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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 6, Problem 15P

Textbook Problem

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6.14 through 6.17 Use the moment-area method to determine the slopes and deflections at points *B* and *C* of the beam shown.

FIG. P6.15, P6.41

To determine

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

Given information:

The Young’s modulus (*E*) is 70 GPa.

The moment of inertia (*I*) is

**Calculation:**

Consider elastic modulus *E* of the beam is constant.

Show 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;

Determine the bending moment at *C*;

Determine the bending moment at *B*;

Determine the bending moment at *A*;

Show the

Elastic curve:

The sign of *A* of the given beam is fixed and the slope at *A* is zero. Therefore, the tangent to the elastic curve at *A* is horizontal.

Show the elastic curve diagram as in Figure (3).

The slope at point *B* can be calculated by evaluating the change in slope between *A* and *B*.

Express the change in slope using the first moment-area theorem as follows:

Here, *b* is the width,

Substitute 6 m for *b*,

Determine the slope at B using the relation;

Substitute 70 GPa for *E* and *I*.

Hence, the slope at point *B* is

The deflection of *B* with respect to the undeforemd axis of the beam is equal to the tangential deviation of *B* from the tangent at *A*.

Express the deflection at *B* using the second moment-area theorem as follows:

Here, *b* is the width of triangle and rectangle,

Substitute 6 for *b*,

Determine the deflection at *B* using the relation;

Substitute 70 GPa for *E* and *I*.

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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