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Engineering and Tech / Mechanics of Materials 7 / Chapter 1 / Problem 1.69

Mechanics of Materials | 7th Edition | ISBN: 9780073398235 | Authors: Ferdinand P. Beer; E. Russell Johnston Jr.; John T. DeWolf; David F. Mazurek

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The two portions of member AB are glued together along a

Chapter 1, Problem 1.69

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QUESTION:

The two portions of member AB are glued together along a plane forming an angle \(\boldsymbol{\theta}\) with the horizontal. Knowing that the ultimate stress for the glued joint is 2.5 ksi in tension and 1.3 ksi in shear, determine (a) the value of \(\boldsymbol{\theta}\) for which the factor of safety of the member is maximum, (b) the corresponding value of the factor of safety. (Hint: Equate the expressions obtained for the factors of safety with respect to the normal and shearing stresses.)

Questions & Answers

QUESTION:

The two portions of member AB are glued together along a plane forming an angle \(\boldsymbol{\theta}\) with the horizontal. Knowing that the ultimate stress for the glued joint is 2.5 ksi in tension and 1.3 ksi in shear, determine (a) the value of \(\boldsymbol{\theta}\) for which the factor of safety of the member is maximum, (b) the corresponding value of the factor of safety. (Hint: Equate the expressions obtained for the factors of safety with respect to the normal and shearing stresses.)

ANSWER:

Step 1 of 8

We have to determine the optimum angle of inclination for which factor of safety for normal stress will be equal to that fro shearing stress

Given data are

Area of cross section

Ultimate stress in tension

Ultimate stress in shear =

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