Design of Combined Bending and Compression Members in Steel

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Design of Combined Bending and Compression
Members in Steel
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Combined stresses
Bi-axial bending
Bending and compression
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• Multi-story steel rigid frame

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• Rigid frames, utilizing moment connections, are
  well suited for specific types of buildings where
  diagonal bracing is not feasible or does not fit
  the architectural design
• Rigid frames generally cost more than braced
  frames (AISC 2002)

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• Vierendeel steel truss cycle bridge Beaufort
  Reach, Swansea

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• Typical crane columns

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fmax fa fbx fby lt fdes
( Pf / A ) ( Mfx / Sx ) ( Mfy / Sy ) lt fdes
(Pf / Afdes) (Mfx / Sxfdes) (Mfy / Syfdes)
lt 1.0
(Pf / Pr) (Mfx / Mr) ( Mfy / Mr) lt 1.0
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Cross-sectional strength
Pf/Pr
1.0
1.0
Mf/Mr
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Slender beam-columns

• What if column buckling can occur ?
• What if lateral-torsional buckling under bending
  can occur ?

Use the appropriate axial resistance and moment
resistance values in the interaction equation
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Beam-column in a heavy industrial setting
BMD
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Moment amplification
PE Euler load
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Interaction equation
Axial load
Bending about y-axis
Bending about x-axis
?1 moment gradient factor (see next slide)
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Moment gradient factor for steel columns with end
moments
M1
?1 0.6 0.4(M1/M2) 0.4 i.e. when moments
are equal and cause a single curvature, then ?1
1.0 and when they are equal and cause an
s-shape, then ?1 0.4
M2
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Steel frame to resist earthquake forces
Warehouse building, Los Angeles
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Moment gradient factor for other cases
v
?1 1.0
?1 0.85
?1 1.0
?1 0.6
?1 0.4
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Design of steel beam-columns

• Laterally supported
• Cross-sectional strength
• Supported in the y-direction
• Overall member strength
• Use moment amplification factor
• Use buckling strength about x-axis (Crx)
• Laterally unsupported
• Buckling about y-axis (Cry)
• Lateral torsional buckling (Mrx)
• Use moment amplification factors
• Usually the most critical condition
• Note Mry never includes lateral-torsional
  buckling

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Example of different support conditions
This column unsupported
These two columns supported in y-direction by
side wall
x direction
y direction