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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Chapter 6 Combined Forces