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Structural Analysis

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

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BuyFindarrow_forward

Structural Analysis

6th Edition
KASSIMALI + 1 other
Publisher: Cengage,
ISBN: 9781337630931
Chapter 6, Problem 13P
Textbook Problem
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Determine the slope and deflection at point A of the beam shown by the moment-area method.

Chapter 6, Problem 13P, Determine the slope and deflection at point A of the beam shown by the moment-area method. FIG.

FIG. P6.13, P6.39

To determine

Find the equations for slope and deflection of the beam at point A using moment area-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 beam as in Figure (1).

Refer Figure (1),

Consider clockwise as negative and counterclockwise as positive.

Determine the moment at support B;

MB=12×w×L×(23×L)=wL23

Here, w is the uniformly distributed load and L is the distance.

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

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)

Elastic curve:

The sign of M/EI diagram is negative, therefore, the beam bends downward. The support B of the given beam is fixed and the slope at B is zero. Therefore, the tangent to the elastic curve at B is horizontal.

Show the elastic curve diagram as in Figure (3).

The slope at point A can be calculated by evaluating the change in slope between A and B.

Express the change in slope using the first moment-area theorem as follows:

θA=θAB=AreaoftheM/EIbetweenAandB=0LEEIdx=0Lwx22EI(1x3L)dx        (1)

Integrate Equation (1) with respect to x.

θA=θAB=w2EI0L(x2x33L)dx=w2EI(x33x43L×4)0L=w2EI(L33L4

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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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