A punch for making hole with diameter d=20mm, plate thickness t=800, punching force P=110KN.

A) calculate the shear stress in plate.

B)Calculate average compressive stress in the punch.

To tackle the problem of calculating the shear stress in the plate and the average compressive stress in the punch, we need to break down the given information and apply some fundamental principles of mechanics. Let's start with the details provided: the diameter of the punch (d) is 20 mm, the thickness of the plate (t) is 800 mm, and the punching force (P) is 110 kN.

Calculating Shear Stress in the Plate

Shear stress is defined as the force applied per unit area. In this case, the area over which the force is acting is the shear area of the punch, which can be calculated using the formula:

• Shear Area (A) = Perimeter of the punch × Thickness of the plate
• Perimeter of the punch = π × Diameter = π × d

Now, let's compute the shear area:

• Diameter (d) = 20 mm = 0.02 m
• Perimeter = π × 0.02 m ≈ 0.06283 m
• Thickness (t) = 800 mm = 0.8 m
• Shear Area (A) = 0.06283 m × 0.8 m ≈ 0.050264 m²

Now, we can calculate the shear stress (τ) using the formula:

• Shear Stress (τ) = Force (P) / Shear Area (A)

Substituting the values:

• P = 110 kN = 110,000 N
• τ = 110,000 N / 0.050264 m² ≈ 2,189,000 N/m² or 2.19 MPa

Average Compressive Stress in the Punch

Next, we need to determine the average compressive stress in the punch. This stress is calculated similarly, but we focus on the cross-sectional area of the punch instead. The formula for average compressive stress (σ) is:

• Compressive Stress (σ) = Force (P) / Cross-sectional Area (A₁)

The cross-sectional area of the punch can be calculated as:

• Cross-sectional Area (A₁) = π × (d/2)²

Calculating the cross-sectional area:

• A₁ = π × (0.02 m / 2)² = π × (0.01 m)² ≈ 3.14 × 0.0001 m² ≈ 0.000314 m²

Now, substituting this into the compressive stress formula:

• σ = 110,000 N / 0.000314 m² ≈ 350,000,000 N/m² or 350 MPa

Summary of Results

To summarize:

• Shear Stress in the Plate: approximately 2.19 MPa
• Average Compressive Stress in the Punch: approximately 350 MPa

This analysis shows how to apply basic principles of mechanics to find shear and compressive stresses in a punching operation. Understanding these stresses is crucial for ensuring that both the punch and the plate can withstand the applied forces without failure.