Question
A circular punch 20 mm in diameter is used to punch a hole through a steel plate 10 mm thick. If the force necessary to drive the punch through the metal is 250 kN, determine the maximum shearing stress developed in the material.
Answers
GPT 3.5
To find the maximum shearing stress developed in the material, we can use the formula for shear stress:
Shear stress = Force / Area
First, let's find the area of the circular punch.
The area of a circle is given by the formula:
Area = π * (diameter/2)^2
Given that the diameter of the punch is 20 mm, we can calculate the area:
Area = π * (20/2)^2 = π * 10^2 = 100π mm^2
Next, let's convert the area from mm^2 to m^2:
Area = 100π * (1 m / 1000 mm)^2 = 100π * (1/1000)^2 = 100π * 1/1000^2 = 100π/10^6 m^2
Now let's substitute the values into the formula for shear stress:
Shear stress = Force / Area
Shear stress = 250 kN / (100π/10^6 m^2) = (250/100π) * 10^6 N/m^2 = 2500/π * 10^6 N/m^2 ≈ 795.77 MPa
Therefore, the maximum shearing stress developed in the material is approximately 795.77 MPa.
Shear stress = Force / Area
First, let's find the area of the circular punch.
The area of a circle is given by the formula:
Area = π * (diameter/2)^2
Given that the diameter of the punch is 20 mm, we can calculate the area:
Area = π * (20/2)^2 = π * 10^2 = 100π mm^2
Next, let's convert the area from mm^2 to m^2:
Area = 100π * (1 m / 1000 mm)^2 = 100π * (1/1000)^2 = 100π * 1/1000^2 = 100π/10^6 m^2
Now let's substitute the values into the formula for shear stress:
Shear stress = Force / Area
Shear stress = 250 kN / (100π/10^6 m^2) = (250/100π) * 10^6 N/m^2 = 2500/π * 10^6 N/m^2 ≈ 795.77 MPa
Therefore, the maximum shearing stress developed in the material is approximately 795.77 MPa.