used to fastened two 25mm thick plate If the shearing stress of rivet is 80MPa. What tensile force is applied to each plate to shear the rivet
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The tensile force applied to each plate to shear the rivet is 40MPa.
To calculate the tensile force applied to each plate to shear the rivet, we need to use the formula for shear stress:
Shear Stress = Force / Area
First, let's calculate the area of the rivet:
Area = π * (diameter/2)^2
Given that the diameter is 20mm, we can calculate the area:
Area = π * (20mm/2)^2
Area = 3.14 * (10mm)^2
Area ≈ 314 mm²
Next, we'll substitute the given shear stress value into the formula to find the force required:
80MPa = Force / 314 mm²
To convert the shear stress from MPa to N/mm², we need to multiply by 1 million:
80MPa = Force / 314 mm²
80,000 N/mm² = Force / 314 mm²
Now, we can solve for the force:
Force = 80,000 N/mm² * 314 mm²
Force ≈ 25,120 N
Therefore, a tensile force of approximately 25,120 Newtons would be applied to each plate to shear the rivet.
To find the tensile force applied to each plate to shear the rivet, we first need to calculate the area of the rivet that is subject to shearing.
Step 1: Calculate the area of the rivet cross-section:
The cross-section of a rivet is circular, and its area can be calculated using the formula for the area of a circle:
Area = π * (radius)^2
Given that the diameter of the rivet is 20mm, the radius can be calculated as half the diameter, which is 10mm or 0.01m:
Radius = 0.01m
Therefore, the cross-sectional area of the rivet is:
Area = π * (0.01)^2 = 0.000314 m^2
Step 2: Calculate the force applied on each plate:
The shearing stress (τ) can be calculated using the formula:
τ = Force / Area
Rearranging the formula, we get:
Force = τ * Area
Given that the shearing stress (τ) is 80MPa, we need to convert it to pascals (Pa) before using it in the calculation:
1 MPa = 1,000,000 Pa
Therefore, the shearing stress (τ) in pascals is:
τ = 80MPa * 1,000,000 = 80,000,000 Pa
Substituting the values, we can calculate the force applied on each plate:
Force = 80,000,000 Pa * 0.000314 m^2 = 25,120 N
Therefore, the tensile force applied to each plate to shear the rivet is 25,120 Newtons.