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Strength of Materials - Engineering

Q1:

The maximum diameter of the hole that can be punched from a plate of maximum shear stress 1/4th of its maximum crushing stress of punch, is equal to (where t = Thickness of the plate)

A t

B 2t

C 4t

D 8t

ANS:C - 4t

We know that Shearing pull Ps = pie/4* d^2*τ.
Therefore tao(shear stress) = 4Ps/pie d^2.

Same, crushing pull Pc = d*t*σ.
Therefore σ (crushing stress) = Pc/dt.

Now, as per question τ = 1/4 σ.
Solving this, we found d = 16/π *t.

So, dmax = 5.06t its coming, taking nearer value, its 4t.