International Edition---engineering Mechanics: Statics, 4th Edition
International Edition---engineering Mechanics: Statics, 4th Edition
4th Edition
ISBN: 9781305501607
Author: Andrew Pytel And Jaan Kiusalaas
Publisher: CENGAGE L
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Chapter 9, Problem 9.17P

A W 8 × 67 section is joined to a C 10 × 20 section to form a structural member that has the cross section shown. Calculate I ¯ x and I ¯ y for this cross section. (See Probs. 9.13 and 9.16 for the properties of the structural sections.)

Chapter 9, Problem 9.17P, A W867 section is joined to a C1020 section to form a structural member that has the cross section

Expert Solution & Answer
Check Mark
To determine

The values of I¯x and I¯y for the given cross section shown.

Answer to Problem 9.17P

  I¯x=358 in4

  I¯y=167.5 in4

Explanation of Solution

Given information:

The cross-sectional properties of the structural shape W8×67

  A=19.7 in.2,  Ix=272 in.4,   Iy=88.6 in.4

Cross sectional properties of structural steel section C10×20 :

  A=5.88 in.2,  Ix=78.9 in.4,  Iy=2.81 in.4

Calculations:

International Edition---engineering Mechanics: Statics, 4th Edition, Chapter 9, Problem 9.17P , additional homework tip  1

International Edition---engineering Mechanics: Statics, 4th Edition, Chapter 9, Problem 9.17P , additional homework tip  2

For the composite area: (representing the data in tabular form)

    Part  I¯x(in4)  A(in2)  y¯(in)  Ay¯(in3)  I¯x+Ay¯2  Iy(in4)
    12.815.888.77351.59455.478.9
    227219.704.5088.65670.988.6
    sum25.58140.241126.3167.5

For the assembly:

  The centroid:y¯= A y ¯ A=140.2425.58=5.482 inMoment of inertia about the xaxis:Ix=( I ¯ x A y ¯ 2 )=1126.3 in4Moment of inertia about the yaxis:Iy=Iy=167.5 in4Hence,Moment of inertia about the centroidal xand yaxis:I¯x=IxAy¯2=1126.3(25.58)( 5.4822)I¯x=358 in4and,I¯y=Iy  (since section is symmetric about y-axis)I¯y=167.5 in4

Conclusion:

For the composite cross-section, I¯x=358 in4 and I¯y=167.5 in4.

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Chapter 9 Solutions

International Edition---engineering Mechanics: Statics, 4th Edition

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