Punching a plate: maximum permissible hole diameter from shear versus punch crushing A plate of thickness t is punched. The plate’s maximum shear stress is one-fourth of the punch’s maximum crushing stress. Find the maximum hole diameter that can be punched without exceeding either limit. Choose the correct expression in terms of t.

Difficulty: Medium

Correct Answer: t

Explanation:

Given limits
Let allowable shear of plate = τ and allowable crushing of punch = σ_c, with τ = σ_c/4.

For a punched hole of diameter d
Shear force capacity (plate): P = τ (π d t)Crushing stress on punch: σ_cr = P / (π d² / 4)

Set crushing at limit
σ_c = [τ (π d t)] / (π d² / 4) = τ (4 t / d)Using τ = σ_c/4 ⇒ σ_c = (σ_c/4)(4 t / d) = σ_c (t / d)⇒ d = t

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