3. Thin-walled steel members Production, speciality of design, basic cases of design, design of joints, Eurocode approach. Thickness of sheeting/member: 0.45-15 mm (EN 1993-1-3, 2006) Profiles: open closed profiled sheets Jäkl profiles in CR 20-50 mm 50-160 mm + special cassettes (liner trays) Advantages: Drawbacks: small mass, precise fabrication, quality surface price, corrosion, fire resistance Fabrication: by cold-forming of steel hot - or cold - rolled sheets: - by rolling ("profiling" of open or closed sections: up to 15 m), - by drawing (first welded tube, creating centre point and drawing through a bell: up to 12 m), - by pressing (on a press brake: max. 9 m). O3 1
Speciality of design: influence of strengthening due to cold working, local buckling of plates (always class 4 cross section), plates are usually stiffened by longitudinal stiffeners (to restrict buckling), shear lag at wide flanges (both in compression and tension) of profiles in bending, web crushing/crippling/buckling under local forces. The calculation may neglect rounded corners: for r < 5 t Local buckling effects are accounted for by using effective p widths in accordance with EN 1993-1-5 (Plated structural elements) r 1. Influence of strengthening due to cold working f u t ~ 4t f ya f plastic (permanent) corner deformation In parts which does not buckle the increased average yield strength f ya may be used: f ya = f + ( f f ) u k = 7 for rolling, otherwise k = 5 number corners 2 ( f + f ) k nt u Ag 2 gross cross-sectional area O3 2
2. Buckling of unstiffened plates ritické napětí critical stress a) Lokální boulení a) local buckling c) total buckling c) Celkový vzpěr b) Distorzní voulení b) distortional buckling a) b) c) a) b) c) Délka polovlny vočení half wave length of buckling Flat parts: λ ρ A eff (common 4 class cross-section p procedure) 1 3. Buckling of stiffened plates Models consider stiffeners as continuous 1 elastic supports, e.g.: O3 3
The spring stiffness per unit length = 1/δ (results from deflection due to unit load). Critical stress of the effective stiffener on elastic foundation: b e2 A s, I s N = (Engesser formula) cr, s 2 E Is effective stiffener b) Náhradní systém b 1,e2 b 2,e1 stiffener slenderness: λ d = f σ cr, s Corresponding reduction factor χ d, reduces the plate thickness t of the effective stiffener to effective thickness of t eff. Value usually covers also influence of distortion of the cross section. 4. Shear lag effect In case of wide flange both in tension or compression (b 0 > L/50) the effective width s (b eff = β b 0 ) shall be used in accordance with EN 1993-1-5. O3 4
5. Crushing/crippling/buckling under transverse local forces. s s e (distance between contrary local loading) s s c h w φ Satisfy: F Ed R w,rd local web resistance R w,rd function of: t, r, l a, φ, f y, e, h w, s s, c effective bearing length : 1) l a = 10 mm 2) l a = s s Formulas for local resistance result from experiments. Eurocode distinguishes: one web - unstiffened web more webs - stiffened web O3 5
Resistance of cross-sections: Tension: take f ya Compression: take f and effective cross section Plný průřez full section e N e N N S d NR d Účinný průřez effective cross section buckling as usual: χ A N b,rd = γ eff M1 f - buckling curves acc. to EN 1993-1-3, - usually necessary to check also torsional or torsional-flexural buckling. Moment: take f and effective cross section M = χ W b,rd LT eff f γ M1 b eff /2 t b eff /2 tred M Rd - buckling curve b, plast. - shear lag if necessary, elast. -if W eff = W el the strength may be increased (see EN3): - in tension fibres plasticity (yielding) is possible. effective O3 6
Shear: h V = sinφ w b, Rd t fbv / γ M0 Joints of thin-walled profiles shear buckling strength (see formulas in EN 1993-1-3) -welds: spot welds (up to t = 4 + 3 mm), ds corrosion!! arc spot welds (up to total t = 4 mm), not allowable in roofs ds fillet welds (formulas for parent material t 4 mm). - bolts: self-tapping/drilling screws (ø 3-8 mm) common bolts (preloaded bolts are not recommended). - cartridge fired pins - blind (one-sided) rivets -gluing tubular with pin peen rivet Note: Majority of design strengths follow experimental values (given in Eurocode). O3 7
Complementary note: Ordinary thin-walled profiles have sectional parameters (or resistances) given by distributors in tables (e.g. trapezoidal sheeting, purlins, liner trays...). Significant is cooperation of trapezoidal sheeting with structural frames (stressed skin design), see lecture 9. For purlins and liner trays the Eurocode EN 1993-1-3 gives procedure: - precise, - simplified. Model of a purlin secured by trapezoidal sheeting under uplift loading: q Ed q Ed k h q Ed k h q Ed z y Oh v rovině in-plane bending roucení a příčný oh lateral bending and torsion model of free flange (beam on elastic foundation) The simplified approach provides design of simply and continuously supported girders under gravity and uplift loadings with help of coefficients given in tables. O3 8