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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 6, Problem 33P

Textbook Problem

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Use the moment-area method to determine the slopes and deflections at points *B* and *D* of the beam shown.

FIG. P6.33, P6.59

To determine

Find the slope *B* and *D* of the given beam using the moment-area method.

Given information:

The Young’s modulus (*E*) is 29,000 ksi.

The moment of inertia (*I*) is

**Calculation:**

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

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

Refer Figure (1),

Consider upward is force is positive and downward force is negative.

Consider clockwise moment is negative and counterclockwise moment is positive.

Split the given beam into two sections such as *AC* and *CE*.

Consider the portion *CE*:

Draw the free body diagram of the portion *CE* as in Figure (2).

Refer Figure (2),

Consider a reaction at *C* and take moment about point *C*.

Determine the reaction at *E*;

Determine the reaction at support *A*;

Show the reaction of the given beam as in Figure (3).

Refer Figure (3),

Determine the moment at *A*:

Determine the bending moment at *B*;

Determine the bending moment at *C*;

Determine the bending moment at *D*;

Determine the bending moment at *E*;

Show the

Show the elastic curve diagram as in Figure (5).

Refer Figure (4),

Determine the slope at *B*;

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

Substitute 12 ft for

Substitute 29,000 ksi for *E* and *I*.

Hence, the slope at *B* is

Determine the deflection between *A* and *B* using the relation;

Here,

Substitute 12 ft for

Substitute 29,000 ksi for *E* and *I*.

Hence, the deflection at *B* is

To determine the slope at point *E*, it is necessary to determine the deflection at point *C* and the deflection between *C* and *E*.

Determine the deflection at *C* and *A* using the relation;

Substitute 12 ft for

Determine the deflection between *C* and *E* using the relation;

Substitute 12 ft for

Structural Analysis

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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...

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