Question

Find the maximum diameter of hole that can be punch in a M.S plate 10 mm thick having ultimate shear of 200 N/mm2. The allowable crushing stress in punch material is 350 N/mm2.

Answer 1

Question #81305

Find the maximum diameter of hole that can be punch in a M.S plate 10 mm thick having ultimate shear of 200 N/mm². The allowable crushing stress in punch material is 350 N/mm².

Answer:

Based on the puncher stress, the maximum allowable axial force is

$$F = \sigma_{pm} \frac{\pi d^2}{4},$$

where $\sigma_{pm} = 350\ \mathrm{N/mm^2}$ – the crushing stress in punch material,

$d$ is the diameter of hole to be punched.

Based on the shear stress of the plate, the force required to punch a hole is

$$F = \sigma_{MS} \pi dt,$$

where $\sigma_{MS} = 200\ \mathrm{N/mm^2}$ – the ultimate shear of the M.S. plate,

$t = 10\ \mathrm{mm}$ – the thickness of the M.S. plate.

For the maximum diameter of a hole, the forces in (1) and (2) are the same. Thus

$$\sigma_{pm} \frac{\pi d^2}{4} = \sigma_{MS} \pi dt,$$ $$d = 4t \frac{\sigma_{MS}}{\sigma_{pm}}.$$

Substitute into (3)

$$d = 4 \cdot 10 \frac{200}{350} = 22.9\ \mathrm{mm}.$$

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