Direct Analysis Method Explanation

8/9/2019 Direct Analysis Method Explanation

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Design for Stability

CE470 Spring 2014

J. Liu


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What is Stability?

• “the capacity of a compression member,

element, or frame to remain in positionand support load, even if forced slightlyout of line or position by an added lateralforce” (Galambos, 1998)

Figure from NASCC: The Steel Conference 2014, Session N40, Geschwindner


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5 factors that influence stability

• Member, component, and connectiondeformations

• Second-order effects (P-D and P-d)

• Geometric imperfections (out-of-plumbness orout-of-straightness)

• Stiffness reductions due to inelasticity (residualstresses)

• Variability in component and system stiffness

“The Evolution of Stability Provisions in the AISC Specification,” C.J. Carter, 2013.


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AISC Chapter C: Design for Stability

• Direct Analysis Method of Design

▫ Calculation of required strengths – Section C2

▫ Calculation of available strengths – Section C3

• Alternative Methods of Design

▫ “Effective Length” method and first-order analysis

method permitted for structures that satisfy theconstraints in Appendix 7

• Use of approximate method of second-orderanalysis (B1, B2) permitted as an alternative

(Appendix 8) to “rigorous” second-order analysis


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Appendix 7 - Constraints


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Appendix 7 – Required Strengths


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Appendix 7 – Available Strengths


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“B1,B2” OK


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Notional Loads

Y 2

Y 1

N 2=0.002a Y 2

N 1=0.002a Y 1

AISC C2.2b

a =1.0 (LRFD)

N i=0.002a Y i


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Notional Loads

N 2=0.002a Y 2Y 2

Y 1N 1=0.002a Y 1

AISC Code of Standard Practice (Section 16.3)

Member “out-of-plumbness”

1

500


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Y 2

Y 1N 1=0.002a Y 1

Notional Loads

AISC C2.2b

N 2=0.002a Y 2


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Direct Analysis Method - Advantages

• No K-factor calculations (K = 1.0)

▫ Good! K often difficult to predict; alignmentcharts utilize many assumptions

• Internal forces more accurately represented

▫ At ultimate capacity (e.g., inelasticity)

• Method applies logically & consistently to allframing systems

▫ Braced frames, moment frames, trusses, etc.

• More economical in some cases


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Just one example for K …


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Direct Analysis Method

AISC C2

Y 2

Y 1

Notional Loads Direct Modeling of

Imperfections

OR

N 2=0.002a Y

2

Y 2

Y 1N 1=0.002a Y 1


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Adjustments to Stiffness

AISC C2.3

Y 2

Y 1OR

Reduced stiffnesses 0.8EA and 0.8t bEI(including in B1-B2 amplification, if used)

N 2=0.002a Y

2

Y 2

Y 1N 1=0.002a Y 1


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Adjustments to Stiffness

AISC C2.3


18/25“Stability Analysis: It’s not as Hard as you Think,” C.M. Hewitt, 2008.


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5 factors that influence stabilityEffective Length Method• Member, component, and connection

deformations – addressed directly in analysis

• Second-order effects (P-D and P-d) – rigoroussecond-order analysis or first-order with B1-B2

• Geometric imperfections (out-of-plumbness

[notional loads] or out-of-straightness [columndesign equations for effect on memberstrength])



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5 factors that influence stabilityDirect Analysis Method• Member, component, and connection

deformations – addressed directly in analysis

• Second-order effects (P-D and P-d) – rigoroussecond-order analysis or first-order with B1-B2

• Geometric imperfections (out-of-plumbness

[notional loads or direct modeling] or out-of-straightness [column design equations; andreduced stiffness for effect on structurestiffness])



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5 factors that influence stabilityDirect Analysis Method, cont’d. • Stiffness reductions due to inelasticity (residual

stresses) -- column design equations; and

reduced stiffness for effect on structure stiffness

• Variability in component and system stiffness – in resistance and safety factors!



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AISC C-C2.3


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Direct Analysis Method“Step-by-Step” • Create a model of the lateral force resisting

frame, including the leaning columns.

• Reduce the stiffnesses (modify E) of the lateralframing members in your model.

• Apply notional loads or directly model the

imperfections• Conduct a second-order analysis (“rigorous” or

B1-B2 amplification on first-order)

“Stability Analysis: It’s not as Hard as you Think,” C.M. Hewitt, 2008.


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“Step-by-Step” cont’d.

• Design members using the AISC Specificationand K=1.0.

▫ If using structural analysis program to do this,reset E to 29,000 ksi.

• Check lateral drift limits for wind and seismic.

“Stability Analysis: It’s not as Hard as you Think ” C M Hewitt 2008

Direct Analysis Method Explanation

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