A circular hole of diameter d = 10 cm is to be punched out of a plate having an ultimate shearing stress, σ s = 2 × 10 8 pa as shown in the figure. If the maximum compressive strength on the punch is limited to σ c = 4 × 10 8 pa , determine the maximum thickness 't' of the plate.

Step-by-step solution

Shear Area, A s = 2 π r × t where, 2 π r → the perimeter of the hole and t → the thickness of the hole. ⇒ A = 2 π 0 . 1 2 t = 0 . 1 π t . Force = shear   stress × Area ⇒ F = σ s × A s ⇒ F = 2 × 10 8 × 0 . 1 π t ⇒ F = 2 × 10 7 π t . compressive   stress = Force Area ⇒ σ c = F π d 2 2 ⇒ 4 × 10 8 = 2 × 10 7 π t π 0 . 1 2 2 ⇒ t = 4 × 10 8 8 × 10 9 = 1 2