Design by Analysis - NAFEMS€¦ · Design by Analysis Design codes ... Contents BS 5950 Part 1 •...

FENET THEMATIC NETWORKCOMPETITIVE AND SUSTAINABLE GROWTH(GROWTH) PROGRAMME

Design by Analysis

Design codes influence the analysis procedure

Dr. Casimir Katz – SOFiSTiK AG

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Projects not covered by the current design codes

Hall 26, Fair Hannover

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Munich Airport Hangar

New goverment district Berlin

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Bridge „Wilde Gera“

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Munich Airport Center

Membrane Roof, Hamburg

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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

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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

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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).

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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.

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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

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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.

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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.

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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

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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.»

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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“

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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.

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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 !

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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

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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!

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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

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Example IThe removed corner

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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!

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Example IIReinforced Concrete Slab

Concrete C 20Steel S 500Thicknessh = 16 cm

5.00 5.00

gk/qk = 5.50 / 2.75 kN/m2

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Required static heights

11.419.5

15.611.4

DIN 1045Nov. 1976

EC 2 E DIN 1045Feb. 1997

E DIN 1045Nov. 1998

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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

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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

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Deformed System

ux

uy

εu

εoεm ∫ ⋅= dxu mx ε

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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

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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.

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