Some Features of the European Norm Some Features of the European Norm for Cold-Formed Steel Designfor Cold-Formed Steel Design

in comparison in comparison with the AISI Specificationwith the AISI Specification

S. Ádány*, B. Schafer***Budapest University of Technology and Economics

**Johns Hopkins University

OutlineOutline

• 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

The EurocodesThe 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

Eurocode 3Eurocode 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• …• …

Some comments on EurocodesSome 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

Principle of verificationsPrinciple of verifications

• Limit state design:

• Partial safety factor for the resistance: M • Partial safety factor for the loads: G, Q

• Combination factor:

dkQGM

kd EERR ,...,

Basic notationsBasic notations

• Design value of resistance – subscript „Rd”• Design value of actions – subscript „Ed”• Yield strength: fy

• Slenderness: • Reduction factor for buckling:

Scope of EC3 Part 1.3Scope 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)

MaterialsMaterials

• 60+ standardized steel material

• Yield strength: 220 – 700 MPa (32 – 101 ksi)

• According to EN and ISO standards

• Restrictions may apply for higher strength materials

• Other materials are allowed

• Requirements for other mats. are given

Hardening due to cold-formingHardening 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:

Rounded cornersRounded 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

Geometrical limitsGeometrical limits

• b/t ratios, similar to AISI Spec.• + limit for web inclination

• + limit for edge stiffeners

Buckling - general procedureBuckling - general procedure

1. critical stress calculation (in function of half-wave length)

2. identification of buckling modes

3. calculation of effective widths based on the minimum local buckling stress

4. calculation of reduced thickness based on distortional buckling stress

5. calculation of reduction factor for overall buckling resistance based on effective cross-section

Local bucklingLocal buckling

• Effective width approach

• Effective width: similar to Winter formula, but modified

– for outstand elements

– for stress gradient

• Effective sections:

Distortional bucklingDistortional 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 !

Distort. buckl. – C/Z sectionsDistort. 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

• 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°:

Bending moment resistance Bending moment resistance

elastic resistance

elastic resistance with hardening

partial or full plastic resistance

Bending moment resistance 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

• Torsion must be considered:– from St Venant torsion– and 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

Torsional moment resistance Torsional moment resistance

• 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

Other cross-sectional resistances Other cross-sectional resistances

• Buckling resistance is obtained from cross-sectional axial resistance, with a reduction factor ()

• 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

Buckling resistance for compression Buckling resistance for compression

• 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

Buckling res. for comp. - torsion Buckling res. for comp. - torsion

• 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 (LT)• 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

Buckling resistance for bending Buckling resistance for bending

• 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

Buckling res. for bending – contnd.Buckling res. for bending – contnd.

• 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

Serviceability limit statesServiceability limit states

• 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 (…, …)

Design assisted by testDesign assisted by test

• Combination of tests and mathematical models is allowed

• Evaluation of test results:Measured data

Adjusted resultsMean value

Characteristic valueDesign value

Design assisted by test – contnd.Design assisted by test – contnd.

• Basic model:

• Verification:– Normal force + „vertical” bending + lateral bending– Buckling

• Simplified method is also available

Beams restrained by sheetingBeams restrained by sheeting

• A numerical example has been worked out• Local and distortional buckling of Z/C beams

Numerical exampleNumerical example

EXAMPLE

Thank you.Thank you.

elastic

plastic

elastic with hardeningTo Figure

elastic

plastic

shear buckling

shear yielding