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6th Edition

KASSIMALI + 1 other

Publisher: Cengage,

ISBN: 9781337630931

Chapter 6, Problem 48P

Textbook Problem

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Using the conjugate-beam method, determine the smallest moments of inertia *I* required for the beams shown in Figs. P6.18 through P6.22, so that the maximum beam deflection does not exceed the limit of 1/360 of the span length (i.e., Δ_{max} ≤ *L*/ 360).

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

Take moment about point *D*.

Determine the reaction at support *A* using the relation;

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

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

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

Substitute

Structural Analysis

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