BuyFind*arrow_forward*

6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 6, Problem 6P

Textbook Problem

49 views

6.1 through 6.6 Determine the equations for slope and deflection of the beam shown by the direct integration method. *EI* = constant.

FIG. P6.6

To determine

Find the equations for slope and deflection of the beam using direct integration method.

**Calculation:**

Consider flexural rigidity *EI* of the beam is constant.

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

Refer Figure (1),

Consider upward force is positive and downward force is negative.

Consider clockwise is negative and counterclowise is positive.

Determine the support reaction at *A* using the relation;

Determine the support reaction at *B* using the relation;

Show the reaction values as in Figure (2).

Take a section at a distance of *x*.

Show the section as in Figure (2).

**Consider the segment AB:**

Refer Figure (2),

Write the equation for bending moment at *x* distance.

Write the equation for

Write the equation for slope as follows:

Integrate Equation (1) with respect to *x*.

Write the equation for deflection as follows:

Integrate Equation (2) with respect to *x*.

Find the integration constants

Write the boundary conditions as follows:

Apply the above boundary conditions in Equation (3):

Write the boundary conditions as follows:

Apply the above boundary conditions in Equation (3):

Find the equation for slope.

Substitute

Thus, the equation for slope is

Find the equation for deflection.

Substitute

Thus, the equation for deflection is

**Consider segment BC;**

Show the distance at a distance of *x* as in Figure (4).

Refer Figure (2),

For segment *BC* the limit should be

Write the equation for bending moment at *x* distance.

Write the equation for

Write the equation for slope as follows:

Integrate Equation (4) with respect to *x*.

Write the equation for deflection as follows:

Integrate Equation (5) with respect to *x*.

Write the boundary conditions as follows:

The slope at left and right of support *B* is equal

Structural Analysis

Show all chapter solutions

Ch. 6 - 6.1 through 6.6 Determine the equations for slope...Ch. 6 - 6.1 through 6.6 Determine the equations for slope...Ch. 6 - Determine the equations for slope and deflection...Ch. 6 - Determine the equations for slope and deflection...Ch. 6 - 6.1 through 6.6 Determine the equations for slope...Ch. 6 - 6.1 through 6.6 Determine the equations for slope...Ch. 6 - Determine the slope and deflection at point B of...Ch. 6 - 6.7 and 6.8 Determine the slope and deflection at...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 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...

Find more solutions based on key concepts

Show solutions using Figure 5-27, what is the advantage of the suspended type magnet over the other two types of magnets?

Solid Waste Engineering

Repeat Problem 2.2 with the following results of a sieve analysis: 2.2 Following are the results of a sieve ana...

Fundamentals of Geotechnical Engineering (MindTap Course List)

Three groups of students from the Geotechnical Engineering class collected soil-aggregate samples for laborator...

Principles of Geotechnical Engineering (MindTap Course List)

A W1499 of A992 steel is used as a beam with lateral support at 10-foot intervals. Assume that Cb=1.0 and compu...

Steel Design (Activate Learning with these NEW titles from Engineering!)

For Problems 16.33 through 16.38, draw the isometric view of the following objects. Make the necessary measurem...

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

True or False? No-start, surging, or stalling can be caused by an EGR valve that does not open.

Automotive Technology: A Systems Approach (MindTap Course List)

Identify several specific characteristics of intelligent behavior.

Fundamentals of Information Systems

Where does the water flow after leaving the impeller wheel? a. ______________________________ b. ______________...

EBK ELECTRICAL WIRING RESIDENTIAL

As a team, develop a set of criteria that you would use to evaluate the effectiveness of a mobile advertising c...

Principles of Information Systems (MindTap Course List)

Clearance between the vertical band saw guides and the blade should be ______________.

Precision Machining Technology (MindTap Course List)

Explain the difference between scaling up and scaling out.

Database Systems: Design, Implementation, & Management

Find the forces Q1,Q2, and Q3 so that the two forces systems are equivalent.

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

You have just set up a new wireless network at your house, and you want to determine whether your Linux laptop ...

Network+ Guide to Networks (MindTap Course List)

Identify several benefits of green computing Initiatives that have been broadly adopted.

Fundamentals of Information Systems

Accrued Wages A company employs a part-time staff of 50 employees, each earning $10 per hour and working 30 hou...

Cornerstones of Financial Accounting

A circular cylindrical steel tank (see figure) contains a volatile fuel under pressure, A strain gage at point ...

Mechanics of Materials (MindTap Course List)

Explain the need for the two-phase commit protocol. Then describe the two phases.

Database Systems: Design, Implementation, & Management

List and describe two specialized alternatives not often used as a continuity strategy.

Management Of Information Security

Explain how vacuum is used to provide a power assist.

Automotive Technology

Indicate the changes (using the shorthand representation) that you would need to make to the original TAL Distr...

A Guide to SQL

What are four organizational levels common to many businesses? Which level typically requires data that support...

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

Explain the impact of the Internet on plagiarism.

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

Calorie (energy) and horsepower (power) are two non-SI units that you might see on occasion. A. Death Valley Na...

Fundamentals of Chemical Engineering Thermodynamics (MindTap Course List)

What does CISSP stand for? Use the Internet to identify the ethical rules CISSP holders have agreed to follow.

Principles of Information Security (MindTap Course List)

What are the two basic methods of automatically starting a synchronous motor?

Electric Motor Control

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)