design by analysis - nafems€¦ · design by analysis design codes ... contents bs 5950 part 1 •...
TRANSCRIPT
FENET THEMATIC NETWORKCOMPETITIVE AND SUSTAINABLE GROWTH(GROWTH) PROGRAMME
Design by Analysis
Design codes influence the analysis procedure
Dr. Casimir Katz – SOFiSTiK AG
2
FENET THEMATIC NETWORKCOMPETITIVE AND SUSTAINABLE GROWTH(GROWTH) PROGRAMME
Projects not covered by the current design codes
Hall 26, Fair Hannover
3
FENET THEMATIC NETWORKCOMPETITIVE AND SUSTAINABLE GROWTH(GROWTH) PROGRAMME
Munich Airport Hangar
New goverment district Berlin
4
FENET THEMATIC NETWORKCOMPETITIVE AND SUSTAINABLE GROWTH(GROWTH) PROGRAMME
Bridge „Wilde Gera“
5
FENET THEMATIC NETWORKCOMPETITIVE AND SUSTAINABLE GROWTH(GROWTH) PROGRAMME
Munich Airport Center
Membrane Roof, Hamburg
6
FENET THEMATIC NETWORKCOMPETITIVE AND SUSTAINABLE GROWTH(GROWTH) PROGRAMME
What is the purpose of a design code ?
• The customer wants a product which has assured properties even if he does not exactly know about them
• The safety requirements of the public has to be fulfilled
• Thus a design code may contain:– Clear technical definitions especially of required
material properties and tests– General guidelines for the design– Hints for comprehensive design methods– Simplified design methods
7
FENET THEMATIC NETWORKCOMPETITIVE AND SUSTAINABLE GROWTH(GROWTH) PROGRAMME
Example: Design codes for structural steelwork
• D: Stahlbauten Bemessung und Konstruktion; Stabilitätsfälle, Knicken von Stäben und StabwerkenSteel structures, design and construction, Stability, Buckling of beams and frames (paperback, 93 pages)
• F: Règles de calcul des construction en acierAnalysis rules for structural steel constructions (hardcover, 397p.)
• GB: Structural use of steelwork in building, Code of practice for design.(loose-leaf edition, 219 pages)
• I: Norme tecniche per il calcolo, l'esecuzione ed il collaudo delle strutture in cemento armato, normale e precompresso e per le strutture metalliche. (21 pages for structural steel)
• RU: SNIP 23.81 (260 pages)• EC: Design of Steel Structures, 344 pages
8
FENET THEMATIC NETWORKCOMPETITIVE AND SUSTAINABLE GROWTH(GROWTH) PROGRAMME
Contents of CM 66
• Preamble [Préambule]• Safety requirements in constructions [Justification de la sécurité dans les
constructions]• Material types [Nuances d’acier]• General rules for the analysis of resistances and defomations
[Règles générales concernant les calculs de résistance et de déformation]
• Connections [Assemblages]• Special rules for selected types of elements [Règles spéciales à certains
éléments]• Design by tests [Épreuves des ouvrages]• Appendices [Annexes] 28 chapters with comments and additional tools, partly
in the form of a tutorial. A list of used notations and the evaluation of the torsionalinertia for a thin walled open section, how to get a buckling length, moment redistribution in frames (old fashioned).
9
FENET THEMATIC NETWORKCOMPETITIVE AND SUSTAINABLE GROWTH(GROWTH) PROGRAMME
Contents BS 5950 Part 1
• General• Limit states design• Properties of materials and section properties• Design of structural members• Continuous structures• Connections• Loading tests• Annexes
9 chapters with normative descriptions for torsional buckling, buckling length evaluations and buckling of plates.
10
FENET THEMATIC NETWORKCOMPETITIVE AND SUSTAINABLE GROWTH(GROWTH) PROGRAMME
Contents DIN 18800
• Part 1– General, Materials, Principals for the construction, Actions– Design– Connections– 4 pages Annex
• Part 2– General– Imperfections– Single beams and lattice girders– Frames– Design elastic-plastic and lateral torsional buckling– 1 page Annex
11
FENET THEMATIC NETWORKCOMPETITIVE AND SUSTAINABLE GROWTH(GROWTH) PROGRAMME
Structural Stability in CM 66
• All design checks are done for a single beam. (Numerous examples to determine the buckling length)
• Factors for the stresses depending on the slendernessk1 σ + kf σf ≤ σe (Index f for flexion)
• Similar formulas for lateral torsional buckling defined.[Déversement en flexion simple et flexion composée]
In Additif 80:
• A load factor αcr of the buckling load is introduced.
• For αcr > 5 linear theory is sufficient.
• For αcr < 5 load factors and limits for the rotation for columns are given.
12
FENET THEMATIC NETWORKCOMPETITIVE AND SUSTAINABLE GROWTH(GROWTH) PROGRAMME
Structural Stability BS 5950
•All design checks are done for a single beam. (Formulas to determine the buckling length)
•For the limit state of stability the structure has to be loaded with notional horizontal forces. These are 0,5% = 1/200 of the vertical loadings.
From the horizontal deformation δ with these loads and the height of the storey h a critical load factor λcr [sway mode elastic critical load factor] is defined:
λcr = h/200δ
• For λcr ≥ 10 no further checks are requested
• For 4 ≤ λcr ≤ 10 factors are given to augment the forces and moments
• For λcr ≤ 4 second order theory has to be used.
13
FENET THEMATIC NETWORKCOMPETITIVE AND SUSTAINABLE GROWTH(GROWTH) PROGRAMME
Structural Stability DIN 18800
• Table 1 defines the analysis methods
•Elastic – elastic
•Elastic – plastic
•Plastic – plastic
• Effects to be accounted for:
•Non linear material
•Imperfections (2nd Order Theory)
•Deformations in connections
•Plate buckling as limits of b/t ratio
14
FENET THEMATIC NETWORKCOMPETITIVE AND SUSTAINABLE GROWTH(GROWTH) PROGRAMME
2nd Order Theory
DIN 18800: General Method:
«Anstelle der in Tabelle 1 angegebenen Verfahren dürfen auch vereinfachte Nachweise geführt werden»
CM 66: Only a hint:
«Lorsque exceptionnellement on a besoin d’une meilleure approximation, il est nécessaire de tenir compte de la présence des irrégularités de forme et de structure qui influent sur la position des points d’inflexion dans un système hyperstatique de barres réelles, comme elles influent sur la charge d’affaissement d’une barre bi-articulée. »
BS 5950:
«Detailed recommendations for practical direct application of "second order" methods of global analysis (based on the final deformed geometry of the frame), including allowances for geometrical imperfections and residual stresses, strain hardening, the relationship between member stability and frame stability and appropriate failure criteria, are beyond the scope of this document. However, such use is not precluded provided that appropriate allowances are made for these considerations.»
15
FENET THEMATIC NETWORKCOMPETITIVE AND SUSTAINABLE GROWTH(GROWTH) PROGRAMME
Legal base (Germany)
• German BGB §§ 631 ff. (contracts of manufacture)– „The work has to be fulfilled in such a way, that it has the
assured properties and has no faults reducing or annihilating the value or the fitness for the general purpose or that assured by the contract“
• VOB § 13. (Contracting in Civil Engineering)– „The contractor assures that his work has the assured
properties and fits the generally accepted technical rules and has no faults, reducing or annihilating the value or the fitnessfor the general purpose or that assured by the contract“
16
FENET THEMATIC NETWORKCOMPETITIVE AND SUSTAINABLE GROWTH(GROWTH) PROGRAMME
generally accepted technical rules
• Not the state of art of science• Not the contents of the design codes• Not the way how it was since a long time before
(Conserving the stone age)• It is more than the absence of errors• Thus
– It has to be technical rule for the design or build of a structure
– The theoretical base has to be known and generally accepted.
– The rule itself has to be broadly known and generally to be accepted.
17
FENET THEMATIC NETWORKCOMPETITIVE AND SUSTAINABLE GROWTH(GROWTH) PROGRAMME
Deviations
• General Rules are not the only way to deal with a problem !
• Deviations should be possible !– e.g. Load values, safety factors– e.g. Design procedures
• Legal consequences:– Conforming to the codes ?– Reliability in case of damage or even before ?
• Esthetical and technical consequences– Only square houses allowed ?– Technical progress is always something new !
18
FENET THEMATIC NETWORKCOMPETITIVE AND SUSTAINABLE GROWTH(GROWTH) PROGRAMME
Why should we deviate ?
• If a design code does not cover the problem itself– Modern architecture– Unusual load cases
• If we want to be more economical• Implies that the provisions of the design codes are on
the safe side, but quite often they are not:– Stability cases of DIN 18800– Plastic Resistance of sections Mplas = 1.14 Mel– Shear design of concrete: Lever arm = 0.9 d– Crack width of concrete with tabulated values– Buckling length itself
19
FENET THEMATIC NETWORKCOMPETITIVE AND SUSTAINABLE GROWTH(GROWTH) PROGRAMME
The problem of safety
• Analysis is done in general on a determined problem (geometry, material, loads)
• Common approach:– Analysis based on mean values– Design based on lower/upper bound limits
• Sometimes it is sufficient to apply safety factors to the loads and materials
• In many coupled problems it is not.(e.g. dynamics, capacity design etc.)
• Probabilistic Analysis– Monte Carlo Methods– Sensitivity Analysis ?– Beyond the scope of this presentation!
20
FENET THEMATIC NETWORKCOMPETITIVE AND SUSTAINABLE GROWTH(GROWTH) PROGRAMME
Problems with Software
• Software writing is implementing Algorithms• Algorithms have to be complete• Engineering art has empirical components• The provisions are often not precisely known• Gaps have to be closed• Codes are made for manual calculations• The software programmer has to interpret the design
code for cases he does not know in advance !• Design codes should have some logic !• Software is never perfect, especially not for the case
of design
21
FENET THEMATIC NETWORKCOMPETITIVE AND SUSTAINABLE GROWTH(GROWTH) PROGRAMME
Example IThe removed corner
22
FENET THEMATIC NETWORKCOMPETITIVE AND SUSTAINABLE GROWTH(GROWTH) PROGRAMME
The removed corner
Moment Q 1 Q 2 Q 3 Q 4 Q 5 Q 6
800 42.5 42.8 44.1 46.3 49.2 52.9
1000 56.5 56.6 58.3 61.1 64.9 70.1
1200 96.6 80.4 77.6 81.4 99.5 238.2
Required reinforcement:
The design codes give a higher strength if parts of the structure are removed!
23
FENET THEMATIC NETWORKCOMPETITIVE AND SUSTAINABLE GROWTH(GROWTH) PROGRAMME
Example IIReinforced Concrete Slab
Concrete C 20Steel S 500Thicknessh = 16 cm
5.00 5.00
gk/qk = 5.50 / 2.75 kN/m2
24
FENET THEMATIC NETWORKCOMPETITIVE AND SUSTAINABLE GROWTH(GROWTH) PROGRAMME
Required static heights
11.419.5
15.611.4
DIN 1045Nov. 1976
EC 2 E DIN 1045Feb. 1997
E DIN 1045Nov. 1998
25
FENET THEMATIC NETWORKCOMPETITIVE AND SUSTAINABLE GROWTH(GROWTH) PROGRAMME
Check for deflections
To allow for additional pay load it isrecommended to limit the deflectionsfor quasi permanent loadings to
cml
f eff 0.1500
00.5500
==≤
Combination coefficient ψ2 = 0.3
26
FENET THEMATIC NETWORKCOMPETITIVE AND SUSTAINABLE GROWTH(GROWTH) PROGRAMME
Check for deflections
Deformation
by analysis
allowed
Deformation
uncracked 0.24 cm
cracked 1.79 1.0 cm
Stiffness according to
1.07Cracked with tension Stiffening
cm
27
FENET THEMATIC NETWORKCOMPETITIVE AND SUSTAINABLE GROWTH(GROWTH) PROGRAMME
Deformed System
ux
uy
εu
εoεm ∫ ⋅= dxu mx ε
28
FENET THEMATIC NETWORKCOMPETITIVE AND SUSTAINABLE GROWTH(GROWTH) PROGRAMME
Changed Boundary Condition
5.00
Concrete C 20Steel S 500thicknessh = 16 cm
5.00
gk/qk = 5.50 / 2.75 kN/m2
quasi permanent loading = 5.50 + 0.3 x 2.75 kN/m2
calc f = 0.51 cm
29
FENET THEMATIC NETWORKCOMPETITIVE AND SUSTAINABLE GROWTH(GROWTH) PROGRAMME
Conclusion
• Requirements for a usable design code– General provisons for the materials, loadings and safety– General provisions for the tasks to do– Clearly stated sources and intensions– Clear logic = Complete Algorithms– „Limit states of assumptions“– Methods only in appendices / references = not mandatory
• NAFEMS and the FE-Community– Implementation of codes may be wrong within software– The code may be wrong and the software correct.– There is hardly a benchmark for the code validation– Do not allow design codes to be written without people
knowing about software.