Lateral Torsional Buckling (sections class 1-3) - Column Item COx

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Sophie Barrett
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1 Page /7 Lateral Torsional Buckling (sections class -3) - according to EN 993--:005 (EC3) section and eqn. numbers refer to this code (Form EC3-LTB_ mcd - adopted) Profile chosen Profile "HEA40" Yield limit f y.k 355 N mm Partial safety factor for material γ M. f y.k Design strength f y.d f y.d = 33 N γ M mm Young's modulus E. 0 5 N mm Section Properties b profile 30 mm I y 7763 cm 4 W y 675 cm 3 40 mm I z 769 cm 4 W z 3 cm 3 A profile 76.8 cm I T 4 cm 4 I ω cm 6 Select CLASS of cross-section CLASS Factor from elastic to plastic section modulus if CLASS = 3 only elastic properties may be used α pl.y wenn( CLASS = 3,,.4) α pl.y =.4 α pl.z wenn( CLASS = 3,,.50) α pl.z =.50 Design resistances of cross section N pl.d A profile f y.d N pl.d = 479kN M pl.y.d α pl.y W y f y.d M pl.y.d = 48kNm +49(0) , Fax Date of release: Printed: :56 EC3-LTB_0-0-0.xmcd

2 Page /7 M pl.z.d α pl.z W z f y.d M pl.z.d = knm System length - distance of gable ends L 6.00m L = 6.00 m Actions from excentrically connected beam: (the moment from offset will be carried to the upper and lower parts of the member to equal parts) V y.ed 00kN Moments about major axis End moment M (+/-): 0.5 V y.ed + 0mm = 4kNm End moment M < M (+/-): M.y 0kNm Relation of end moments M.y ψ y ψ y = Moment from transverse loads (positive only) bild M 3.y 50kNm Position of Maximum (dist. from M) a y.5m a y = 500mm ( ) a y M y.s M.y + L M.y + M 3.y M y.s = 53.4kNm Design moment, maximum by absolute value +49(0) , Fax Date of release: Printed: :56 EC3-LTB_0-0-0.xmcd

3 Page 3/7 ( ) max, M.y, M y.s = 53kNm see Table B.3 M y.s α y.s wenn M y.s <,, 0 α y.s = α y.h wenn M y.s >,, 0 α y.h = M y.s Flexural buckling about minor axis Factor for buckling length β z.0 buckling length L cr.z β z L L cr.z = 6.00 m π EI z Bifurcation load N cr.z.d N cr.z.d = 449kN L γ cr.z M N pl.d normalised Slenderness λ bar.z λ bar.z =.308 N cr.z.d η p η p = 0.96 b profile Buckling curve (table 6.) - ONLY rolled sections and t,f =< 40 mm BC z "b" if η p >. BC z = "c" "c" if η p. Imperfection factor (table 6.) α z 0.34 if BC z = "b" α z = if BC z = "c" Reduction factor according to eq. (6.49) ( ) Φ z α z λ bar.z 0. + λ bar.z Φ z = (0) , Fax Date of release: Printed: :56 EC3-LTB_0-0-0.xmcd

4 Page 4/7 χ z if λ bar.z 0. χ z = Φ z + Φ z λ bar.z if λ bar.z > 0. Design buckling resistance under normal compression N b.z.rd χ z N pl.d N b.z.rd = 956kN Elastic critical moment for lateral-torsional buckling according to DIN Element 3, eq. 9: I ω L cr.z I T c c = 8. cm Distance of centroid from attack of transverse forces; positive, if a torsion about the centroid produces a restoring force I z input "t" for top, "m" for middle, "b" for bottom z "t" z p if z = "t" z p = 5mm 0mm if z = "m" if z = "b" +49(0) , Fax Date of release: Printed: :56 EC3-LTB_0-0-0.xmcd

5 Page 5/7 Moment coefficient according to DIN Table 0 ζ.77 bild3 Critical Moment for LTB (DIN Element 3, eq. 9): M cr.y.d ζ N cr.z.d c z p z p M cr.y.d = 34kNm normalised slenderness (eq. (6.56)) λ bar.lt M pl.y.d λ bar.lt = 0.85 M cr.y.d Buckling curve (table 6.5) - ONLY rolled sections BCLT "b" if η p BCLT = "b" "c" if η p > Imperfection factor (table 6.3) Reduction factor according to eq. (6.57) α LT 0.34 if BCLT = "b" α LT = if BCLT = "c" Parameters λ bar.lt β 0.75 According to (4) LTB may be ignored, if λ,lt / λ,lt,0 <= λ bar.lt =.9 λ bar.lt.0 According to (4) LTB may be ignored, if M,Ed / (Mcr.y * (λ,lt,0)^) <= +49(0) , Fax Date of release: Printed: :56 EC3-LTB_0-0-0.xmcd

6 Page 6/7 ( ) M cr.y.d γ M =.545 λ bar.lt.0 Φ LT α LT λ bar.lt λ bar.lt.0 + β λ bar.lt Φ LT = χ LT χ LT = Φ LT + Φ LT βλ bar.lt checking limits χ LT min χ LT,.0, χ LT = λ bar.lt Correction factor from table 6.6 k c 0.8 Modification factor eq. (6.58) ( ) ( ) f 0.5 k c.0 λ bar.lt 0.8 f min( f, ) f = 0.9 bild Design buckling resistance in bending M b.rd Modified reduction factor χ LT.mod min χ LT, χ LT.mod = f χ LT.mod M pl.y.d M b.rd = 5kNm k zy k yy Stability check according to eq. (6.6) utilisation of flexural buckling about major axis by N +49(0) , Fax Date of release: Printed: :56 EC3-LTB_0-0-0.xmcd

7 Page 7/7 utilisation of LTB by My η.my k yy η.my = 0.73 M b.rd Stability check according to eq. (6.6) utilisation of LTB by My η.my k zy η.my = 0.73 M b.rd Utilisation in cross section check (without interaction): utilisation by My: η My η My = 0.68 M pl.y.d +49(0) , Fax Date of release: Printed: :56 EC3-LTB_0-0-0.xmcd

STEEL MEMBER DESIGN (EN :2005)

STEEL MEMBER DESIGN (EN :2005) GEODOMISI Ltd. - Dr. Costas Sachpazis Consulting Company for App'd by STEEL MEMBER DESIGN (EN1993-1-1:2005) In accordance with EN1993-1-1:2005 incorporating Corrigenda February 2006 and April details type;