Question

Assume that if the shear stress in steel exceeds about 4.00  10⁸ N/m², the steel ruptures.

(a) Determine the shearing force necessary to shear a steel bolt 1.10 cm in diameter.

N

(b) Determine the shearing force necessary to punch a 1.75-cm-diameter hole in a steel plate 0.560 cm thick.

N

Answer 1

a)

Here the maximum shear stress of the steel can withstand,above which it reptures,

The diameter of the steel bolt,

So,The area of cross section of the steel bolt,

We have,shear force=shear stress*area of cross section.

So,The shear force needded to shear the bolt,

b)

Here the diameter of hole to be punched is,

Thickness of the steel plate,

The area of the cylinder of the hole punched by shear force(Shear area)=Circumference of hole*thickness of the steel plate.

Cicumference of the hole,

So,The cylindrical area of the hole(Shear area),

So,The cylindrical area of the hole,

maximum shear stress of the steel can withstand,above which it reptures,

So,The shear force needed to punch the hole,=Shear area*Shear stress

Shear force neccessary to punch the hole,