GATE Papers >> Mechanical >> 2016 >> Question No 260

Question No. 260 Mechanical | GATE 2016
In a sheet metal of 2 mm thickness a hole of 10 mm diameter needs to be punched. The yield strength in tension of the sheet material is 100 MPa and its ultimate shear strength is 80 MPa. The force required to punch the hole (in kN) is __________

Answer : 4.9 : 5.1


Solution of Question No 260 of GATE 2016 Mechanical Paper

$ \style{font-family:'Times New Roman'}{\mathrm t=2\;\mathrm{mm}\;\;\;\;\mathrm d=10\;\mathrm{mm}\;\;\;\;{\mathrm\tau}_\mathrm s=80\;\mathrm{MPa}} $

Force required for punching

$ \style{font-family:'Times New Roman'}{\begin{array}{l}\mathrm F={\mathrm{πdtτ}}_\mathrm s\\\mathrm F=\mathrm\pi\times10\times2\times80\\\mathrm F=5026.548\;\mathrm N=5.0265\;\mathrm{kN}\end{array}} $

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