c7 advanced design of bridges -...
TRANSCRIPT
C7 Advanced design of bridges
Jakub Dolejš
Tomáš Rotter
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List of lectures
1. Loading of bridges2. Load capacity of plate girder web3. Basis of fracture mechanics4. Cable stayed and suspension bridges5. Railway bridges with ballast bed6. Road bridges with orthotropic deck7. Spatial interaction of bridge structures8. Bridges with arched plan, rigid frame bridges9. Arch bridges10. Loading tests of steel bridges11. Fatigue12. Modelling of bridges13. Load-carrying capacity of steel bridges
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Objectives of the lecture 11
• General
• Definitions
• Fatigue strength
• Details
• EN 1993-1-9
Objectives
General
Definitions
Fatigue strength
Details
EN 1993-1-9
(Romeijn)
• Metal fatigue is a well-known phenomenon – Wohler - German engineer – fatigue of railroad car axles
• Steel bridges are susceptible to localized failures-cracking due to fatigue.
• Fatigue failure
- predetermined crack length, - or loss of stiffness, - or separation of the component being designed
• Fatigue crack propagation usually precedes brittle fracture
GeneralObjectives
General
Definitions
Fatigue strength
Details
EN 1993-1-9
– fatigue
• The process of initiation and propagation of cracks through a structural part due to action of fluctuating stress
– design life
• The reference period of time for which a structure is required to perform safely with an acceptable probability that failure by fatigue cracking will not occur.
– fatigue life
• The predicted period of time to cause fatigue failure under the application of the design spectrum.
DefinitionsObjectives
General
Definitions
Fatigue strength
Details
EN 1993-1-9
– stress history
• A record or a calculation of the stress variation at a particular point in a structure during a loading event.
– rainflow method
• Particular cycle counting method of producing a stress-range spectrum from a given stress history.
– reservoir method
• Particular cycle counting method of producing a stress-range spectrum from a given stress history.
DefinitionsObjectives
General
Definitions
Fatigue strength
Details
EN 1993-1-9
– nominal stress
• A stress in the parent material or in a weld adjacent to a potential crack location calculated in accordance with elastic theory excluding all stress concentration effects.
– stress range
• The algebraic difference between the two extremes of a particular stress cycle derived from a stress history.
– stress-range spectrum
• Histogram of the number of occurrences for all stress ranges of different magnitudes recorded or calculated for a particular loading event.
DefinitionsObjectives
General
Definitions
Fatigue strength
Details
EN 1993-1-9
• Fatigue is caused by the stress range experienced by the detaildue to applied cyclic live loading.
• Other influences:– Stress concentrations at weld toes in poorly designed details – Internal defects and heat affected zones in welded
connections – Detail configurations that simulate a large initial pre-crack – Out-of-plane distortion of girder web gaps due to unaccounted
secondary lateral forces.
Fatigue strengthObjectives
General
Definitions
Fatigue strength
Details
EN 1993-1-9
Fatigue strength
Actual stress history
Objectives
General
Definitions
Fatigue strength
Details
EN 1993-1-9
Fatigue strength
Reference stress history
Objectives
General
Definitions
Fatigue strength
Details
EN 1993-1-9
• Alternating cyclic stresses (even in the elastic range) cause fatigue failure in metal components or details.
– Fatigue crack initiation– Fatigue crack propagation– Brittle fracture
• Fundamental fatigue behavior of a metal is expressed in terms of a constant amplitude cyclic stress range vs. number of cycles to failure (Sr - N) curve.
Fatigue strengthObjectives
General
Definitions
Fatigue strength
Details
EN 1993-1-9
Fatigue strength
Fatigue failure process
Objectives
General
Definitions
Fatigue strength
Details
EN 1993-1-9
Details
([4] http://www.fgg.uni-lj.si/kmk/ESDEP)
Crack is initiated at a discontinuity (weld)
Objectives
General
Definitions
Fatigue strength
Details
EN 1993-1-9
Details
Example of detail types
Objectives
General
Definitions
Fatigue strength
Details
EN 1993-1-9
Details
Example of construction details
Objectives
General
Definitions
Fatigue strength
Details
EN 1993-1-9
Details
Example of construction details
Objectives
General
Definitions
Fatigue strength
Details
EN 1993-1-9
EN 1993-1-9
Detail class
Objectives
General
Definitions
Fatigue strength
Details
EN 1993-1-9
EN 1993-1-9
Annex A [normative] – Determination of fatigue load parameters and verification formats
Determination of loading events
Stress history at detail
Objectives
General
Definitions
Fatigue strength
Details
EN 1993-1-9
EN 1993-1-9
Cycle counting
Stress range spectrum
0,1n =Σ
Objectives
General
Definitions
Fatigue strength
Details
EN 1993-1-9
EN 1993-1-9
Cycles to failure
Damage summation
(Palmgren-Miner rule)
∑=n
i Ri
Eid N
nD
Objectives
General
Definitions
Fatigue strength
Details
EN 1993-1-9
Thank you for your kind attention
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Notes to users of the lecture
• This session is a basic information about actions on bridgesand requires about 60 min lecturing.
• The use of relevant standards of national standard institutions are strongly recommended.
• Keywords for the lecture:
steel bridge, action, road bridge, railway bridge, Eurocodes, fatigue.
References:
[1] Eurocode 3: Design of steel structures; Part 1.9: Fatigue strength of steel structures.
[2] A. Romeijn - CT5126 Fatigue lecture book, 2006-7
[3] A. H. Varma – Michigan state university Special course on of AASHTO LRFD Specifications, presentation 2003
[4] http://www.fgg.uni-lj.si/kmk/ESDEP