Eurocode 3 vs AISI: Cold-Formed Steel Design Comparison

1. Some Features of the European Norm for Cold-Formed Steel Designin comparison with the AISI Specification S. Ádány*, B. Schafer** *Budapest University of Technology and Economics **Johns Hopkins University

2. Outline • Introduction • Some features of cold-formed EC3 • Materials • Geometry • Local and distortional buckling • Member resistance • Design assisted by testing • Beams restrained by sheeting • Numerical example

3. The Eurocodes • Eurocode 0 (EN 1990) – Basis of the design • Eurocode 1 (EN1991) – Actions (loads) • Eurocode 2 (EN 1992) – Concrete structures • Eurocode 3 (EN 1993) – Steel structures • Eurocode 4 (EN 1994) – Composite (steel/concrete) str. • … • … Note: ENV, prEN – certain preliminary versions

4. Eurocode 3 • Part 1.1 – General rules • Part 1.2 – Fire design • Part 1.3 – Cold-formed steel • Part 1.5 – Plated structures • … • Part 2 – Steel bridges • … • …

5. Some comments on Eurocodes • Not ready - some parts exist only in a very first draft version • Continuously changing • Flexible – „everything is allowed if the safety is OK” • National Application Document (NAD) can modify almost everything

6. Principle of verifications • Limit state design: • Partial safety factor for the resistance: gM • Partial safety factor for the loads: gG, gQ • Combination factor: y

7. Basic notations • Design value of resistance – subscript „Rd” • Design value of actions – subscript „Ed” • Yield strength: fy • Slenderness: l • Reduction factor for buckling: c

8. Scope of EC3 Part 1.3 • Cold-formed profiled sheeting • Cold-formed beams / columns • Thickness: 0.45 mm ≤ tcor ≤ 15 mm (can be further limited by NADs)

9. Materials • 60+ standardized steel material • Yield strength: 220 – 700 MPa (32 – 101 ksi) • According to EN and ISO standards • Restrictions may applyfor higher strength materials • Other materials are allowed • Requirements for other mats. are given

10. Hardening due to cold-forming • Basic yield strength (fyb)  average yield strength (fya) • To be applied for the whole section • For fully effective sections, only • The formula:

11. Rounded corners • In general: fictitious plane elements are introduced • Upper limit: • r ≥ 0.04tE/fy test is necessary • Lower (optional) limit: • r ≤ 5t and r ≤ 0.1bp  the effect can be neglected

12. Geometrical limits • b/t ratios, similar to AISI Spec. • + limit for web inclination • + limit for edge stiffeners

13. Buckling - general procedure • critical stress calculation (in function of half-wave length) • identification of buckling modes • calculation of effective widths based on the minimum local buckling stress • calculation of reduced thickness based on distortional buckling stress • calculation of reduction factor for overall buckling resistance based on effective cross-section

14. Local buckling • Effective width approach • Effective width: similar to Winter formula, but modified • for outstand elements • for stress gradient • Effective sections:

15. Distortional buckling • Reduced thickness is determined for the stiffeners (or other distorted parts) • For C/Z sections: hand method is given • For other sections: numerical method is necessary • Effective widths must be calculated prior to reduced thickness !

16. Distort. buckl. – C/Z sections • The basic model: • Equivalent spring stiffness is given only for C/Z sections: • Dist. buckl. stress  critical stress of a bar on elastic foundation • Reduction factor for the stiffener: • Iteration for the thickness is necessary

17. Bending moment resistance • If the cross-section is not fully effective: • If the cross-section is fully effective: • If fully effective, + uniaxial bending about principal axis, + no torsion, + no any of torsional buckling, + web inclination is less than 30°: elastic resistance elastic resistance with hardening partial or full plastic resistance

18. Bending moment resistance • If first yielding is in the tension flange: • Bending moment redistribution is allowed. • Effect of shear lag must be considered. (only a reference is given) partial plastic resistance

19. Torsional moment resistance • Torsion must be considered: • t from St Venant torsion • t and s from warping • No formulae given how to calculate stresses from torsion. • Stresses from torsion must be summarized with stresses from other actions. • Hardening effect can be considered. • For shear, torsion: gross cross-section • For normal force, bending moments: effective section

20. Other cross-sectional resistances • Tension: increased yield strength (fya) is used • Compression: hardening may be considered shift of neutral axis must be considered • Biaxial bending: linear interaction • Shear: plastic and buckling resistances webs with longitudinal stiffeners are handled • Crippling: detailed empirical formulae webs with longit. stiffeners are handled • Interaction: shear+axial+bending is handled

21. Buckling resistance for compression • Buckling resistance is obtained from cross-sectional axial resistance, with a reduction factor (c) • For reduction: the European buckling curves are used • Flexural buckling: • Resistance is calculated on the effective area • However, a reduced slenderness is used to calculate the reduction factor • fya can be used for fully effective sections

22. Buckling res. for comp. - torsion • Torsional and torsional-flexural buckling: • basically the same as flexural buckling • numerical methods for calculation of critical force is allowed with the gross cross-section • guidance for end-conditions is given for some practical cases

23. Buckling resistance for bending • The given method can only be used: • for practically rigid cross-sections • if no significant angle between principal axes of gross and effective cross-sections • Buckling resistance is obtained from cross-sectional bending resistance, with a reduction factor (cLT) • For reduction: a special LT buckling curve is used • Resistance is calculated on the effective area • However, a reduced slenderness is used to calculate the reduction factor • fya can be used for fully effective sections

24. Buckling res. for bending – contnd. • Second-order moments may be necessary to consider • Interaction for double symmetrical cross-sections: • reference to Part 1.1 • two methods („German” vs. „French”) • Interaction for other cross-sections

25. Serviceability limit states • Relevant norms: • EN 1990 (Basis of design) • EN 1993-1-1 (General rules for steel) • EN 1993-1-3 (Cold-formed) • Only guidance is given, limit values (deflection, etc) must be agreed with the client • For cold-formed: • Fictitious moment of inertia is proposed • Influence of slip must be considered

26. Design assisted by test • Long list of principles are given: • planning, execution, evaluation and documentation • Several specific tests are described • Tests on profiled sheets (single-span, double-span, internal support, end-support tests) • Tests on beams/columns (stub column, member buckling, cross-s. tension, c.s. bending) • Tests on assemblages / structures (acceptance, strength, prototype failure, calibration) • Tests on torsionally restrained beams (…, …)

27. Design assisted by test – contnd. • Combination of tests and mathematical models is allowed • Evaluation of test results: Measured data Adjusted results Mean value Characteristic value Design value

28. Beams restrained by sheeting • Basic model: • Verification: • Normal force + „vertical” bending + lateral bending • Buckling • Simplified method is also available

29. Numerical example • A numerical example has been worked out • Local and distortional buckling of Z/C beams  EXAMPLE

30. Thank you.

46. elastic plastic elastic with hardening To Figure