# -10 Derive the equations of the deflection curve for beam AB with sliding support at A and roller support at B, supporting a distributed load of maximum intensity q 0 acting on the right-hand half of the beam (see figure). Also, determine deflection δ A , angle of rotation θ B , and deflection δ c at the midpoint. Use the fourth-order differential equation of the deflection curve (the load equation).

### 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 9.4.10P
Textbook Problem
101 views

## -10 Derive the equations of the deflection curve for beam AB with sliding support at A and roller support at B, supporting a distributed load of maximum intensity q0acting on the right-hand half of the beam (see figure). Also, determine deflection δ A , angle of rotation θ B , and deflection δ c at the midpoint. Use the fourth-order differential equation of the deflection curve (the load equation).

To determine

To derive: the equations of deflection curve for beam. Also, find deflection δA , Angle of rotation θB , and deflection δC at the midpoint.

### Explanation of Solution

Given:

EIv''''=q=0(0xL2)

Upon integration

EIv'''=C1(0xL2)

Upon integration

EIv''=C1x+C2(0xL2)

Boundary condition 1:

v'''(0)=V(0)

Therefore,

C1=0

Boundary condition 2:

v''(0)=M(0)=q0L212

Therefore,

C2=q0L212

EIv''=q0L212(LxL2)

Upon integration

EIv'=q0L2x12+C3(LxL2)

Boundary condition 3:

v'(0)=0

Therefore,

C3=0

EIv=q0L2x224+C4(0xL2)

EIv''''=2q0+2q0xL(L2xL)

Upon integration

EIv'''=2q0x+q0x2L+C5(L2xL)

Upon integration

EIv''=q0x2+q0x33L+C5x+C6(L2xL)

Boundary condition 4:

v'''(L2)=V(L2)=0

Therefore,

C5=3q0L4

Boundary condition 5:

v''(L2)=M(L2)=q0L212

Therefore,

C6=q0L212

EIv''=q0x2+q0x33L+3q0Lx4q0L212

Upon integration

EIv'=q0x33+q0x412L+3q0Lx28q0L2x12+C7

Boundary condition 6

v'L(L2)=v'R(L2)

Therefore,

C7=5192qL<

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Additional Engineering Textbook Solutions

Find more solutions based on key concepts
A______ can be used to measure cutting fluid concentrations.

Precision Machining Technology (MindTap Course List)

Describe the Big Data phenomenon.

Database Systems: Design, Implementation, & Management

Explain why computer incidents are so prevalent.

Fundamentals of Information Systems

Give an example of a linear model in engineering.

Engineering Fundamentals: An Introduction to Engineering (MindTap Course List)

What is evidentiary material?

Management Of Information Security

What is a system requirement, and how are system requirements classified?

Systems Analysis and Design (Shelly Cashman Series) (MindTap Course List)

What is a cybersquatter? (64) What is the goal of the Anticybersquatting Consumer Protection Act (ACPA)? (64)

Enhanced Discovering Computers 2017 (Shelly Cashman Series) (MindTap Course List)

Why are some propane and natural gas tips made with a deep, recessed center?

Welding: Principles and Applications (MindTap Course List)

If your motherboard supports ECC DDR3 memory, can you substitute non-ECC DDR3 memory?

A+ Guide to Hardware (Standalone Book) (MindTap Course List)