Question

Assume 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 1.25 cm in diameter.

(b) Determine the shearing force necessary to punch a 2.60-cm-diameter hole in a steel plate 0.590 cm thick.

Answer 1

here,

for steel to repture,

the shearing stress , S = 4 * 10^8 N/m^2

a)

diameter , d = 1.25 cm = 0.0125 m

the shearing force necessary to shear a steel bolt , F = S * pi * ( d/2)^2

F= 4 * 10^8 * pi * ( 0.0125/2)^2 N

F = 4.91 * 10^4 N

b)

diameter , d = 2.6 cm = 0.026 m

the shearing force necessary to shear a steel bolt , F = S * pi * ( 0.026/2)^2

F= 4 * 10^8 * pi * ( 0.026/2)^2 N

F = 2.12 * 10^5 N