   # -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. ### Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347 ### 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. 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''=qL22qx22

EIv'=qL2x2qx36+C2

EIv=qL2x24qx424+C2x+C3

B

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