LIVE Course for free

Rated by 1 million+ students
Get app now
0 votes
in General by (30.0k points)
closed by
A hole of diameter d is to be punched in a plate of thickness t. For the plate material, the maximum crushing stress is 4 times the maximum allowable shearing stress. For punching the biggest hole, the ratio of diameter of hole to plate thickness should be equal to
1. 1/4
2. 1/2
3. 1
4. 2

1 Answer

0 votes
by (53.7k points)
selected by
Best answer
Correct Answer - Option 3 : 1



in sheet metal operation, punching operation the process in which sheared part is considered as scrap and the remaining part is desired part.

For punching opreration,

⇒ Punch tool size = Hole size = d

The maximum crushing stress induced in the punching tool,

\( ⇒ {{\bf{\sigma }}_{{\bf{cmax}}}} = \frac{{4{\bf{F}}}}{{{\bf{\pi }}{{\bf{d}}^2}}}\;\;\;\;\; \ldots \left( 1 \right)\;\)

The maximum allowable shearing stress,

\( ⇒ {{\bf{\tau }}_{{\bf{smax}}}} = \frac{{\bf{F}}}{{{\bf{\pi dt}}}}\;\;\;\;\;\; \ldots \left( 2 \right)\;\)

where, F = Punching force, d = diameter of the hole (punching tool diameter), t = thickness of the metal sheet



σcmax = 4τsmax

\( ⇒ \frac{{4{\bf{F}}}}{{{\bf{\pi }}{{\bf{d}}^2}}} = 4 \times \frac{{\bf{F}}}{{{\bf{\pi dt}}}}\;\)

⇒ d = t

⇒ The ratio of the diameter of the hole to plate thickness = 1

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.