   # -12 Derive the equation of the deflection curve for a cantilever beam AB supporting a load P at the free end (see figure). Also, determine the deflection δ B and angle of rotation θ b at the free end. Use the second-order differential equation of the deflection curve. ### 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 9.3.12P
Textbook Problem
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## -12 Derive the equation of the deflection curve for a cantilever beam AB supporting a load P at the free end (see figure). Also, determine the deflection δ B and angle of rotation θ b at the free end. Use the second-order differential equation of the deflection curve. To determine

Expression for the deflection curve, deflection and angle of rotation.

### Explanation of Solution

Given information:

Formula used:

Elv''=M=P(Lx)

Calculation:

We know the bending moment equation, i.e.: Elv''=M=P(Lx) ;

Integrate the above equation;

Elv'=PLx+px22+C1

Since the boundary condition is, v'(0)=0 ;

So, C2=0 ;

Again integration;

EIv=PLx22+p

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