Explanation Given information: The couple applied on the bar is denoted by M . Consider the radius of the bar on application of couple M is ρ . The radius of curvature of the bar after the removal of couple is ρ R . The radius of curvature of the bar on the onset of yield is ρ Y . Calculation: Show the expression for the yield moment M Y as follows: M Y = E I ρ Y (1) Show the expression for the moment M as follows: M = 3 2 M Y ( 1 − 1 3 ρ 2 ρ Y 2 ) M M Y = 3 2 ( 1 − 1 3 ρ 2 ρ Y 2 ) Consider the ratio of M M Y is denoted by m . Substitute m for M M Y . m = 3 2 ( 1 − 1 3 ρ 2 ρ Y 2 ) 2 3 m = 1 − 1 3 ρ 2 ρ Y 2 Multiply both side of the Equation by 3. 2 m = 3 − ρ 2 ρ Y 2 ρ 2 ρ Y 2 = 3 − 2 m (2) Show the relation between ρ and ρ R as follows: 1 ρ R = 1 ρ − M E I 1 ρ R = 1 ρ − M E I Substitute m M Y for M

7th Edition

ISBN: 9780073398235

Author: Ferdinand P. Beer, E. Russell Johnston Jr., John T. DeWolf, David F. Mazurek

Publisher: McGraw-Hill Education

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Chapter 4.6, Problem 93P

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Show that the radii of curvature of bar satisfy the relation:

1ρR=1ρ{1−32ρρY[1−13(ρρY)2]}

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Chapter 4.6, Problem 92P

Chapter 4.6, Problem 94P

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Show that the radii of curvature of bar satisfy the relation: 1 ρ R = 1 ρ { 1 − 3 2 ρ ρ Y [ 1 − 1 3 ( ρ ρ Y ) 2 ] }

Solution Summary: The author explains that the radii of curvature of bar satisfy the relation.

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Show that the radii of curvature of bar satisfy the relation:

1ρR=1ρ{1−32ρρY[1−13(ρρY)2]}

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Chapter 4 Solutions

Show that the radii of curvature of bar satisfy the relation: 1 ρ R = 1 ρ { 1 − 3 2 ρ ρ Y [ 1 − 1 3 ( ρ ρ Y ) 2 ] }

Solution Summary: The author explains that the radii of curvature of bar satisfy the relation.

Concept explainers

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Show that the radii of curvature of bar satisfy the relation: 1ρR=1ρ{1−32ρρY[1−13(ρρY)2]}

Want to see the full answer?

Chapter 4 Solutions

Show that the radii of curvature of bar satisfy the relation:

1ρR=1ρ{1−32ρρY[1−13(ρρY)2]}