BuyFindarrow_forward

Structural Analysis

6th Edition
KASSIMALI + 1 other
Publisher: Cengage,
ISBN: 9781337630931

Solutions

Chapter
Section
BuyFindarrow_forward

Structural Analysis

6th Edition
KASSIMALI + 1 other
Publisher: Cengage,
ISBN: 9781337630931
Chapter 6, Problem 57P
Textbook Problem
1451 views

6.57 and 6.58 Use the conjugate-beam method to determine the slope and deflection at point D of the beam shown in Figs. P6.31 and P6.32.

FIG. P6.31, P6.57

Chapter 6, Problem 57P, 6.57 and 6.58 Use the conjugate-beam method to determine the slope and deflection at point D of the

To determine

Find the slope θD and deflection ΔD at point D of the given beam using the conjugate-beam method.

Explanation of Solution

The Young’s modulus (E) is 200 GPa.

The moment of inertia (I) is 262×106mm4.

Calculation:

Consider elastic modulus E of the beam is constant.

Show the free body diagram of the given beam as in Figure (1).

Refer Figure (1),

Consider upward is positive and downward is negative.

Consider clockwise is negative and counterclowise is positive.

Determine the support reaction at A using the Equation of equilibrium;

MC=0RA×10(120×3)=0RA=36010RA=36kN

Determine the reaction at support C using the relation;

V=0RA+RC120=0RC=12036RC=84kN

Show the reactions of the given beam as in Figure (2).

Refer Figure (2),

Determine the bending moment at A;

MA=(84×10)(120×7)=840840=0

Determine the bending moment at B;

MB=(36×7)=252kNm

Determine the bending moment at C;

MC=36(10)+(120×3)=360+360=0

Show the M/EI diagram for the given beam as in Figure (3).

Show the M/EI diagram for the conjugate-beam as in Figure (4).

Consider counterclockwise is positive and clockwise is negative.

Take moment about C:

Determine the support reaction at A using the Equation of equilibrium;

RA(10)12(252EI)(7)(3+13×7)12(252EI)(3)(23×3)=0RA=5,460kNm310EIRA=546kNm2EI

Determine the shear force at D using the relation;

SD=RA+(12×b1×h1)

Here, b is the width and h is the height of the triangle.

Substitute 546kNm2EI for RA, 10 m for b1, and (252EI) for h1.

SD=546kNm2EI+(12×10×252EI)=714kNm2EI

Determine the slope at D using the relation;

θD=714kNm2EI

Substitute 200 GPa for E and 262×106mm4 for I

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

Chapter 6 Solutions

Structural Analysis
Show all chapter solutions
add
Ch. 6 - Determine the slope and deflection at point B of...Ch. 6 - Determine the slope and deflection at point B of...Ch. 6 - Determine the slope and deflection at point A of...Ch. 6 - Use the moment-area method to determine the slopes...Ch. 6 - 6.14 through 6.17 Use the moment-area method to...Ch. 6 - 6.14 through 6.17 Use the moment-area method to...Ch. 6 - 6.14 through 6.17 Use the moment-area method to...Ch. 6 - Determine the smallest moment of inertia I...Ch. 6 - Determine the smallest moment of inertia I...Ch. 6 - Determine the smallest moment of inertia I...Ch. 6 - 6.18 through 6.22 Determine the smallest moment of...Ch. 6 - 6.18 through 6.22 Determine the smallest moment of...Ch. 6 - 6.23 through 6.30 Determine the maximum deflection...Ch. 6 - 6.23 through 6.30 Determine the maximum deflection...Ch. 6 - 6.23 through 6.30 Determine the maximum deflection...Ch. 6 - 6.23 through 6.30 Determine the maximum deflection...Ch. 6 - Determine the maximum deflection for the beam...Ch. 6 - 6.23 through 6.30 Determine the maximum deflection...Ch. 6 - 6.23 through 6.30 Determine the maximum deflection...Ch. 6 - 6.23 through 6.30 Determine the maximum deflection...Ch. 6 - 6.31 and 6.32 Use the moment-area method to...Ch. 6 - Use the moment-area method to determine the slope...Ch. 6 - Use the moment-area method to determine the slopes...Ch. 6 - 6.33 and 6.34 Use the moment-area method to...Ch. 6 - Use the conjugate-beam method to determine the...Ch. 6 - Use the conjugate-beam method to determine the...Ch. 6 - Use the conjugate-beam method to determine the...Ch. 6 - Use the conjugate-beam method to determine the...Ch. 6 - 6.39 Determine the slope and deflection at point A...Ch. 6 - 6.40 through 6.43 Use the Conjugate-beam method to...Ch. 6 - Use the conjugate-beam method to determine the...Ch. 6 - 6.40 through 6.43 Use the Conjugate-beam method to...Ch. 6 - 6.40 through 6.43 Use the Conjugate-beam method to...Ch. 6 - 6.44 through 6.48 Using the conjugate-beam method,...Ch. 6 - 6.44 through 6.48 Using the conjugate-beam method,...Ch. 6 - 6.44 through 6.48 Using the conjugate-beam method,...Ch. 6 - Using the conjugate-beam method, determine the...Ch. 6 - Using the conjugate-beam method, determine the...Ch. 6 - 6.49 through 6.56 Determine the maximum deflection...Ch. 6 - 6.49 through 6.56 Determine the maximum deflection...Ch. 6 - 6.49 through 6.56 Determine the maximum deflection...Ch. 6 - Determine the maximum deflection for the beams...Ch. 6 - Determine the maximum deflection for the beams...Ch. 6 - 6.49 through 6.56 Determine the maximum deflection...Ch. 6 - 6.49 through 6.56 Determine the maximum deflection...Ch. 6 - 6.49 through 6.56 Determine the maximum deflection...Ch. 6 - 6.57 and 6.58 Use the conjugate-beam method to...Ch. 6 - Use the conjugate-beam method to determine the...Ch. 6 - 6.59 and 6.60 Use the conjugate-beam method to...Ch. 6 - 6.59 and 6.60 Use the conjugate-beam method to...

Additional Engineering Textbook Solutions

Find more solutions based on key concepts
Show solutions add
What does the integral sign represent?

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

Cloud Services Public, Private, Hybrid, and Personal Clouds (IaaS) When deciding how to host data and apps on t...

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

Explain the difference between a distributed database and distributed processing.

Database Systems: Design, Implementation, & Management

What is the difference between a threat agent and a threat?

Principles of Information Security (MindTap Course List)

Band saw cutting speeds are given in _________.

Precision Machining Technology (MindTap Course List)

Give three examples of Smartphone operating system.

Fundamentals of Information Systems

What is the purpose of an EISP?

Management Of Information Security

How has the proliferation of mobile devices affected IT professionals?

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

Name three items that are manufactured using welding.

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)