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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 32P
Textbook Problem
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Use the moment-area method to determine the slope and deflection at point D of the beam shown.

Chapter 6, Problem 32P, Use the moment-area method to determine the slope and deflection at point D of the beam shown. FIG.

FIG. P6.32, P6.58

To determine

Find the slope and deflection at point D of the given beam using the moment-area method.

Explanation of Solution

Given information:

The Young’s modulus (E) is 70 GPa.

The moment of inertia (I) is 2,340×106mm4.

Calculation:

Consider flexural rigidity EI of the beam is constant.

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

Refer Figure (1),

Consider upward is positive and downward is negative.

Consider clockwise is negative and counterclowise is positive.

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

MC=0RC×10(15×4×(42+10))(180×5)=0RC=1,62010RC=162kN

Determine the reaction at support C;

V=0RA+RC(15×4)180=0RA=240162RA=78kN

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

Refer Figure (2),

Determine the bending moment at A;

MA=(162×10)(180×5)(15×4×(42+10))=1,6201,620=0

Determine the bending moment at B;

MB=(78×5)=390kNm

Determine the bending moment at C;

MC=78×10(180×5)=780900=120kNm

Determine the bending moment at D;

MD=(78×14)(180×9)+(162×4)(15×4×42)=1,0921,620+648120=1,7401,740=0

Determine the distance where the bending moment is zero using the relation;

Mx=078x180(x5)=078x180x+900=0102x=900

x=900102x=8.82m

Hence, the bending moment is zero at 8.82 m from support A and 3.82 m from point B.

Show the M/EI diagram for the given beam as in Figure (3).

Show the elastic curve diagram as in Figure (4).

Refer Figure (3).

Determine the deflection between A and C using the relation;

ΔAC=MomentoftheareaoftheM/EIdiagrambetweenAandCaboutC=(12b1h1)(23×b1)+(12b2h2)(5+13×b2)(12b3h3)((5+3.82)+23×b3)

Here, b1 is the width of rectangle, h1 is the height of the triangle, b2 is the width of the triangle, h2 is the height of the triangle,, b3 is the width of the triangle, and h3 is the height of the triangle.

Substitute 5 m for b1, 390EI for h1, 3.82 m for b2, 390EI for h2, (5m3.82m) for b3, and 120EI for h3.

ΔAC=[(12×5×390EI)(23×5)+(12×3.82×390EI)(5+13×3.82)(12×(53.82)×120EI)((5+3.82)+23×1.18)]=1EI(3,250+4,673680)=7,243kNm3EI

Determine the slope at point C using the relation;

θC=7,243kNm3(L)EI

Here, L is the length between the supports

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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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