(a) Explanation Given information: The modulus of elasticity ( E ) is 200 GPa . The moment ( M ) is 350 N ⋅ m . The radius of curvature ( ρ ) is 2.4 m . The width of the prismatic bar is 20 mm . Calculation: Find the bending moment ( M ) using the Equation as follows: Refer Equation 4.43 in section 4.6A Members Made of Elastoplastic Material in the textbook. M = 3 2 M Y ( 1 − 1 3 ρ 2 ρ Y 2 ) (1) Substitute I c σ Y for M and E 2 c 2 σ Y 2 for ρ in Equation (1). M = 3 2 × I c σ Y ( 1 − 1 3 ρ 2 σ Y 2 E 2 c 2 ) (2) Refer Equation 4.34 in section 4.6A Members Made of Elastoplastic Material in the textbook. I c = b ( 2 c 3 ) 12 c Substitute b ( 2 c 3 ) 12 c for I c in Equation (2). M = 3 2 × ( b ( 2 c 3 ) 12 c ) σ Y ( 1 − 1 3 ρ 2 σ Y 2 E 2 c 2 ) = 3 2 × ( b ( 8 c 3 ) 12 c ) σ Y ( 1 − 1 3 ρ 2 σ Y 2 E 2 c 2 ) = 3 2 × ( b ( 2 c 3 ) 3 c ) σ Y ( 1 − 1 3 ρ 2 σ Y 2 E 2 c 2 ) = σ Y b c 2 ( 1 − 1 3 ρ 2 σ Y 2 E 2 c 2 ) (3) Find the distance ( c ) between neutral axis and extreme fibre as follows: c = 1 2 h (4) Here, h is height of prismatic bar (b) To determine Find the thickness of the elastic core of the bar.

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 95P

(a)

To determine

Find the yield strength of the steel.

(b)

To determine

Find the thickness of the elastic core of the bar.

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Chapter 4.6, Problem 94P

Chapter 4.6, Problem 96P

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Find the yield strength of the steel.

Solution Summary: The author calculates the bending moment (M) using Equation 4.43 in section 4.6A Members Made of Elastoplastic Material in the book.

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Find the yield strength of the steel.

Find the thickness of the elastic core of the bar.

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Chapter 4 Solutions