Question

A rectangle shaped opening will be removed from the sheet metal with single punch. The sides of the rectangle are 15 mm and 60 mm. The thickness of the sheet metal is 3 mm. The ultimate tensile strength of the material is 190 MPa. Calculate the necessary force to cut the sheet metal

Answer 1

The force needed to cut the metal sheet is; F = 34200N

Step-by-step explanation:

Solution:

Data Given;

Length of rectangle = 60mm = 0.06m

Thickness of the rectangle = 3mm = 0.003m

Shear stress = 190Mpa = 190 * 10⁶Pa

In calculating the force to cut the sheet metal, we use the formula;

Stress = Force/Area-----------------------1

Area = length * thickness

= 0.06 * 0.003

= 0.00018m²

Substituting into equation 1, we have

190 * 10⁶ = F/0.00018

Cross multiplying, we have

F = 190* 10 ⁶ * 0.00018

F = 34200N

Answer 2

The force needed to cut the sheet metal is 171 kN.

Step-by-step explanation:

Force (F) needed to cut the sheet metal is the ultimate tensile strength of the material multiplied by the area of the rectangle.

ultimate tensile strength = 190 MPa = 1.9×10^8 Pa

area of rectangle = (15/1000) × (60/1000) = 0.015×0.06 = 0.0009 m^2

F = 1.9×10^8 × 0.0009 = 171,000 N = 171,000/1000 = 171 kN