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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 6, Problem 56P

Textbook Problem

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6.49 through 6.56 Determine the maximum deflection for the beams shown in Figs. P6.23 through P6.30 by the conjugate-beam method.

FIG. P6.30, P6.56

To determine

Find the maximum deflection for the beam using the conjugate-beam method.

Given information:

The Young’s modulus is 200 GPa.

The moment of inertia is

**Calculation:**

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

The given beam can be taken into two segments to draw the *A* to *D*; the reactions are calculated by considering all the forces acting throughout the span. Second segment is a simply supported beam of span *B* to *C* and the reaction at each support can be calculated by considering the load acting between *B* and *C*.

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

Refer Figure (1),

Determine the support reaction at *A*;

Determine the support reaction at *B*;

Show the reactions of the 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 *D*;

**Consider span BC:**

Show the free body diagram of the beam as in Figure (3).

Refer Figure (3),

Determine the support reaction at *B*;

Determine the support reaction at *C*;

Determine the bending at the centre of beam *BC*;

Show the reaction and moment as in Figure (4).

Show the conjugate beam diagram for the whole span as in Figure (5).

Refer Figure (5),

The end condition of the original beam is free but in the conjugate-beam method the ends are changed to fixed end and the reaction at point *B* and *C* are calculated by considered the intermediate supports *B* and *C* as hinge.

Show the conjugate-beam diagram for the beam portion BC as in Figure (6).

Determine the conjugate beam reaction at *B*;

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

Substitute

Structural Analysis

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