# Type 4: Problems on shear stress

1. A steel punch can be worked to compressive stress of 800 N/mm2 . Find the least diameter of the hole which can be punched through a steel plate of 10 mm thick if ultimate shear stress of the plate is 300 N/mm2 .

(Ans:d=15mm)

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2. A Circular hole of diameter 20 mm is to be punched through a plate of 10 mm thick. Find the force required to punch a hole, if shear strength of material is 250 N/mm2 .Hence find the compressive stress developed in the punch material.

(Ans:F=157.079 kN, Comp stress=500 N/mm2 )

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3. Determine the smallest size of hole that can be punched in 12 mm thick MS plate having ultimate shear stress of 390 N/mm2 , if permissible crushing stress for the punch material is 2.4 kN/mm2.

(Ans:d=7.8mm)

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4. A force of 31.68 kN is required to punch a circular hole of 14 mm diameter in metal plate of 2 mm thickness. Calculate the ultimate shear stress and compressive stress developed in the punching rod.

(Ans:Shear Stress=360.32 N/mm2 ,Comp.Stress=205.90 N/mm2 )

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5. A rectangular hole of size 10 mm x 15 mm is to be punched through a plate of 5mm. Find the force required to punch the hole if shear stress in the plate material is 300 N/mm2 .

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