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Transcript of Structural Eurocodes
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Structural Eurocodes
EN 1993 Design of Steel
Structures
John J Murphy Chartered Engineer
Department of Civil, Structural & Environmental Engineering Cork Institute of Technology
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Designers guide to Eurocode 3: Design of Steel Structures(L Gardner and D A Nethercot) Thomas Telford
Access Steel website that provides much information on design
to EC3
Access Steel is a unique electronic resource to ensure that the
European steel construction community takes maximum advantage
from the commercial opportunities arising from the Eurocodes.
With input from six leading institutes for steel construction in Europe,it provides harmonised information for clients, architects and
engineers on:
multi storey commercial buildings
single storey buildings
residential construction
fire safety engineering
http://www.access-steel.com/
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Partners
Steel Construction Institute (SCI) (UK)
Centre Technique Industriel de la Construction Metallique (CTICM ) (France)
Stalbyggnadsinstutet Swedish Institute of Steel Construction (SBI) (Sweden)
Rheinish-Westfalische Technische Hochschule Aachen (RWTH) (Germany)
Labein Tecnalia (Spain)
Profilarbed Research (PARE) (Luxembourg)
Sponsors
Arcelor-Mittal, Corus, Peiner Trger, Voest Alpine, Ruuki, Dillinger, SSAB
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EN 1993-1-1: General rules and rules for buildingsEN 1993-1-2: Structural fire design
EN 1993-1-3: Cold formed thin gauge members and sheeting
EN 1993-1-4: Structures in stainless steelEN 1993-1-5: Strength and stability of planar plated
structures without transverse loadingEN 1993-1-6: Strength and stability of shell structures
EN 1993-1-7: Strength and stability of plate structures loaded transversally
EN 1993-1-8: Design of jointsEN 1993-1-9: Fatigue strength
EN 1993-1-10: Fracture toughness assessment
EN 1993-1-11: Design of structures with tension components made of steel
EN 1993-1-12: Use of high strength steels
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Department of Civil, Structural &Environmental Engineering Cork
IwItIWplWeliy,zAEC3
HJISZrx,yABS5950
tf,t
wdB,hVMNf
y
LTf
yf
yEC3
T,tdB,DVMPpcpbpyBS5950
Symbols
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Department of Civil, Structural &Environmental Engineering Cork
Table 3.1: fy fu
Clause 3.2.6 E = 210000 N/mm2 G 81000 N/mm2, = 0.3
S275: t < 40 mm f y = 275 N/mm2
fu = 430 N/mm2
40 mm < t < 80 mm fy = 255 N/mm2 fu = 410 N/mm
2
Material properties taken from EN 10025-2, which gives additional
values for different thicknesses.
So for S275 16 mm < t < 40 mm fy = 265 N/mm2. Table 3.1 is asimplification of EN 10025-2.
5.5 Classification of cross sections
Table 5.2 { = (235/fy)} Class 1,2,3,4
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5 Structural Analysis
5.1.1 (2) Calculation model and basic assumptions should reflect
structural behaviour.
5.1.2 (2) Depending on joint behaviour simple, continuous, semi-
continuous
5.2.1 (3) First order analysis when cr = Fcr/FEd 10 elastic analysis15 plastic analysisFcr: Elastic critical buckling load FEd: Design load
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Ed
y
N
Af3.0
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5.2.2 Structural stability of frames
5.2.2 (3) b) Second order effects accounted for partially by
global analysis and partially through individual member
stability checks according to 6.3
5.2.2 (5) If cr 3, amplify all horizontal loads by
cr11
1
Second order effects likely to arise in unbraced structures
and in bracing design of braced structures
If cr
< 3, second order analysis is necessary
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( )m115.0 +
5.3 Imperfections
5.3.2 (3) a) Global initial sway imperfection: = 0 * h * m0: Initial value =1/200
h: Reduction factor for column height = 2/h (2/3 h 1)(h: structure height)
m: Reduction factor for number of columns in a row =
Recommendation (SCI) - use 0 i.e let h = m = 1.0
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which translates as NEd/Ncr 0.25
Use equivalent horizontal forces (EHFs) for
all load combinations
Ed
y
N
Af5.0
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6 Ultimate limit states
6.1 Material factors MM0 = 1.00 (cross-sections) M1 = 1.00 (Buckling)
M2 = 1.25 (Fracture) (1.1 in UK)
6.2.3 Tension
(1) NEd Nt,Rd(2) Npl,Rd = Afy/M0 gross section(3) Nu,Rd = 0.9Anetfu/M2 bolt holes
EN 1993-1-8: 4.13(2) For equal angle leg or unequal angle
connected (by welding) by its larger leg Aeff= Agross
EN 1993-1-8: 3.10.3(2) Nu,Rd formulae for resistance of angle
connected through one leg using 1,2 or 3+ bolts
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6.2.4 Compression
(1) NEd Nc,Rd(2) Nc,Rd = Afy/M0 (class 1,2,3)
Aefffy/M0 (class 4)
EN 1993-1-5 Clause 4.4:
Aeff is determined by excluding ineffective portion of
section.
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6.2.5 Bending moment
(1) MEd Mc,Rd
(2) Mc,Rd = Mpl,Rd = Wplfy/M0 (class 1,2)Wel,minfy/M0 (class 3)Weff,minfy/M0 (class 4)
(4) Fastener holes in tension flange may be ignored provided:
Af,net 0.9fu/ M2 Affy/ M0
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6.2.6 Shear(1) VEd Vc,Rd(2) Vpl,Rd = Av(fy/3)/M0(3) I section Av = A 2btf+ (tw + 2r)tfbut not less than hwtw(6) Shear buckling if hw/tw > 72/ may be conservatively taken as 1EN1993-1-5 Clause 5.1 Note 2: = 1.2 up to and including S460;
otherwise 16.2.8 Bending and shear
(2) VEd1
0.5Vpl,Rd
no effect on Mc,Rd(3) Reduced moment resistance: reduced design yield strength (1-)fy
2
,
12
=
Rdpl
Ed
V
V
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1,,
,
,,
,
+
RdzN
Edz
RdyN
Edy
M
M
M
M
6.2.9 Bending and axial force
6.2.9.1 Class 1 and 2 cross-sections
(4) Axial force can be ignored:yy axis: if NEd 0.25Npl,Rd and NEd 0.5hwtwfy/M0zz axis: if NEd hwtwfy/M0(5) Values of reduced moment capacities: MN,y,Rd, MN,z,Rd
(6)
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Conservative alternative for all sections: 6.2.1 (7)
1,
,
,
,++
Rdz
Edz
Rdy
Edy
Rd
Ed
M
M
M
M
N
NEq 6.2
As buckling is generally critical and will override Eq.
6.2, the more exact equations in 6.2.9 need not generally
be considered.
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6.3 Buckling resistance of members
Elastic buckling theory (Euler)Ncr =
2EI/l2 for ideal strut
This value is modified by various imperfections:
Geometric imperfections (initial curvature)
Eccentricity of loading
Residual stresses (locked-in due to differential cooling)
Non-homogeneity of material properties
End restraintsThese are taken into account in the Perry-Robertson formula
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EC3 provides solution for this equation. Effectively cr = fy
}{ EyEyEy
cr ++++=
2)2/))1(((2
)1(
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6.3.1 Uniform members in compression
6.3.1.1 Buckling resistance(1) NEd Nb,Rd
(3) Nb,Rd = Afy/ M1 (class 1,2,3)
Aefffy/ M1 (class 4)
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2.0
22
1
+
=22 )2.0(15,0 ++=
cr
y
N
Af=
cr
yeff
N
fA=
6.3.1.2 Buckling curves
(1)
(but 1)
(class 1,2,3)
: imperfection factor (Table 6.1) (Table 6.2)Ncr: Elastic critical buckling load
(chi) can also be obtained from Figure 6.4
(4) If
(class 4)
2.0 crEd NN 04.0( ) buckling effects can be ignored
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1
=
6.3.1.3 Slenderness for flexural buckling
fcr = Ncr/A = 2EI/Al2 = 2EAi2/Al2 = 2E/2
Lettingfcr =fy limiting slenderness 1 = (E/fy)0.5 = 93.9
= Lcr/iz
cr
y
N
Af
(ratio of actual slenderness to slenderness at boundary between
yielding and elastic buckling) =(E/fcr)0.5/ ((Efy)
0.5) = (fy/fcr)0.5
=
: non-dimensional slenderness
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5.0
2
2
2
2
+=
z
tcr
z
w
cr
zcr
EI
GIL
I
I
L
EIM
gg
z
tcr
z
w
wcr
zcr zCzC
EI
GIL
I
I
k
k
L
EICM 2
5.0
2
22
22
2
2
1
++
=
6.3.2 Uniform members in bending
Beam behaviour analogous to column behaviour
Beam subject to equal moments at each end
This is expanded to:
for other load situations.
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Mcr: Elastic critical buckling load
C1, C2, k, kw: constants
zg: Eccentricity of load relative to centroid of beam
(destabilizing load)
C1: depends on moment diagram
k, kw: depend on support conditions (generally 1)
C2: does not apply when zg = 0 (non destabilizing
loads)
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NCCI SN003a-EN-EU and NCCI SN006a-EN-EU (cantilevers)
provide information on calculation of Mcr.
Program to calculate Mcr
can be downloaded from
http://www.cticm.eu
The results for buckling and lateral torsional buckling are similar to
those in BS5950 (Annex C buckling (exact), Annex B lateraltorsional buckling)
6.3.2.1 Buckling resistance
(1) MEd Mb,Rd(3) Mb,Rd = LTWyfy/M1Wy = Wpl,y (class 1,2) Wy = Wel,y (class 3) Wy = Weff,y (class 4)
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22
1
LTLTLT
LT
+
=
222.015,0 LTLTLTLT ++=
cr
yy
LTM
fW
=
4.0LT crEd MM 16.0
6.3.2.2 Lateral torsional buckling curves General case(1)
(but 1)
LT: imperfection factor (Table 6.3) (Table 6.4)(3) LT can also be obtained from Figure 6.4
(4) If ( )buckling effects can be ignored
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NCCI SN002a: Simplified assessment of
119.0
1
z
LTC= where z = Lcr/iz, 1 = (E/fy)
1.3481.365pinned, central P
1.1271.132pinned, udl
2.552.752-1
2.572.927-.75
2.332.704-.5
2.052.281-.251.771.8790
1.621.563.25
1.311.323.5
1.141.141.75
1.001.0001
C1 (SN003a)C1 (Designers Guide) (= M1/M2)
C1 = 1.88 1.4 + 0.5 2 (C1 2.70)
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22
1
LTLTLT
LT
+=
2
1
LT
2
0,
2)(15,0 LTLTLTLTLT ++=
4.00, =LT
75.0=
6.3.2.3 Lateral torsional buckling curves for rolledsections or equivalent welded sections
(1) For members in bending (beams)
but 1 and
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2
)8.0(0.211(5.01 =
LTckf
LT: imperfection factor (Table 6.3) (Table 6.5)(2) LT,mod = LT/f ( 1)
kc: Table 6.6
6.3.2.3 used for rolled sections of standard dimensions
6.3.2.2 can be used for all sections including plate girders
(bigger than standard sections), castellated and cellularbeams
( 1)
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1,,
,
,
,
,,++
Rdzc
EdZ
yz
Rdb
Edy
yy
Rdyb
Ed
M
M
kM
M
kN
N
1,,
,
,
,
,,++
Rdzc
EdZ
zz
Rdb
Edy
zy
Rdzb
EdM
M
kM
M
kN
N
6.3.3 Uniform members in bending and compressionFor Class 1,2,3 sections, Equations 6.61 and 6.62 reduce to:
Eq. 6.61
Eq.6.62
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k values in Annex A, Annex B.
Annex A is more precise (French-Belgian)
Annex B is easier to use (Austrian-German)
Table B.3:
If =1 (uniform moment in column no lateral load on column)Cmy = Cmz = CmLT = 1
If =0 (M varies from 0 to Mmax no lateral load on column) Cmy= Cmz = CmLT = 0.6
Members susceptible to torsional deformations:
(Table B.2/ Table B.1)
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=
Rdzb
Ed
mLTRdzb
Ed
mLT
z
zy N
N
CN
N
CMAXk
,,,, )25.(
1.0
1,)25.0(
1.0
1
+
+=
yRdb
Edmy
Rdyb
Edymyyy
N
NC
N
NCMINk
,,,
8.01,)2.0(1
+
+=
Rdzb
Edmz
Rdzb
Edzmzzz
N
NC
N
NCMINk
,,,,
4.11,)6.02(1
kyz = 0.6kzz kzy = 0.6kyy
(Table B.2/ Table B.1) 4.0
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For columns in simple construction N generally dominates,
UC sections are less likely to buckle about yy axis Equation 6.62 likely to be critical.As N dominates, k values can be chosen conservatively
Access Steel (NCCI SN048b-EN-GB) suggests kzy= 1, kzz=
1.5 (conservatively)
15.1,,
,
,
,
,,
++
Rdzc
EdZ
Rdb
Edy
Rdzb
Ed
M
M
M
M
N
N
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7 Serviceability limit states
Deflections to be agreed with client BS5950 values proposed in
UK National Annex
Guidance is also provided in NCCI SN034a-EN-EU
Cantilever: Length/180Beams carrying plaster or other brittle finish: Span/360
Other beams: Span/200
Horizontal deflection limits also provided
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EN 1993-1-8 Design of Joints
Table 2.1 Partial safety factors for joints
Bolts, Plates in bearing, Welds M2 = 1.25 (UK: 1.5 for grade 4.6)Slip resistance at sls M3,ser = 1.1Preload of high strength bolts M7 = 1.1
2.5 Design Assumptions (1) Joints should be designed on the
basis of a realistic assumption of the distribution of internal
forces and moments.Identify a load path through the joint and
check all links in chain.
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2.7 Eccentricity at connections
Table 3.1 Bolt strength fy, fu
3 Connections made with bolts, rivets or pins
3.1.2 Preloaded bolts
Table 3.2
Bearing: Fv,Ed Fv,Rd Fv,Ed Fb,RdSlip (sls): Fv,Ed,ser Fv,Rd,ser Fv,Ed Fv,Rd Fv,Ed Fb,Rd(use grade 8.8 or 10.9)
Tension: Include prying action
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Table 3.3 End, edge distances (e) Spacings (p)
(d0 bolt hole diameter)
e1, p1: Parallel to load e2, p2: Perpendicular to load
3.6.1 (2) Preload in bolts: Fp,Cd = 0.7 fub As/ M7
(10) Single lap joints with one bolt row(12) Bolts through packing
Table 3.4 Design resistance
Shear resistance Fv,Rd = v fub As/ M2 v = 0.6 or 0.5Bearing resistance Fb,Rd = k1 ab fu d t/ M2ab = Min. (ad, fub/fu, 1) end bolts ad = e1/3do
inner bolts ad = p1/3do 0.25
k1 = Min. (2.8 e2/do -1.7, 2.5) edge bolts
k1 = Min. (1.4 e2/do -1.7, 2.5) inner bolts
Tension & Combined Shear and Tension also included
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3.8 Long joints
3.9 Design slip resistance Fs,Rd = (ksn)Fp,C)/ M3ks = 1 for bolts in normal holes (Table 3.6)
n is the number of friction surfaces: slip factor (Table 3.7)Class A: shot/ grit blasted, spray metallised with aluminium or zinc
based coating certified to provide a slip factor of 0.5
Class B: shot/ grit blasted, painted with alkali-zinc silicate paint toproduce a thickness of 50 80 mClass C: wire brushed or flame cleaned
Class D: untreated
3.10.2 Design for block tearing
(2) Veff,1,Rd = fu Ant/ M2 + (1/3)fy Anv/ M0 Eq 3.9
(3) Veff,2,Rd = 0.5 fu Ant/ M2 + (1/3)fy Anv/ M0 Eq 3.10
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Section 4 Welded connections
4.5.2 Effective throat thickness
4.5.3.2 Directional method
4.5.3.3 Simplified method for the design resistance of fillet weld
(1) Fw,Ed Fw,Rd(2) Fw,Rd = fvw,d * a (throat thickness) = 0.7 * leg length(3) fvw,d = fu/(3 * * M2) : Table 4.1 (= 0.85 for S275)
5 Analysis, classification and modelling
Table 5.1 Joint modelling
6 Structural Joints connecting H or I sections
Table 6.1 Basic joint components
Table 6.2 Design resistance of a T-stub
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=
2
,,
0,
1,
jd
Edj
fccjd
Edj
c
f
N
bhf
NMAXA
Column Base plate
6.2.8.2, Figure 6.19
6.2.5 Equivalent T-stub in compression
(3) FC,Rd = fjd * beff* leff(7) fjd = j FRdu/ (beff leff) j = EN 1992-1-1 Clause 3.1.6 (1) fcd = cc fck/ c; cc = 1, c = 1.5NCCI SN037a fjd = j * * fcd ( = 1.5)
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y
Mjd
pf
fct
03 =
Large projection
Short projection (when Ac,0 < 0.95bh) base plateSelect plate dimensions determine c (Figure 6.4)
Min. outstand: tf6.2.5(4)
y
Mjd
p
f
fct
03 =
EN 1993 1 5 Plated structural elements
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0.1
5.0
F
cr
ywwy
F
F
ftl=
w
wFcr
h
tEkF
3
9.0=
EN 1993-1-5 Plated structural elements
Section 6 Resistance to transverse forces (web bearing andbuckling)
Figure 6.1 kF6.2 Design resistance FRd =(fywLefftw)/ M1
Leff= Fly6.3 Length of stiff bearing
6.4 Reduction factor F =
6.5 Effective loaded length
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F
F
212
2
1
,2 mmtlmt
lm
tl fef
e
fe +++
++
csbut
hf
Etkl s
wyw
wFe +=
2
2
g
m1 = fyfbf/fywtw
m2 = 0.02 (hw/tf)2 if > 0.5,
ly is the minimum of:
6.6 Verification 1/)( 1
2 =
Mweffyw
Ed
tLf
F
0.50 if
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vveff 7.035.0, += yyeff 7.050.0, += zzeff 7.035.0, +=
Effective lengths
Truss members: EN 1993-1-1:
Annex BB.1.1: Lcr = L (for chord members)
Annex BB.1.2 (angles as web members):
Members in compression ends held in position (BS5950 in
absence of EC3 guidance)
1.0LNot restrained in direction at either end
0.85LRestrained in direction at one end
0.85LPartially restrained in direction at both ends
0.7LBoth ends effectively restrained in direction
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Members in bending compression flange laterallyrestrained, nominal torsional restraint against rotation
about longitudinal axis at supports (NCCI SN009a)
1.0Both flanges free to rotate on plan
0.85Compression flange partially restrained
against rotation on plan
0.8Both flanges partially restrained against
rotation on plan
0.75Compression flange fully restrainedagainst rotation on plan
0.7Both flanges fully restrained against
rotation on plan
KSupport conditions
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NCCI SN005a:
Simple construction assume loads applied at 100 mmfrom face of column (flange or web). Resulting moment
can be distributed between upper and lower levels in
accordance with stiffness
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End Plate NCCI: SN013, SN014
Use full depth end plate if VEd > 0.75 Vc,RdMin. number of bolts = VEd/75
Plate dimensions
14020010> 500 mm
901508, 10< 500 mm
Cross-centres(mm)
bp(mm)
tp(mm)
Beamdepth
Weld size (S275):
1086Leg length (mm)
75.54Throat (mm)
15129Beam web (mm)
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Bolts in shear: Shear resistance multiplied by 0.8 to account for
presence of some tension in bolts
End plate in shear (gross section): Shear resistance divided by
1.27 to allow for bending moment in plate
Weld design: Shear resistance divided by 1.27 to allow for
bending moment in plate
End plate in shear (block shear): may need to consider Veff,1,Rd(3.10.2 (2)) and Veff,2,Rd (3.10.2 (3))
End plate in bending when bolt cross-centre distance is large,
bending in plate reduces shear resistance
Beam web in shear to be checked for depth = plate depth
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Weld design a 0.39tw,b1
Ductility requirements:
py
ubp
f
fdt
,8.2
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