chapter 6 combined forces
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Engr. Nimfa Maren S. Tabucal1stSemester 2015-1016
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6.1 Introduction
6.2 Second-Order Effect
6.3 Amplified First Order Elastic Analysis
6.4 Bi-axial Bending
6.5 Beam-Column
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Member subjected to axial compression andbending is known as Beam-Column
Axial load is normally transferred by
column, adjacent beams, and/or girders
Bi-axial bending moments developed fromspace action of the framing system
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Primary/ First-Order Moments
- end-moments and/or in-spantransverse loads in addition to axialloads
Second Moments
- Additional moments induced by theinteraction of axial force withdeflections
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Equilibrium is based on DEFORMED GEOMETRY
Initially, consider a member subjected to flexure only.
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Initially, consider a member subjected to flexure only.
Application of load results in mid-span deflection d0
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Now, consider the same member but with Axial load, P.
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Axial force acting through deformations results inadditional moment P(d0) at center of span.
Additional moment then results in displacement d.
Resulting in additional moment P(d)
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E
P
P1
1
0
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E
m
P
P
CMM
1
0
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Equivalent Moment Factor, Cm
M1 is the smaller moment in absolute value
(+) ratio if reverse curvature bending
(-) ratio if single-curvature bending
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Beam is subjected to both bending about themajor axis (x-axis) and minor axis (y-axis)
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Two cases:
Case I:
Loads Applied Through the Center
of the Shear
Case II:
Loads NOT Applied Through theCenter of the Shear
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CASE I LATCS)
(LRFD)
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CASE I LATCS)
Bending about major axis
- AISC Section F2 to F3
- Chapter 5
Bending about minor axis
- AISC Section F6
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Summarized in AISC Chapter H1
Doubly and symmetric members inFlexure and Compression
Doubly and symmetric members inFlexure and Tension
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Doubly and Symmetric Members in
Flexure and Tension
Equations are same with members incombined flexure and compression
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