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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 6, Problem 22P

Textbook Problem

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6.18 through 6.22 Determine the smallest moment of inertia *I* required for the beam shown, so that its maximum deflection does not exceed the limit of 1/360 of the span length (i.e., Δ_{max} ≤ *L*/360). Use the moment-area method.

FIG. P6.22, P6.48

To determine

Find the smallest moment of inertia (*I*) required for the beam if the deflection does not exceed the limit

Given information:

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

**Calculation:**

Consider the 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 counterclockwise is positive.

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

Determine the reaction at support *E*;

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

Refer Figure (2),

Determine the bending moment at *E*;

Determine the bending moment at *D*;

Determine the bending moment at *C*;

Determine the bending moment at *B*;

Determine the bending moment at *A*;

Show the

Show the deflected shape of the given beam as in Figure (4).

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

Substitute

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

Substitute

Structural Analysis

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