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column and buckling
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1Elastic Buckling
Illustrations: Daniel L. Schodek: Structures, fifth edition; Pearson Prentice-Hall, 2004
Schodek fig. 7.1
Illustrations: Daniel L. Schodek: Structures, fifth edition; Pearson Prentice-Hall, 2004
Schodek fig. 7.1
Metastable
Illustrations: Daniel L. Schodek: Structures, fifth edition; Pearson Prentice-Hall, 2004
Schodek fig. 7.3
2Column Buckling Formula
Pcr = 2EIL2
Pcr = Critical force that initiates buckling failure
E = Modulus of elasticity of material (material stiffness)
I = Moment of inertia (geometric stiffness)
L = Unbraced column length
Notice it does NOT matter what the STENGTHof the material is!
Its all about STIFFNESS
(Euler Buckling Equation)
Illustrations: Daniel L. Schodek: Structures, fifth edition; Pearson Prentice-Hall, 2004
Schodek fig. 7.3, 7.1
Schodek fig. 7.5
EffectiveLengthFactors
Illustrations: Daniel L. Schodek: Structures, fifth edition; Pearson Prentice-Hall, 2004Schodek fig. 7.10
3Illustrations: Daniel L. Schodek: Structures, fifth edition; Pearson Prentice-Hall, 2004
Schodek fig. 7.7
Real Columns
Columns: Design Considerations
Have significant architectural impact due to how they affect spaceEstablish an organizing grid (structural bay)Define lengths of primary girders and beams framing into them
Columns: Design Considerations
Most critical structural element Typically no redundancy Remove a column and all above it that it
supports will fall Controlled demolition by selected removal
of columns
Loads to columns typically computed by tributary area
4A B C D E F G H I J K L
23
1
45
67
89
10
30 9 30 9 30 8 11 8 16 16 8
21
25
7
7
21
Col Tributary Area = (9+30)/2+(21+7)/2=546 ft2(2 floors) = 1092 ft2
Columns: Design Considerations
Layout of column grid is important for space planningCan be difficult to coordinate with varying needs if different floors, especially if parking is below Sometimes use transfer girders to carry
floors above Expensive option and requires much
deeper member than regular girder
Columns:Intermediate-Length
Intermediate-length columns are normally what is actually used in actual constructionFailure mode is a combination of crushing action and buckling action simultaneouslyComputing the allowable axial stress for these involves complex equations
Columns:Intermediate-Length
Fortunately, the equations can be simplified to a table lookup based on the column slenderness ration. (for steel, see table C-36)For pinned-ended columns, the capacity can be looked up directly in tables that relate member size to load capacity relative to the height of the column.
5Illustrations: Daniel L. Schodek: Structures, fifth edition; Pearson Prentice-Hall, 2004
Schodek fig. 7.3 Columns: Influences on Buckling Capacity
Ratio of length to cross-sectional area slenderness ratioEnd support conditionsIntermediate bracing 2% rule of thumb for bracing design: For
most cases bracing can be achieved with only 2% of the compressive force in the column!
Elastic buckling is not an issue of strength. It is rather one of stiffness.
Columns: Influences on Buckling Capacity
Eccentric loading dramatically reduces capacity Creates a moment at the top of column that causes
stress needing to be resisted in addition to axial load.
P- (P-Delta) Effect: As building moves laterally, this induces an
eccentric loading, even on columns concentricallyloaded.
For some materials (e.g. concrete), design for a minimal eccentricity is mandatory by code.
Illustrations: Daniel L. Schodek: Structures, fifth edition; Pearson Prentice-Hall, 2004
6Columns: Transfer Girder
Transfer Grider Column Variations
BCE Place, Toronto, Ontario, Canada Santiago Calatrava
7Bath House, Jewish Community Center, Trenton, New Jersey Louis Kahn
8Hurva Synagogue, Jerusalem, Israel (unbuilt project) Louis Kahn Dulles International Airport Terminal, Chantilly, Virginia Eero Saarinen
Illustration: Understanding Structures, Fuller Moore, WCB/ McGraw-Hill, 1999 Stuttgart Airport, Germany Von Gerkan Maarg
9Stuttgart Airport, Germany Von Gerkan Maarg
Stuttgart Airport, Germany Von Gerkan MaargStudent Model by Caroline Addis, Philadelphia University
Rose Center for Earth & Space, NYC Polsheck & Partners
Stanstead Airport, Essex, England Norman Foster
10
Stanstead Airport, Essex, England Norman Foster
Stanstead Airport, Essex, England Norman Foster
Foster & Partners web site
Stanstead Airport, Essex, England Sir Norman FosterStudent Model by James Fickes, Philadelphia University Lincoln School Library, Sprekles, CA
11
Hong Kong & Shanghai Bank, Hong Kong, China Norman Foster
Illustration: Understanding Structures, Fuller Moore, WCB/ McGraw-Hill, 1999
Illustration: Understanding Structures, Fuller Moore, WCB/ McGraw-Hill, 1999 Illustration: Understanding Structures, Fuller Moore, WCB/ McGraw-Hill, 1999
12
Alamillo Bridge, Near Barcelona, Spain Santiago Calatrava
Illustration: Understanding Structures, Fuller Moore, WCB/ McGraw-Hill, 1999
Library, Phillips Exeter Academy, Exeter, NU Louis I Kahn
13
Sendai Mediatheque, Sendai, Japan Toyo Ito
Tokyo International Forum, Tokyo, Japan Rafael Violy
14