Bundle: Mechanics Of Materials, Loose-leaf Version, 9th + Mindtap Engineering, 2 Terms (12 Months) Printed Access Card
Bundle: Mechanics Of Materials, Loose-leaf Version, 9th + Mindtap Engineering, 2 Terms (12 Months) Printed Access Card
9th Edition
ISBN: 9781337594301
Author: Barry J. Goodno, James M. Gere
Publisher: Cengage Learning
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Chapter 11, Problem 11.9.7P
To determine

The value of the allowable axial load pressure for the different lengths.

Expert Solution & Answer
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Answer to Problem 11.9.7P

The value of the allowable axial load pressure for the different lengths is:

    S.No Length of column( ft) Axial load ,Pallow( k )
    1 06 58.8
    2 12 43.0
    3 18 23.1
    4 24 13.0

Explanation of Solution

Given Information:

The outside diameter of the steel pipe column, do =4.5 in.

The thickness of the steel pipe column, t = .237 in.

The value of the young modulus, E = 29000 ksi

The value of maximum stress, sy = 36 ksi

Concept Used:

For pinned end, K=1

Here, r = radius of gyration.

  Lcr=2π2EσyLc=criticallength ofcolumn in ft

  σallow_max=σyn1

Then we try different value of σallow

  A=Pσallow

Then select the trial column

  n1=NA        if(KLr)>KLcr&n1=53+3(KLr)8(KLcr)((KLr))38(KLcr)3if(KLr)KLcrn2=2312         if(KLr)>KLcr&n2=NA          if(KLr)KLcr

  σallow=σy[1n1(1(KLr)22(KLcr)2)]if(KLr)KLcrσallow=σy[(KLcr)22n2i(KLr)2]if(KLr)>KLcrPallow=σallow×A

Calculation:

For pinned end, K = 1.

  di=4.52(0.237)=4.026in.A=π4(4.524.0262)=3.1740in.2I=π64(4.544.0264)=7.2326in.4r=7.23263.1740=1.5095in.(Lr)max=200Lmax=200×1.5095=301.9in.=25.16ft

Here, r = radius of gyration.

  Lc=1.50952π22900036=1.5095×126.09=190.33in.=15.86ftFori=1,L1=6ftasL1<Lc

  So,n11=53+3(61.5095)8(15.861.5095)(61.5095)38(15.861.5095)3=1.667+.14190.00234=1.806Fori=2,L2=12ft

  AsL2<LcSo,n12=53+3(121.5095)8(15.861.5095)(121.5095)38(15.861.5095)3=1.667+.28370.0541=1.896Fori=3,L3=18ft

   As L3>Lcn23=2312=1.917Fori=4,L4=24ftAsL4>Lcn24=2312=1.917

  σallow=σy[1n1i(1(KLir)22(KLcr)2)]ifKLirKLcrthisisusedforL1&L2σallow=σy[(KLcr)22n2i(KLir)2]ifKLir>KLcrthisisusedforL3&L4

For L1 = 6 ft.

  σallow=36[11.805(1(61.5095)22(15.861.5095)2)]=18.517ksiPallow=18.517×3.1740=58.77k=58.8k

For L2 =12 ft

  σallow=36[11.896(1(121.5095)22(15.861.5095)2)]=13.55ksiPallow=13.55×3.1740=43.0k=43k

For L3 =18 ft.

  σallow=36[(15.861.5095)22×1.917(181.5095)2]=7.289ksiPallow=7.289×3.1740=23.14k=23.1k

For L4 = 24 ft,

  σallow=36[(15.861.5095)22×1.917(241.5095)2]=4.10ksiPallow=4.10×3.1740=13.01k=13.0k

Conclusion:

The value of the allowable axial load pressure for the different lengths is:

    S.No Length of column( ft) Axial load ,Pallow( k )
    1 06 328
    2 12 243
    3 18 134
    4 24 75.3

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Chapter 11 Solutions

Bundle: Mechanics Of Materials, Loose-leaf Version, 9th + Mindtap Engineering, 2 Terms (12 Months) Printed Access Card

Ch. 11 - The figure shows an idealized structure consisting...Ch. 11 - Rigid column ABCD has an elastic support at B with...Ch. 11 - An idealized column is made up of rigid bars ABC...Ch. 11 - An idealized column is composed of rigid bars ABC...Ch. 11 - Repeat Problem 11.2-14 using L = 12 ft, ß = 0.25...Ch. 11 - An idealized column is composed of rigid bars ABC...Ch. 11 - Column AB has a pin support at A,a roller support...Ch. 11 - Slender column ABC is supported at A and C and is...Ch. 11 - Calculate the critical load PCTfor a W 8 × 35...Ch. 11 - Solve the preceding problem for a W 250 × 89 steel...Ch. 11 - Solve Problem 11.3-3 for a W 10 × 45 steel column...Ch. 11 - A horizontal beam AB is pin-supported at end A and...Ch. 11 - A column ABC is supported at ends A and C and...Ch. 11 - Find the controlling buckling load (kN) for the...Ch. 11 - A column, pinned at top and bottom, is made up of...Ch. 11 - Repeat Problem 11.3-9. Use two C 150 × 12.2 steel...Ch. 11 - A horizontal beam AB is pin-supported at end A and...Ch. 11 - -12 A horizontal beam AB is supported at end A and...Ch. 11 - A horizontal beam AB has a sliding support at end...Ch. 11 - A slender bar AB with pinned ends and length L is...Ch. 11 - A rectangular column with cross-sectional...Ch. 11 - .16 Three identical, solid circular rods, each of...Ch. 11 - Three pinned-end columns of the same material have...Ch. 11 - A long slender column ABC is pinned at ends A and...Ch. 11 - The roof over a concourse at an airport is...Ch. 11 - The hoisting arrangement for lifting a large pipe...Ch. 11 - A pinned-end strut of aluminum (E = 10,400 ksi)...Ch. 11 - The cross section of a column built up of two...Ch. 11 - The truss ABC shown in the figure supports a...Ch. 11 - A truss ABC supports a load W at joint B, as shown...Ch. 11 - An S6 × 12.5 steel cantilever beam AB is supported...Ch. 11 - The plane truss shown in the figure supports...Ch. 11 - A space truss is restrained at joints O, A,B, and...Ch. 11 - 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A simply supported slender column is subjected to...Ch. 11 - A brass bar of a length L = 0.4 m is loaded at end...Ch. 11 - Determine the bending moment M in the pinned-end...Ch. 11 - Plot the load-deflection diagram for a pinned-end...Ch. 11 - Solve the preceding problem for a column with e =...Ch. 11 - A wide-flange member (W200 × 22.5) is compressed...Ch. 11 - A wide-f hinge member (W 10 × 30) is compressed by...Ch. 11 - Solve the preceding problem (W 250 × 44.8) if the...Ch. 11 - The column shown in the figure is fixed at the...Ch. 11 - An aluminum box column with a square cross section...Ch. 11 - Solve the preceding problem for an aluminum column...Ch. 11 - A steel post /t if with a hollow circular cross...Ch. 11 - A frame ABCD is constructed of steel wide-flange...Ch. 11 - A steel bar has a square cross section of width b...Ch. 11 - ]11.6-2 A brass bar (E = 100 GPa) with a square...Ch. 11 - A square aluminum bar with pinned ends carries a...Ch. 11 - A pinned-and column of a length L = 2A m is...Ch. 11 - A pinned-end strut of a length L = 5.2 ft is...Ch. 11 - A circular aluminum tube with pinned ends supports...Ch. 11 - A steel W 12 × 35 column is pin-supported at the...Ch. 11 - A steel W 310 x 52 column is pin-supported at the...Ch. 11 - A steel column (E = 30 x 103 ksi) with pinned ends...Ch. 11 - A W410 × S5 steel column is compressed by a force...Ch. 11 - A steel column ( E = 30 X 103 ksi) that is fixed...Ch. 11 - AW310 × 74 wide-flange steel column with length L...Ch. 11 - A pinned-end column with a length L = 18 ft is...Ch. 11 - The wide-flange, pinned-end column shown in the...Ch. 11 - A W14 × 53 wide-flange column of a length L = 15...Ch. 11 - A wide-flange column with a bracket is fixed at...Ch. 11 - Determine the allowable axial load Pallowa W 10 X...Ch. 11 - Determine the allowable axial load Pallowfor a W...Ch. 11 - Determine the allowable axial load Pallowfor a W...Ch. 11 - Select a steel wide-flange column of a nominal...Ch. 11 - Prob. 11.9.5PCh. 11 - Select a steel wide-flange column of a nominal...Ch. 11 - 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