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Column Design 1Lecture 24

Architectural Structures IENDS 231

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ARCHITECTURAL STRUCTURES I:STATICS AND STRENGTH OF MATERIALS ENDS 231

DR. ANNE NICHOLS

SPRING 2008

lecturetwenty four

column design



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Design Methods• know

– loads or lengths• select

– section or load– adequate for

strength and no buckling



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Allowable Stress Design (ASD)• AICS 9th ed

• slenderness ratio

– for kl/r ≥ Cc

( )22

23

12..

rKlE

SFfF critical

aπ

==

rKl

= 126.1 with Fy = 36 ksi= 107.0 with Fy = 50 ksi



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Cc and Euler’s Formula• Kl/r < Cc

– short and stubby– parabolic transition

• Kl/r > Cc– Euler’s relationship– < 200 preferred

yc F

EC22π

=



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Cc and Euler’s Formula



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Short / Intermediate • Le/r < Cc

– where

( )..2

1 2

2

SFF

Cr

KlF y

ca

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡−=

( ) ( )3

3

88

3

35..

cc Cr

Kl

Cr

KlSF −+=



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Procedure for Analysis1. calculate KL/r

• biggest of KL/r with respect to x axes and y axis

2. find Fa from Table 10.1 or 10.2• pp. 361 - 364

3. compute Pallowable = Fa⋅A• or find factual = P/A

4. is P ≤ Pallowable? (or is factual ≤ Fa?)• yes: ok• no: overstressed and no good



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Procedure for Design1. guess a size (pick a section)2. calculate KL/r

• biggest of KL/r with respect to x axes and y axis

3. find Fa from Table 10.1 or 10.2• pp. 361 - 364

4. compute Pallowable = Fa⋅A• or find factual = P/A



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Procedure for Design (cont’d)5. is P ≤ Pallowable? (or is factual ≤ Fa?)

• yes: ok• no: pick a bigger section and go back to step

2.

6. check design efficiency

• percentage of stress =

• if between 90-100%: good• if < 90%: pick a smaller section and go back

to step 2.

%PP

allowable

actual 100⋅



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Column Charts



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Wood Columns• slenderness ratio = L/dmin = L/d1

– d1 = smaller dimension– le/d ≤ 50 (max)

– where is the allowable compressive strength parallel to the grain

cc FAPf ′≤=

cF ′



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Allowable Wood Stress

• where:Fc = compressive strength

parallel to grainCD = load duration factorCM = wet service factor

(1.0 dry)Ct = temperature factorCF = size factorCp = column stability factor

( )( )( )( )( )pFtMDcc CCCCCFF =′

(Table 10.3)



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Strength Factors• wood properties and load duration, CD

– short duration• higher loads

– normal duration • > 10 years

• stability, Cp– combination curve - tables

( ) pDcpcc CCFCFF ==′ *



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Cp Charts – Appendix A, Table 14



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Column Charts – Appendix A, 12 & 13



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Procedure for Analysis1. calculate Le/dmin

2. obtain F´c– compute

• KcE =0.3 sawn • KcE = 0.418 glu-lam

3. compute Fc* ≈ FcCD

4. calculate FcE/Fc* and get Cp (table 14)

5. calculate

( )2dLcE

cEe

EKF =

pcc CFF *=′



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Procedure for Analysis (cont’d)6. compute Pallowable = F′c⋅A

• or find factual = P/A

7. is P ≤ Pallowable? (or factual ≤ F′c?)• yes: OK• no: overstressed & no good



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Procedure for Design1. guess a size (pick a section)2. calculate Le/dmin

3. obtain F´c– compute

• KcE =0.3 sawn • KcE = 0.418 glu-lam

4. compute Fc* ≈ FcCD

5. calculate FcE/Fc* and get Cp (table 14)

6. calculate

( )2dLcE

cEe

EKF =

pcc CFF *=′



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Procedure for Design (cont’d)6. compute Pallowable = F′c⋅A

• or find factual = P/A

7. is P ≤ Pallowable? (or factual ≤ F′c?)• yes: OK• no: pick a bigger section and go back to step 2.



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LRFD design• limit states for failure

1. yielding

2. buckling

λc – column slenderness parameterAg - gross area

ncu PP φ≤

gcrnc AFP == 85.0φ

5.1≤cλ

5.1>cλEF

rKl y

c πλ = r

Le



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• flanges continuously connected to the web or webs and width-thickness rations < limiting values– no local buckling of flange or web

– for

– for

Compact Sections

5.1≤cλ

5.1>cλ

( ) yλ

cr F.F c2

6580=

yc

cr Fλ.F ⎥

⎦

⎤⎢⎣

⎡= 2

8770



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Column Charts

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