Structural Steel Design (6th Edition)
Structural Steel Design (6th Edition)
6th Edition
ISBN: 9780134589657
Author: Jack C. McCormac, Stephen F. Csernak
Publisher: PEARSON
Question
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Chapter 11, Problem 11.1PFS
To determine

Whether a W14×30 tension member is satisfactory for the given conditionss.

Expert Solution & Answer
Check Mark

Answer to Problem 11.1PFS

Satisfied

Explanation of Solution

Given:

  Fy=50ksiFu=65ksiPD=80kPL=100kMDx=10ftkMLx=12ftkLb=12ftCb=1.0

Calculation:

The sectional properties are as follows:

Refer Table 3-2, “W shapes properties” in the AISC steel construction manual.

  Lp=5.26ftLr=14.9ftϕbMpx=177kipftM pxΩb=118kipftϕbBF=6.95kipsBFΩb=4.65kipsϕb=0.9Ωb=1.67

The ultimate load by LRFD is

  Pu=1.2PD+1.6PLPu=1.2(80)+1.6(100)Pu=256kips

The design moment is

  Mux=1.2MDx+1.6MLxMux=1.2(10)+1.6(12)Mux=31.2kft

Refer Table 1-1, “W shapes properties” in the AISC steel construction manual.

  Ag=8.85in.2

The available tensile strength is

  Pn=FyAgPn=50×8.85Pn=442.5kips

The design strength is

  Pc=ϕcPnPc=0.9×442.5Pc=398.25kips

Since, LpLbLr zone 2 will prevails.

The nominal moment strength is

  Mcx=ϕbMnxMcx=Cb[ϕbMpxϕbBF( L b L p)]ϕbMnx=1.0[1776.95(125.26)]ϕbMnx=130.16kft

Check:

  PrPc0.2PrPc=PuPc=256398.250.20.640.2

The section is subjected to both the bending and axial tension:

  PrPc+89( M rx M cx + M ry M cy )1.0256398.25+89( 312 130.16+00)1.00.643+0.89(0.2396)1.00.8561.0

Hence, it’s OK.

The ultimate load by ASD is

  Pa=PD+PLPa=80+100Pa=180kips

The design moment is

  Mux=MDx+MLxMux=10+12Mux=22kft

The design strength is

  Structural Steel Design (6th Edition), Chapter 11, Problem 11.1PFS

Since, LpLbLr zone 2 will prevails.

The nominal moment strength is

  Mcx=M nxΩbMcx=Cb[ M px Ω bBF Ω b( L b L p)]ϕbMnx=1.0[1184.65(125.26)]ϕbMnx=86.7kft

Check:

  PrPc0.2PrPc=PaPc=180264.970.20.680.2

The section is subjected to both the bending and axial tension:

  PrPc+89( M rx M cx + M ry M cy )1.0180264.97+89( 22 86.7+00)1.00.679+0.25551.00.9051.0

Hence, it’s OK.

Conclusion:

Therefore, the tension member W14×30 is satisfied for both LRFD and ASD.

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