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 6.2.8P

A plastic-lined steel pipe has the cross-sectional shape shown in the figure. The steel pipe has an outer diameter d1= 100 mm and an inner diameter d2= 94 mm. The plastic liner has an inner diameter d1= 82 mm. The modulus of elasticity of the steel is 75 times the modulus of the plastic.

  1. Determine the allowable bending moment Mallowif the allowable stress in the steel is 35 M Pa and in the plastic is 600 kPa.

  • If pipe and liner diameters remain unchanged, what new value of allowable stress for the steel pipe will result in the steel pipe and plastic liner reaching their allowable stress values under the same maximum moment (i.e., a balanced design)? What is the new maximum moment?
  •   Chapter 6, Problem 6.2.8P, A plastic-lined steel pipe has the cross-sectional shape shown in the figure. The steel pipe has an

    i.

    Expert Solution
    Check Mark
    To determine

    The allowable bending moment if the allowable stress for steel is 35 MPa and plastic 600 Kpa

    Answer to Problem 6.2.8P

    Allowable bending moment for plastic, Mallowableplastic = 1050.8 N-m

    Allowable bending moment for Copper, Mallowablesteel =768.25 N-m

    Explanation of Solution

    Given:

    Allowable stress for steel, ssteel = 35 MPa

    Allowable stress for plastic, splastic= 600 kPa

    d1= 82 mm

    d2= 94 mm

    d3= 100 mm

    Esteel= 75*Eplastic

    Concept Used:

      Mallowable,steel=σsteel(E steel*I steel+E plasticI plastic)Esteel*d32Mallowable,steel=σsteelπ(E steel*( d 3 4 d 2 4 )+E plasticd14)32*Esteel*d3Mallowable,plastic=σplastic(E steel*I steel+E plasticI plastic)Eplastic*d22Mallowable,plastic=σplasticπ(E steel*( d 3 4 d 2 4 )+E plasticd14)32*Eplastic*d2

    Calculation:

      Mallowable,steel=σsteel(E steel*I steel+E plasticI plastic)Esteel*d32Mallowable,steel=σsteelπ(E steel*( d 3 4 d 2 4 )+E plasticd14)32*Esteel*d3Mallowable,steel=35*106*π(( 94 4 82 4 )+ 1004)32*75*100Mallowable,steel=768.25N.m

      Mallowable,plastic=σplastic(E steel*I steel+E plasticI plastic)Eplastic*d22Mallowable,plastic=σplasticπ(E steel*( d 3 4 d 2 4 )+E plasticd14)32*Eplastic*d2Mallowable,plastic=600*103π*75(( 94 4 82 4 )+ 1004)32*94Mallowable,plastic=1050.8N.m

    Conclusion:

    Allowable bending moment for plastic, Mallowableplastic = 1050.8 N-m

    Allowable bending moment for Copper, Mallowablesteel =768.25 N-m

    ii.

    Expert Solution
    Check Mark
    To determine

    The value of the diameter of the copper rod for a balanced design

    Answer to Problem 6.2.8P

    The maximum moment is 1050.76 N-m in balanced condition

    Explanation of Solution

    Given:

    Allowable stress for titanium, sti = 840 MPa

    Allowable stress for titanium, scu= 700 MPa

    Outer Diameter of the titanium rod, d2 = 40 mm

    Eti= 110 GPa

    Ecu= 120 GPa

    Concept Used:

      Allowablebendingmomentofsteel=Allowablebendingmomentofplasticσsteel(E steel*I steel+E plasticI plastic)Esteel*d32=σplastic(E steel*I steel+E plasticI plastic)Eplastic*d22

    Calculation:

       Allowablebendingmomentofsteel=Allowablebendingmomentofplastic

       σ steel ( E steel * I steel + E plastic I plastic ) E steel * d 3 2 = σ plastic ( E steel * I steel + E plastic I plastic ) E plastic * d 2 2

       σ Steel allowable E Stell * d 3 = σ Plastic allowable E Plastic * d 2

       σ Steel allowable = 600* 10 3 *100 94

       σ Steel allowable =47.87MPa

       Maximumbendingmoment= σ steel ( E steel * I steel + E plastic I plastic ) E steel * d 3 2   M max = 47.87* 10 6 *75( π( ( 94 4 82 4 )+ 100 4 ) ) * 100 2   M max =1050.76N.m

    Conclusion:

    The maximum moment is 1050.76 N-m in balanced condition

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    Chapter 6 Solutions

    Mechanics of Materials (MindTap Course List)

    Ch. 6 - A bimetallic beam used in a temperature-control...Ch. 6 - A simply supported composite beam 3 m long carries...Ch. 6 - A simply supported wooden I-beam with a 12-ft span...Ch. 6 - -14 A simply supported composite beam with a 3.6 m...Ch. 6 - -15 A composite beam is constructed froma wood...Ch. 6 - A wood beam in a historic theater is reinforced...Ch. 6 - Repeat Problem 6.2-1 but now assume that the steel...Ch. 6 - Repeat Problem 6.2-17 but now use a...Ch. 6 - A sandwich beam having steel faces enclosing a...Ch. 6 - A wood beam 8 in. wide and 12 in. deep (nominal...Ch. 6 - A simple beam of span length 3.2 m carries a...Ch. 6 - A simple beam that is 18 ft long supports a...Ch. 6 - The composite beam shown in the figure is simply...Ch. 6 - The cross section of a beam made of thin strips of...Ch. 6 - Consider the preceding problem if the beam has...Ch. 6 - A simple beam thai is IS ft long supports a...Ch. 6 - The cross section of a composite beam made of...Ch. 6 - A beam is constructed of two angle sections, each...Ch. 6 - 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