Ch.1 Problem 1.19 Solution - Edubirdie

University:
Michigan State University
Course:
ERG 100 | Introduction to Engineering Design
Academic year:

2021
Views:

86

Pages:

1
Author:

do3ran7ut

PROBLEM 1.19 The load P applied to a steel rod is distributed to a timber support by an annular washer. The diameter of the rod is 22 mm and the inner diameter of the washer is 25 mm, which is slightly larger than the diameter of the hole. Determine the smallest allowable outer diameter d of the washer, knowing that the axial normal stress in the steel rod is 35 MPa and that the average bearing stress between the washer and the timber must not exceed 5 MPa. SOLUTION Steel rod: A = π 4 (0.022)2 = 380.13 × 10−6 m2 σ = 35 × 106 Pa P = σ A = (35 ×10 6)(380.13 × 10 − 6) = 13.305 × 10 3N Washer: σb = 5 × 106 Pa Required bearing area: Ab = But, Ab = π 4 P σb = 13.305 × 103 5 × 10 6 = 2.6609 × 10 −3 m 2 (d 2 − di2 ) d 2 = di2 + 4 Ab π = (0.025)2 + (4)(2.6609 × 10 − 3) π = 4.013 × 10−3 m2 d = 63.3 × 10− 3 m d = 63.3 mm W

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