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An Introduction to Instabilities

By

PhD, PE, IWwww.L

email: W.Laufs@L

Civil Engineering DColumbia University Ne

http://www.laufsed.com/http://www.laufsed.com/

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Course Overview CIEN E4213 – 6:50pm Tuesdays – 644 MUDD

TA: Christos Vlachos cv2305@columbia.edu 

Lecture 01) Sept 02 2014 ‘Introduction of Buckling’ 

Lecture 02) Sept 09 2014 ‘Euler Cases – part 1 (Columns)’ Lecture 03) Sept 16 2014 ‘Euler Cases – part 2 (Frames)’ Lecture 04) Sept 23 2014 ‘Euler Cases – part 3 (Wired Systems)Lecture 05) Sept 30 2014 ‘Stability Theory for Structures’ 

Lecture 06) Oct 07 2014 ‘Arches and Snap-through’ Lecture 07) Oct 14 2014 ‘Second Order Theory Buckling’ Lecture 08) Oct 21 2014 ‘Lateral Torsional Buckling’ 

• Mid- term Oct 28 2014 no classLecture 09) Nov 04 2014 ‘Plate Buckling’ Lecture 10) Nov 11 2014 ‘Cylinder Buckling’ Lecture 11) Nov 18 2014 ‘Stability of Dome & Shell Structures’ 

Lecture 12) Nov 25 2014 ‘Inelastic Buckling of Structures’ 

Lecture 13) Dec 02 2014 ‘Review Session’, test exam example Lecture 14) Dec 09 2014 ‘Final Exam’, open- book

mailto:cv2305@columbia.edumailto:cv2305@columbia.edu

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grade perc

su

Course Overview CIEN E4213 – 6:50pm Tuesdays – 644 MUDD

homework and overall grades:

Sept 02 2014 homework 01 engineering history

Sept 09 2014 homework 02 timber column buckling

Sept 23 2014 homework 03 masonry column buckling/steel frame buckling

Oct 28 2014 mid- term closed book exam

Nov 04 2014 homework 04 plate buckling/flexural torsional buckling/lateral torsional buckling/snap-through

Dec 02 2014 review session test exam example

Dec 09 2014 final exam open- book

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Course Overview

02) Euler Cases – part 1 (Columns)

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Course Overview

02) Euler Cases – part 2 (Frames)

   L  c  o   l  u  m  n

   E   I

  c  o   l  u  m  n

   E   I

  c  o   l  u  m  n

Lbeam

EIbeam

PP

hinged

hinged

First Buckling Mode:‘anti-

metrical’ 

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Full Frames, relocatable (2D problem)

(= not supported in plane of frame x-x):

1st buckling mode is anti-metrical !

l = 3.0

(anti-metric)

l = 24.6

(symmetric)

l = 30.8(anti-metric)

l = 86.4

(symmetric)

lP lP

EI beam

EI column

no support in x-x 

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l = 24.6

(symmetric)

l = 29.4

(anti-metric)

lP lP

EI beam

EI column

l = 86.4(symmetric)

l = 93.2

(anti-metric)

support in x-x 

Full Frames, non- relocatable (2D problem)

(= supported in plane of frame x-x):

1st buckling mode is symmetrical !

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Practical Example: Arcapita Bank BuildingBahrain Bay, Middle East

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Course Overview

04) Euler Cases – part 3 (Wired Systems)

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Practical Example: DS8 Cable FacadeCanary Wharf, London

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Course Overview

05) Stability Theory for Structures

4 elements

100 elemen

400 eleme

Finite element me

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Practical Example: Wintergarden Slava MoscowMoscow, Russia

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Course Overview

06) Arches and Snap-through

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Physics sense:

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Course Overview

07) Second Order Theory Buckling

Torsional Mode

Sway Mode

Combined Mode

Second ordercorrection term

Second order First order

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Course Overview

08) Lateral Torsional Buckling

Simply supported beamunder flexion

Lateral and torsionaldeflation of the section

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Practical Example: Glass Mullions for AirportCharles de Gaulle, Paris France

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Course Overview

09) Plate Buckling

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von Kármán solution:

Presentation of the software RSTAB

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Course Overview

11) Stability of Dome & Shell Structures

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Practical Example: Dome & Barrel VaultHurlingham Club London

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Course Overview

12) Inelastic Buckling of Structures

Ideal elasto-plastic behavior Impact on buckling critical loa

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Course Overview

13) Review Session

14) Final Exam

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Reference Literature:

1. Timoshenko, S.P & Gere, J.M., ‘Theory of Elastic Stability’, McGraw-Hill, 2nd Edition, New-York, 1961

2. Allen, H.G. & Bulson, P.S., ‘Background to Buckling’, McGraw-Gill, London, 1980

3. Thompson, J.M.T. & Hunt, G.W., ‘ A General Theory of Elastic Stability ’, John Wiley & Sons, London, 1973 

4. Petersen, ‘Statik und Stabilitaet der Baukonstruktionen’, Vieweg, Wiesbaden, 1982

5. C. Massonnet, ‘Résistance des matériaux’, Dunod, Paris, 1963 

6. Theory of Elastic Stability, S. Timoshenko, McGraw Hill.

7. Buckling Strength of Metal Structures, F. and H. Bleich, McGraw Hill.

8. Structural Stability, W.F. Chen and E.M. Lui, Prentice-Hall.

9. Stability Design of Steel Frames, W.F. Chen and E.M. Lui, CRC Press.

10. Buckling of Bars, Plates and Shells, D. Brush and B.O. Almorth, McGraw Hill.

11. Principles of Structural Stability Theory, A. Chajes, Prentice Hall.

12. Principles of Structural Stability, H. Ziegler, Blaisdell.

13. An Introduction to the Elastic Stability of Structures, G. Simitses, Prentice Hall

14. Dynamic Stability of Suddenly Loaded Structures, G. Simitses, Springer Verlag 1990.

15. Thin Wall Sections, A. Gjelsvik, John Wiley.

16. Flexural-Torsional Buckling of Structures, N.S. Trahair, CRC Press 1993.

17. The Stability of Frames, M.R. Horne and W. Merchant, Pregamon.

18. Buckling of Shells for Engineers, L. Kollar, E. Dulacska, John Wiley, 1984.

19. Elastic Instability Phenomena, J.M.T. Thompson, G.W. Hunt, John Wiley.

20. Structural Stability of Columns and Plates, N.G.R. Iyengar, Ellis Horwood/John Wiley.

21. Theory of Stability of Continuous Elastic Structures, M. Como, A. Grimaldi, CRC Press 1995.

22. Stability of Structures, Z. Bazant, L. Cedolin, Oxford.

H k 01

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Homework 01

given: excitement for “Architectural Engineering” 

required: choose a relevant structural engineer of present or past;choose one of his/her building structures that you admire

deliverables: prepare a short presentation of the person and building structure,subjectively briefly explain technical, cultural & esthetic relevance

format: one single pdf (saved to dropbox) with all group member namespresentation (powerpoint or similar) to class

note: give special attention to the quality of graphic presentation (clarity,originality, layout etc. – good graphics do support content!up to 6 pages max

due: evening Mon Sept 6th 

team: groups allowed up to 3 students