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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 6, Problem 53P

Textbook Problem

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Determine the maximum deflection for the beams shown in Figs. P6.23 through P6.30 by the conjugate-beam method.

FIG. P6.27, P6.53

To determine

Find the maximum deflection

Given information:

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

The moment of inertia (*I*) is

**Calculation:**

Consider Young’s modulus *E* of the beam is constant.

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

Refer Figure (2),

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 reactions of the given beam as in Figure (2).

Refer Figure (2),

Determine the bending moment at *A*;

Determine the bending moment at *B*;

The bending moment at *B* is *A* and *B* is *I* but the moment of inertia of portion *B* and *C* is 2*I*. Therefore, the in

Determine the bending moment at *C*;

The bending moment at *C* is *C* and *D* is *I* but the moment of inertia of portion *B* and *C* is 2*I*. Therefore, the in

Show the

Show the conjugate diagram of the given beam as in Figure (4).

Refer Figure (4),

Determine the support reaction at *A* of a conjugate beam using the relation;

The maximum bending moment in the conjugate beam occur at point *M*, at a distance of *B*.

Determine the intensity of load at

Determine the shear force at point *M* using the relation;

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

Substitute

Structural Analysis

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