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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 6, Problem 43P

Textbook Problem

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6.40 through 6.43 Use the Conjugate-beam method to determine the slopes and deflections at points *B* and *C* of the beams Figs. P6.14 through P6.17.

FIG. P6.17, P6.43

To determine

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

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 given beam as in Figure (1).

Refer Figure (1),

Consider upward is positive and downward is negative.

Consider clockwise is negative and counterclowise is positive.

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

Determine the reaction at support *D*;

Show the free body diagram of the given beam as in Figure (2).

Refer Figure (2),

Determine the bending moment at *A*;

Determine the bending moment at *B*;

Determine the bending moment at *C*;

Determine the moment at *D*;

Show the

Show the

Consider counterclockwise is positive and clockwise is negative.

Take moment about *D*:

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

Consider upward is positive and downward is negative.

Determine the shear force at *B* using the relation;

Here,

Substitute

Determine the deflection at point *B* using the relation;

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

Hence, the slope at point *B* is

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

Determine the bending moment *B* using the relation;

Here,

Structural Analysis

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