Mechanics of Materials (MindTap Course List)
Mechanics of Materials (MindTap Course List)
9th Edition
ISBN: 9781337093347
Author: Barry J. Goodno, James M. Gere
Publisher: Cengage Learning
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Chapter 6, Problem 6.8.3P

A beam of wide-flange shape, W 8 x 28, has the cross section shown in the figure. The dimensions are b = 6.54 in., h = 8.06 in., fw = 0.285 in., and tf = 0.465 in.. The loads on the beam produce a shear force V = 7.5 kips at the cross section under consideration.

  1. Use center line dimensions to calculate the maximum shear stress raiaxin the web of the beam.

  • Use the more exact analysis of Section 5,10 in Chapter 5 to calculate the maximum shear stress in the web of the beam and compare it with the stress obtained in part .
  •   Chapter 6, Problem 6.8.3P, A beam of wide-flange shape, W 8 x 28, has the cross section shown in the figure. The dimensions are

    a.

    Expert Solution
    Check Mark
    To determine

    The maximum shear stress τmax in the web of the beam.

    Answer to Problem 6.8.3P

    The maximum shear stress τmax in the web of the beam is, τmax=3447psi

    Explanation of Solution

    Figure :

    Mechanics of Materials (MindTap Course List), Chapter 6, Problem 6.8.3P , additional homework tip  1

    Given:

    The section W8×28 , width b=6.54in , height h=8.06in , thickness out hide tw=0.285in , thickness of flange tf=0.465in , shear force V=7.5k ,

    Concept Used:

    Annuity problem requires the use of the moment of inertia equation as follows:

      IZ=twh312+btfh22

    Here,

      Height of beam =h , web thickness =tw ,  width=b , flange width=bf the moment of inertia about z −axis = IZ

    Annuity problem requires the use of the maximum shear stress equation as follows:

      τmax=(btftw+h4)Vh2IZ

    Here,

      Maximum shear stress =τmax , Shear force = V

    Calculation:

    As per the given problem

      tw=0.285in , tf=0.465in , b=6.54in , h=8.06in

    Annuity problem requires the use of this formula based on centerline dimensions

      IZ=twh312+btfh22

    Substitute these values in the formula

      IZ=[0.465( 8.06)312+6.54×0.465( 8.06)22]=111.216in4

      IZ=111.216in4

    Annuity problem requires the use of this formula

      tw=0.285in , tf=0.465in , b=6.54in , h=8.06in , IZ=111.216in4 , V=7.5k

      τmax=(btftw+h4)Vh2IZ

    Substitute these values in the formula

      τmax=[(6.54×0.4650.285+8.064)(8.06×7.52×111.216)]=3447psi

      τmax=3447psi

    Conclusion:

    The maximum shear stress τmax in the web is calculated by the formula : τmax=(btftw+h4)Vh2IZ

    b.

    Expert Solution
    Check Mark
    To determine

    The maximum shear stress τmax in the web of the beam and compare it with the stress obtain in part (a)

    Answer to Problem 6.8.3P

    The maximum shear stress τmax in the web of the beam is, τmax=3446psi

    Explanation of Solution

    Figure:

    Mechanics of Materials (MindTap Course List), Chapter 6, Problem 6.8.3P , additional homework tip  2

    Given:

    The section W8×28 , width b=6.54in , height h=8.06in ,thickness out hide tw=0.285in , thickness of flange tf=0.465in , shear force V=7.5k ,

    Concept Used:

    Annuity problem requires the use of the equation as follows:

      h2=h+tf

      h1=htf

    Here,

      Height of beam =h , web thickness =tw

    Annuity problem requires the use of the moment of inertia equation as follows:

      I=112(bh23bh13+twh13)

    Here,

      Height of beam =h , web thickness =tw ,  width=b , the moment of inertia = I

    Annuity problem requires the use of the maximum shear stress equation in the web as follows:

      τmax=V8Itw(bh22bh12+twh12)

    Here,

      Maximum shear stress =τmax , shear force = V

    Calculation:

    Based on more exact analysis As per the given problem

      h=8.06in , tf=0.465in

    Annuity problem requires the use of this formula:

      h2=h+tf

    Substitute these values in the formula

      h2=8.06+0.465=8.5in

      h2=8.5in

    Annuity problem requires the use of this formula

      h1=htf

    Substitute these values in the formula:

      h1=8.060.465=7.6in

      h1=7.6in

    Annuity problem requires the use of this formula

      b=6.54in , h1=7.6in , h2=8.5in , tw=0.285in

      I=112(bh23bh13+twh13)

    Substitute these values in the formula

      I=112(6.54×(8.5)36.54(7.6)3+0.285(7.6)3)=109.295in4

      I=109.295in4

    Annuity problem requires the use of this formula

      b=6.54in , h1=7.6in , h2=8.5in , tw=0.285in , I=109.295in4 , V=7.5k

      τmax=V8Itw(bh22bh12+twh12)

    Substitute these values in the formula

      τmax=7.58×109.295×0.285(6.54(8.5)26.54(7.6)2+0.285(7.6)2)=3446psi

      τmax=3446psi

    Conclusion:

    The maximum shear stress τmax in the web of the beam is calculated by putting values in the formula: τmax=V8Itw(bh22bh12+twh12)

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    Chapter 6 Solutions

    Mechanics of Materials (MindTap Course List)

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