Question

what force is required to punch a 25mm diameter hole through a 15mm thick plate. The ultimate shear stress of the material of the plate is 380 MPa. Express the answer in kN.

Answer 1

Answer on Question #49629-Physics-Mechanics-Kinematics-Dynamics

What force is required to punch a 25mm diameter hole through a 15mm thick plate? The ultimate shear stress of the material of the plate is 380 MPa. Express the answer in kN.

Solution

The resisting area is the shaded area along the perimeter and the shear force $V$ is equal to the punching force $P$ .

$$V = \tau A = \tau \cdot \pi d h.$$ $$P = 3 8 0 \cdot 1 0 ^ {6} P a [ \pi \cdot 2 5 \cdot 1 0 ^ {- 3} m \cdot 1 5 \cdot 1 0 ^ {- 3} m ] = 4 4 7 6 7 6. 9 5 N = 4 4 7. 7 k N.$$

Answer: 447.7 kN.

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