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Structural Analysis

6th Edition
KASSIMALI + 1 other
Publisher: Cengage,
ISBN: 9781337630931

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Section
BuyFindarrow_forward

Structural Analysis

6th Edition
KASSIMALI + 1 other
Publisher: Cengage,
ISBN: 9781337630931
Chapter 6, Problem 39P
Textbook Problem
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6.39 Determine the slope and deflection at point A of the beam shown in Figs. P6.13 and P6.14 by the conjugate-beam method.

Chapter 6, Problem 39P, 6.39 Determine the slope and deflection at point A of the beam shown in Figs. P6.13 and P6.14 by the

FIG. P6.13, P6.39

To determine

Find the slope and deflection of the beam at point A using conjugate-beam method.

Explanation of Solution

Calculation:

Consider flexural rigidity EI of the beam is constant.

Consider a section at a distance of x from the free end.

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

Refer Figure (1),

Determine the intensity of load at x;

wL=wxxwx=wLx

Determine the bending moment at distance x;

Mx=12×wLx×x(L13×x)=12wx2(1x3L)

Since there is no support at point A, there will be no reaction.

Determine the support reaction at B using the relation;

V=0RB12×w×L=0RB=wL2

Consider clockwise moment as negative and counterclockwise moment as positive.

Determine the moment at support B;

+MB=0MB+12×w×L×(23×L)=0MB=wL23

Here, w is the uniformly varying load intensity and L is the distance.

Show the section and M/EI diagram for the given beam as in Figure (2).

Conjugate beam method:

In the real beam A is free end B is a fixed but in conjugate-beam method the end conditions has to be change. Change free end A as fixed end and fixed end B as free.

Show the conjugate beam acted upon by the loading from MEI diagram as in Figure (3).

The slope at A in the real beam is equal to the shear force at A of conjugate beam.

Determine the slope (shear force) at A using the relation;

θA=abwxdx=0Lwx22EI(1x3L)dx

Integrate the equation with respect to x

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Chapter 6 Solutions

Structural Analysis
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Ch. 6 - Determine the slope and deflection at point B of...Ch. 6 - Determine the slope and deflection at point B of...Ch. 6 - Determine the slope and deflection at point A of...Ch. 6 - Use the moment-area method to determine the slopes...Ch. 6 - 6.14 through 6.17 Use the moment-area method to...Ch. 6 - 6.14 through 6.17 Use the moment-area method to...Ch. 6 - 6.14 through 6.17 Use the moment-area method to...Ch. 6 - Determine the smallest moment of inertia I...Ch. 6 - Determine the smallest moment of inertia I...Ch. 6 - Determine the smallest moment of inertia I...Ch. 6 - 6.18 through 6.22 Determine the smallest moment of...Ch. 6 - 6.18 through 6.22 Determine the smallest moment of...Ch. 6 - 6.23 through 6.30 Determine the maximum deflection...Ch. 6 - 6.23 through 6.30 Determine the maximum deflection...Ch. 6 - 6.23 through 6.30 Determine the maximum deflection...Ch. 6 - 6.23 through 6.30 Determine the maximum deflection...Ch. 6 - Determine the maximum deflection for the beam...Ch. 6 - 6.23 through 6.30 Determine the maximum deflection...Ch. 6 - 6.23 through 6.30 Determine the maximum deflection...Ch. 6 - 6.23 through 6.30 Determine the maximum deflection...Ch. 6 - 6.31 and 6.32 Use the moment-area method to...Ch. 6 - Use the moment-area method to determine the slope...Ch. 6 - Use the moment-area method to determine the slopes...Ch. 6 - 6.33 and 6.34 Use the moment-area method to...Ch. 6 - Use the conjugate-beam method to determine the...Ch. 6 - Use the conjugate-beam method to determine the...Ch. 6 - Use the conjugate-beam method to determine the...Ch. 6 - Use the conjugate-beam method to determine the...Ch. 6 - 6.39 Determine the slope and deflection at point A...Ch. 6 - 6.40 through 6.43 Use the Conjugate-beam method to...Ch. 6 - Use the conjugate-beam method to determine the...Ch. 6 - 6.40 through 6.43 Use the Conjugate-beam method to...Ch. 6 - 6.40 through 6.43 Use the Conjugate-beam method to...Ch. 6 - 6.44 through 6.48 Using the conjugate-beam method,...Ch. 6 - 6.44 through 6.48 Using the conjugate-beam method,...Ch. 6 - 6.44 through 6.48 Using the conjugate-beam method,...Ch. 6 - Using the conjugate-beam method, determine the...Ch. 6 - Using the conjugate-beam method, determine the...Ch. 6 - 6.49 through 6.56 Determine the maximum deflection...Ch. 6 - 6.49 through 6.56 Determine the maximum deflection...Ch. 6 - 6.49 through 6.56 Determine the maximum deflection...Ch. 6 - Determine the maximum deflection for the beams...Ch. 6 - Determine the maximum deflection for the beams...Ch. 6 - 6.49 through 6.56 Determine the maximum deflection...Ch. 6 - 6.49 through 6.56 Determine the maximum deflection...Ch. 6 - 6.49 through 6.56 Determine the maximum deflection...Ch. 6 - 6.57 and 6.58 Use the conjugate-beam method to...Ch. 6 - Use the conjugate-beam method to determine the...Ch. 6 - 6.59 and 6.60 Use the conjugate-beam method to...Ch. 6 - 6.59 and 6.60 Use the conjugate-beam method to...

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