Chapter 9, Problem 70P

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

Chapter
Section

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

# Assume that if the shear stress in steel exceeds about 4.00 × 108 N/m2, the steel ruptures. Determine the shearing force necessary to (a) shear a steel bolt 1.00 cm in diameter and (b) punch a 1.00-cm-diameter hole in a steel plate 0.500 cm thick.

(a)

To determine

The shearing force necessary to shear the bolt.

Explanation

Given info: The diameter of the bolt is 1.00â€‰cm and shear stress is 4.00Ã—108â€‰N/m2.

The shearing force is defined as F=AÏƒ and the area of the bolt is A=Ï€r2=Ï€(d/2)2. The stress is Ïƒ=F/A.

The formula for the shearing force is,

F=Ï€d2Ïƒ4

• d is diameter of the blot.
• Ïƒ is shearing stress.

Substitute 1.00â€‰cm for d and 4.00Ã—108â€‰N/m2 for Ïƒ to find F

(b)

To determine

The shearing force necessary to punch a hole in a steel plate.

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