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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 17P
Textbook Problem
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6.14 through 6.17 Use the moment-area method to determine the slopes, and deflections at points B and C of the beam shown.

FIG. P6.17, P6.43

Chapter 6, Problem 17P, 6.14 through 6.17 Use the moment-area method to determine the slopes, and deflections at points B

To determine

Find the slope θB&θC and deflection ΔB&ΔC at point B and C of the given beam using the moment-area method.

Explanation of Solution

Given information:

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

The moment of inertia (I) is 4,000in.4.

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;

MD=0RA×36(50×27)=0RA=1,35036RA=37.5kips

Determine the reaction at support D;

V=0RA+RD=50RD=5037.5RD=12.5kips

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

Refer Figure 2,

Determine the bending moment at A;

MA=(12.5×36)(50×9)=450450=0

Determine the bending moment at B;

MB=37.5×9=337.5kipsft

Determine the bending moment at C;

MC=37.5×18(50×9)=225kipsft

Determine the moment at D;

MD=(37.5×36)(50×27)=1,3501,350=0

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 at D using the relation;

ΔDA=MomentoftheareaoftheM/EIdiagrambetweenAandDaboutD=(12b1h1)(27+13×b1)+(12b2h2)(23×b2)

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

Substitute 9 ft for b1, 337.5EI for h1, 27 ft for b2, and 337.5EI for h2.

ΔDA=(12×9×337.5EI)(27+13×9)+(12×27×337.5EI)(23×27)=127,575kips-ft3EI

Determine the slope at point A using the relation;

θA=127,575kips-ft3(L)EI

Here, L is the length of the beam.

Substitute 36 ft for L.

θA=127,575kips-ft3(36)EI=3,543.75kips-ft2EI

Determine the slope at point B using the relation;

θB=θAθAB=θA(12×b×h)

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

Substitute 3,543.75kips-ft2EI for θA, 9.0 ft for b, and 337.5EI for h.

θB=3,543.75kips-ft2EI(12×9.0×337.5EI)=2,025kips-ft2EI

Substitute 29,000 ksi for E and 4,000in.4 for I.

θB=2,025kips-ft2×(12in.1ft)229,000×4,000=0.0025rad

Hence, the slope at B is 0.0025rad_.

Determine the deflection at point B using the relation;

ΔB=LABθAΔBA=LABθA(12×b×h)(13×b)

Here, LAB is the length of portion A and B, ΔBA is the deflection between the point A and B, b is the width of triangle, and h is the height of the triangle.

Substitute 9.0 ft for LAB, 3,543.75kips-ft2EI for θA, 9.0 ft for b, and 337.5EI for h.

ΔB=(9)(3,543

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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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