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 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

Chapter 6, Problem 6P, 6.1 through 6.6 Determine the equations for slope and deflection of the beam shown by the direct

To determine

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

Explanation of Solution

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;

MB=0RA×L(P×a)=0RA=PaLRA=PaL()

Determine the support reaction at B using the relation;

V=0RA+RBP=0RB=P(PaL)RB=PL+PaLRB=P(1+aL)

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.

Mx=RA(x)=PaL(x)=PaxL

Write the equation for MEI as follows:

d2ydx2=1EI(PaxL)        (1)

Write the equation for slope as follows:

Integrate Equation (1) with respect to x.

dydx=θ=1EI(PaL)(xdx)=PaEIL(x22)+C1        (2)

Write the equation for deflection as follows:

Integrate Equation (2) with respect to x.

y=[PaEIL((x22))+C1]dx=Pa2EIL(x33)+C1x+C2        (3)

Find the integration constants C1andC2:

Write the boundary conditions as follows:

Atx=0;y=0:

Apply the above boundary conditions in Equation (3):

0=Pa2EIL((03)3)+C1(0)+C2C2=0

Write the boundary conditions as follows:

Atx=L;y=0:

Apply the above boundary conditions in Equation (3):

0=Pa2EIL(L33)+C1(L)+0C1(L)=PaL26EIC1=PaL6EI

Find the equation for slope.

Substitute PaL6EI for C1 in Equation (2).

θ=PaEIL(x22)+PaL6EI=PaL6EI(13x2L2)

Thus, the equation for slope is PaL6EI(13x2L2)_.

Find the equation for deflection.

Substitute PaL6EI for C1 and 0 for C2 in Equation (3).

y=Pa2EIL(x33)+(PaL6EI)x+0=Pa2EIL(x33)+(PaxL6EI)=PaxL6EI(1x2L2)

Thus, the equation for deflection is PaxL6EI(1x2L2)_.

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 Lx(L+a).

Write the equation for bending moment at x distance.

Mx=P(L+ax)

Write the equation for MEI as follows:

d2ydx2=1EI(P(L+ax))=PEI(L+ax)        (4)

Write the equation for slope as follows:

Integrate Equation (4) with respect to x.

dydx=θ=PEI(L+ax)dx=PEI(Lx+axx22)+C3        (5)

Write the equation for deflection as follows:

Integrate Equation (5) with respect to x.

y=[PEI(Lx+axx22)+C3]dx=PEI(Lx22+ax22x36)+C3x+C4        (6)

Write the boundary conditions as follows:

Atx=L

The slope at left and right of support B is equal

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
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)

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

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

Database Systems: Design, Implementation, & Management

Explain the impact of the Internet on plagiarism.

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)