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 41P
Textbook Problem
898 views

Use the conjugate-beam method to determine the slopes and deflections at points B and C of the beams shown in Figs. P6.14 through P6.17.

Chapter 6, Problem 41P, Use the conjugate-beam method to determine the slopes and deflections at points B and C of the beams

FIG. P6.15, P6.41

To determine

Find the slope θB&θC and deflection ΔB&ΔC at point B and C of the given beam using the conjugate-beam method.

Explanation of Solution

The Young’s modulus (E) is 70 GPa.

The moment of inertia (I) is 500×106mm4.

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),

Since the point C is free end there is no support reaction at Point C. Therefore, the reaction at point C is also equal to zero.

Consider upward is positive and downward is negative.

Consider clockwise is negative and counterclockwise is positive.

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

V=0RA100=0RA=100kN

Determine the bending moment at C;

MC=300kNm

Determine the bending moment at B;

MB=300kNm

Determine the bending moment at A;

MA=100×6+300=900kNm

Show the M/EI diagram for the given beam as in Figure (2).

Conjugate-beam method:

In the given beam system, point A is a fixed end and point B is free end. But in the conjugate-beam method the fixed end of a real beam becomes free and the free end of real beam changed into the fixed end.

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

Calculation of shear at B in the conjugate-beam:

The shear force at B of the conjugate beam is equal to the slope at B on the real beam.

Consider the external forces acting (left of B) upward on the free body diagram as positive.

Determine the shear force at B using the relation;

SB=(bh)(12×b×h)

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

Substitute 6 m for b and 150EI and 300EI for h.

SB=(6×150EI)(12×6×300EI)=1,800kNm2EI

Determine the deflection at point B using the relation;

θB=1,800kNm2EI

Substitute 70 GPa for E and 500×106mm4 for I.

θB=1,800kNm2(70GPa×106kN/m21GPa)(500×106mm4×(1m1,000mm)4)=0.0514rad

Hence, the slope at point B is 0.0514rad_.

The bending moment at B in the conjugate beam is equal to defection at B on the real beam.

Take the clockwise moments of the external forces about B as positive.

Determine the bending moment B using the relation;

MB=(bh)(b2)(12×b×h)(23×b)

Substitute 6 m for b and 150EI and 300EI for h.

MB=(6×150EI)(62)(12×6×300EI)(23×6)=6,300kNm3EI

Determine the deflection at point B using the formula;

ΔB=6,300kNm3EI

Substitute 70 GPa for E and 500×106mm4 for I.

ΔB=6,300kNm3(70GPa×106kN/m21GPa)(500×106mm4×(1m1,000mm)4)=0

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
Estimate the amount of electricity that is projected to be generated from coal in 2017.

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

How many bits does an IPv6 address contain?

Network+ Guide to Networks (MindTap Course List)

What are the Cartesian coordinates of the four points shown at A, B. C, and D?

Precision Machining Technology (MindTap Course List)

Convert P = 5.00 atm into Pa, bar, and psia.

Fundamentals of Chemical Engineering Thermodynamics (MindTap Course List)

Explain the basic requirements for becoming a successful automotive technician.

Automotive Technology: A Systems Approach (MindTap Course List)

What is software as a service (SaaS)?

Fundamentals of Information Systems

What is access control?

Management Of Information Security

List the four activities of the planning phase. Explain how projects are prioritized.

Enhanced Discovering Computers 2017 (Shelly Cashman Series) (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)

Name three methods used to perform welding, cutting, or brazing operations.

Welding: Principles and Applications (MindTap Course List)