Ch.1 Problem 1.5 Solution - Edubirdie

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

2021
Views:

406

Pages:

1
Author:

rehinhea0c

PROBLEM 1.5 Two steel plates are to be held together by means of 16-mmdiameter high-strength steel bolts fitting snugly inside cylindrical brass spacers. Knowing that the average normal stress must not exceed 200 MPa in the bolts and 130 MPa in the spacers, determine the outer diameter of the spacers that yields the most economical and safe design. SOLUTION At each bolt location the upper plate is pulled down by the tensile force Pb of the bolt. At the same time, the spacer pushes that plate upward with a compressive force Ps in order to maintain equilibrium. Pb = Ps For the bolt, σb = Fb 4 Pb = Ab π d b2 or Pb = For the spacer, σs = Ps 4Ps = As π (d 2s − db2 ) or Ps = π 4 π 4 σb db2 σ s (d s2 − d b2 ) Equating Pb and Ps , π 4 σ bd b2 = ds = π 4 σ s (d s2 − d b2 ) § σb · ¨1 + ¸d = σs ¹ b © 200 · § ¨1 + 130 ¸(16) © ¹ d s = 25.2 mm W

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