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Column Design 1Lecture 24
Architectural Structures IENDS 231
S2008abn
ARCHITECTURAL STRUCTURES I:STATICS AND STRENGTH OF MATERIALS ENDS 231
DR. ANNE NICHOLS
SPRING 2008
lecturetwenty four
column design
Column Design 2Lecture 24
Architectural Structures IENDS 231
S2008abn
Design Methods• know
– loads or lengths• select
– section or load– adequate for
strength and no buckling
Column Design 3Lecture 24
Architectural Structures IENDS 231
S2008abn
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
Column Design 4Lecture 24
Architectural Structures IENDS 231
S2008abn
Cc and Euler’s Formula• Kl/r < Cc
– short and stubby– parabolic transition
• Kl/r > Cc– Euler’s relationship– < 200 preferred
yc F
EC22π
=
Column Design 5Lecture 24
Architectural Structures IENDS 231
S2008abn
Cc and Euler’s Formula
Column Design 6Lecture 24
Architectural Structures IENDS 231
S2008abn
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 −+=
Column Design 7Lecture 24
Architectural Structures IENDS 231
S2008abn
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
Column Design 8Lecture 24
Architectural Structures IENDS 231
S2008abn
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
Column Design 9Lecture 24
Architectural Structures IENDS 231
S2008abn
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⋅
Column Design 10Lecture 24
Architectural Structures IENDS 231
S2008abn
Column Charts
Column Design 11Lecture 24
Architectural Structures IENDS 231
S2008abn
Column Charts
Column Design 12Lecture 24
Architectural Structures IENDS 231
S2008abn
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 ′
Column Design 13Lecture 24
Architectural Structures IENDS 231
S2008abn
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)
Column Design 14Lecture 24
Architectural Structures IENDS 231
S2008abn
Strength Factors• wood properties and load duration, CD
– short duration• higher loads
– normal duration • > 10 years
• stability, Cp– combination curve - tables
( ) pDcpcc CCFCFF ==′ *
Column Design 15Lecture 24
Architectural Structures IENDS 231
S2008abn
Cp Charts – Appendix A, Table 14
Column Design 16Lecture 24
Architectural Structures IENDS 231
S2008abn
Column Charts – Appendix A, 12 & 13
Column Design 17Lecture 24
Architectural Structures IENDS 231
S2008abn
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 *=′
Column Design 18Lecture 24
Architectural Structures IENDS 231
S2008abn
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
Column Design 19Lecture 24
Architectural Structures IENDS 231
S2008abn
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 *=′
Column Design 20Lecture 24
Architectural Structures IENDS 231
S2008abn
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.
Column Design 21Lecture 24
Architectural Structures IENDS 231
S2008abn
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
Column Design 22Lecture 24
Architectural Structures IENDS 231
S2008abn
• 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
Column Design 23Lecture 24
Architectural Structures IENDS 231
S2008abn
Column Charts