Explanation Given: The cross-section is shown below: Calculation: The area moment of inertia is calculated as follows: I x = π 4 r o 4 − r i 4 The yield moment is calculated as follows: σ Y = M Y c I σ Y = M Y r o π 4 r o 4 − r i 4 M Y = π 4 r o r o 4 − r i 4 σ Y The resultant components of the stress block are calculated as follows: C 1 = T 1 = 1 2 π × r o 2 σ Y And, C 2 = T 2 = 1 2 π × r i 2 σ Y The plastic moment is calculated as follows: M P = T 1 2 4 r o 3 π − T 2 2 4 r i 3 π = 1 2 π

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Author: Russell C. Hibbeler

Publisher: Pearson Education (US)

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Chapter 6.10, Problem 166P

To determine

The shape factor of the given thick-walled tube cross-section.

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Chapter 6.10, Problem 165P

Chapter 6.10, Problem 167P

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Chapter 6 Solutions

Mechanics of Materials

Ch. 6.2 - and then draw the shear and moment diagrams for...Ch. 6.2 - In each case, express the shear and moment...Ch. 6.2 - In each case, express the shear and moment...Ch. 6.2 - In each case, express the shear and moment...Ch. 6.2 - In each case, draw the shear and moment diagrams...Ch. 6.2 - In each case, draw the shear and moment diagrams...Ch. 6.2 - In each case, draw the shear and moment diagrams...Ch. 6.2 - In each case, draw the shear and moment diagrams...Ch. 6.2 - Prob. 1P Ch. 6.2 - Prob. 2P

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The shape factor of the given thick-walled tube cross-section.

Solution Summary: The shape factor of the thick-walled tube cross-section is 16r_oleft. The yield moment is calculated as follows:

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The shape factor of the given thick-walled tube cross-section.

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Chapter 6 Solutions