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Mechanical EngineeringMechanics of Materials (MindTap Course List)9th Edition
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-4 A beam with a uniform load has a sliding support at one end and spring support at the other. The spring has a stiffness k = 48IE/ L 2 . Derive the equation of the deflection curve by starting with the third-order differential equation (the shear-force equation). Also, determine the angle of rotation θ B at support B.

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Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347

Solutions

Chapter
Section
Problem 9.2.1P
Problem 9.2.2P
Problem 9.2.3P
Problem 9.2.4P
Problem 9.2.5P
Problem 9.2.6P
Problem 9.3.1P
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Problem 9.3.3P
Problem 9.3.4P
Problem 9.3.5P
Problem 9.3.6P
Problem 9.3.7P
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Problem 9.3.10P
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Problem 9.3.14P
Problem 9.3.15P
Problem 9.3.16P
Problem 9.3.17P
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Problem 9.4.1P
Problem 9.4.2P
Problem 9.4.3P
Problem 9.4.4P
Problem 9.4.5P
Problem 9.4.6P
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Problem 9.5.1P
Problem 9.5.2P
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Problem 9.5.4P
Problem 9.5.5P
Problem 9.5.6P
Problem 9.5.7P
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Problem 9.5.10P
Problem 9.5.11P
Problem 9.5.12P
Problem 9.5.13P
Problem 9.5.14P
Problem 9.5.15P
Problem 9.5.16P
Problem 9.5.17P
Problem 9.5.18P
Problem 9.5.19P
Problem 9.5.20P
Problem 9.5.21P
Problem 9.5.22P
Problem 9.5.23P
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Problem 9.6.1P
Problem 9.6.2P
Problem 9.6.3P
Problem 9.6.4P
Problem 9.6.5P
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Problem 9.6.7P
Problem 9.6.8P
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Problem 9.7.1P
Problem 9.7.2P
Problem 9.7.3P
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Problem 9.7.5P
Problem 9.7.6P
Problem 9.7.7P
Problem 9.7.8P
Problem 9.7.9P
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Problem 9.7.12P
Problem 9.8.1P
Problem 9.8.2P
Problem 9.8.3P
Problem 9.8.4P
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Problem 9.8.6P
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Problem 9.9.5P
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Problem 9.9.7P
Problem 9.9.8P
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Problem 9.9.10P
Problem 9.9.11P
Problem 9.9.12P
Problem 9.10.1P
Problem 9.10.2P
Problem 9.10.3P
Problem 9.10.4P
Problem 9.10.5P
Problem 9.10.6P
Problem 9.10.7P
Problem 9.11.1P
Problem 9.11.2P
Problem 9.11.3P
Problem 9.11.4P
Problem 9.11.5P
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Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347
Chapter 9, Problem 9.4.4P
Textbook Problem
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-4 A beam with a uniform load has a sliding support at one end and spring support at the other. The spring has a stiffness k = 48IE/ L2. Derive the equation of the deflection curve by starting with the third-order differential equation (the shear-force equation). Also, determine the angle of rotation θ B at support B.

Chapter 9, Problem 9.4.4P, -4 A beam with a uniform load has a sliding support at one end and spring support at the other. The

To determine

To derive and find: Equation of deflection curve by starting with third − order differential equation and the angle of rotation θB at support B.

Explanation of Solution

Given:

  

Shear − force equation:

  EIv'''=V=−qx

  EIv''=−qx22+C1

B.C 1:

  v''(L)=M(L)=0

Therefore,

  C1=qL22

  EIv''=qL22−qx22

  EIv'=qL2x2−qx36+C2

  EIv=qL2x24−qx424+C2x+C3

B

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Chapter 9 Solutions

Mechanics of Materials (MindTap Course List)
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