Structural Steel Design (6th Edition)
Structural Steel Design (6th Edition)
6th Edition
ISBN: 9780134589657
Author: Jack C. McCormac, Stephen F. Csernak
Publisher: PEARSON
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Chapter 9, Problem 9.1PFS
To determine

The most economical section using LRFD and ASD.

Expert Solution & Answer
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Answer to Problem 9.1PFS

The safe designed section is W30×90

Explanation of Solution

Given Information:

  Structural Steel Design (6th Edition), Chapter 9, Problem 9.1PFS

LRFD:

The design load is

  wu=1.2wD+1.5wLwu=1.2×1.2+1.6×3wu=6.24k/ft

The design moment is

  Mu=wul28Mu=6.24×3628Mu=1010.88k-ft

Assuming self weight as 0.1 k/ft.

The moment due to self weight is

  M=0.1×3628M=16.2k-ft

The total design moment is

  M=1010.88+16.2M=1027.08k-ft

The design strength of beam is

  ϕbMn=ϕbMp=ϕbZxFy

Taking

  ϕbMn=Mu

The required section modulus is

  Zx=1027.08×120.9×50Zx=273.9in3

Selecting the section such that Z>Zrequired

  W30×90

The plastic section modulus is 283 in.3

ASD:

The design load is

  wa=wD+wLwa=1.2+3wa=4.2k/ft

Assuming self weight as 0.1 k/ft.

The total design load is

  w=4.2+0.1w=4.3k/ft

The design moment is

  Mu=wl28Mu=4.3×3628Mu=696.6k-ft

The design strength of beam is

  MnΩ=ZxFy1.67

The required section modulus is

  Zx=696.6×12×1.6750Zx=279.2in.3

Selecting the section from AISC manual such that Z>Zrequired

  W30×90Zx=283in3

Conclusion:

Select W30×90 by both LRFD and ASD.

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