   # An overhanging beam ABC rests on a simple support at A and a spring support at B (see figure). A concentrated load P acts at the end of the overhang. Span AB has length /_, the overhang has length a, and the spring has stiffness k. Determine the downward displacement 6 C of the end of the overhang. (Obtain the solution by using the modified form of Castigliano's theorem.) ### 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 9.9.11P
Textbook Problem
28 views

## An overhanging beam ABC rests on a simple support at A and a spring support at B (see figure). A concentrated load P acts at the end of the overhang. Span AB has length /_, the overhang has length a, and the spring has stiffness k.Determine the downward displacement 6Cof the end of the overhang. (Obtain the solution by using the modified form of Castigliano's theorem.) To determine

Downward displacement δC at the end of overhang.

### Explanation of Solution

Given:

RA=PaL (Downward)

RB=PL(L+a) (Upward)

Bending moment and partial derivative for segment AB:

MAB=RAx=PaxL

dMABdP=axL(0xL)

Bending moment and partial derivative for segment BC:

MBC=PxdMBCdP=x(0xa)

Strain energy of the spring:

US=RB22k=P2( L+a)22kL2

Strain energy of the beam:

UB= M 2dx2EIRB22k

Total strain energy:

U=UB+US

Apply Castigliano’s Theorem:

δC=dUdP=ddP M 2dx2EI+ddP[P2<

### 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

Find more solutions based on key concepts
What is PCI DSS and why is it important for information security?

Principles of Information Security (MindTap Course List)

Calorimeters are devices that are commonly used to measure the heating value of fuels. For example, a Junkers f...

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

Find the rectangular representation of the force F, given that its magnitude is 320 N.

International Edition---engineering Mechanics: Statics, 4th Edition

Convert 10,000 ft-lbf of energy into BTU, Joules, and kilojoules.

Fundamentals of Chemical Engineering Thermodynamics (MindTap Course List)

Because of current standards, head crashes no longer occur.

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

Why is it important to find a good welding position?

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) 