Overview of Eurocode 3

SUMMARY NOTES ON EUROCODE 3

by

Chiew Sing-Ping School of Civil and Environmental Engineering

Nanyang Technological University

CONTENTS

Chapter 1 – Introduction …..……………………………...............................

Pg 2

Chapter 2 – Materials ……..………….…………….…....................................

Pg 3 – 5

Chapter 3 – Section Classification …..…..………………………...............….

Pg 6 – 9

Chapter 4 – Restrained Beams …....…………………………….....................

Pg 10- 13

Chapter 5 – Unrestrained Beams …..………………....……………................

Pg 14 – 20

Chapter 6 – Tension Members ….....………………....................…………….

Pg 21 – 23

Chapter 7 – Compression Members .…..…..............………………………….

Pg 24 - 28

Chapter 8 – Web Bearing and Buckling …...….......…………………………..

Pg 29 - 31

Appendix I – Formulae for Beam Deflection ...….......………………………… Pg 32 Appendix II – Tables of Dimensions and Gross Section Properties ……………… Pg 33 - 40

Training Course on Design of Steel Structures to Eurocode 3

August 2012 2

CHAPTER 1 – INTRODUCTION

1.1 DESIGN REQUIREMENTS

The structure shall be designed to have adequate structural resistance to sustain the actions and influences on it, and it should remain serviceable and be durable. It should also have adequate fire resistance and be robust, i.e. not disproportionately damaged by accident events. The design requirements are outlined in EN1990 Basis of Structural Design and it is based on limit state design.

1.2 LIMIT STATE DESIGN

The principal limit states are the ultimate limit state which is concerned with ‘collapse’ involving yielding, buckling or overturning and the serviceability limit state which is concerned with ‘function’ involving deflection or vibration. Other limit states are fire resistance, durability and robustness. The design principles are as follows: • define relevant limit states

• determine appropriate actions {F}, e.g. dead loads, imposed loads

• determine design effects {E}, e.g. bending moments, deflections

• determine design resistance {R}

• ensure no limit state is exceeded {R > E}

1.3. VERIFICATION BY PARTIAL FACTOR METHOD

The partial factor method is used to verify the relevant limit state is not exceeded. Partial safety factors are applied to characteristic values to obtain design values for actions, material and resistances in verifying the limit state, for e.g. partial factors γ are applied to characteristic values for both actions and material to account for variability, i.e. • γF applied as a multiplier to the characteristic value of an action

• γM applied as a divisor to the characteristic value of material

The value of γ depends on: • the limit state under consideration

• the variable to which it is applied

• the context – e.g. is an action beneficial in relation to the considered effect

The effect of actions depends on the combinations of actions that can occur and EN1990 gives explicit rules on how to determine design values of combined actions. As an example, in ultimate limit state under combined dead and imposed loads, it can be simplified to:

• 1.35Gk + 1.5Qk where Gk and Qk are the characteristic dead and imposed loads respectively

1.4 ACTIONS ON STRUCTURES

Characteristic values of actions are given in various parts of EN1991 Actions on Structures, and actions most relevant to building design in Singapore are:

• dead and imposed loads – EC1 Part 1-1

• wind loads – Part 1-4

• actions on structures exposed to fire – EC1 Part 1-2


August 2012 3

CHAPTER 2 – MATERIALS 2.1 DESIGN STRENGTH OF STEEL [EC3-1-1: Clause 3.2.1]

The nominal values of the yield strength, fy, and the ultimate strength, fu, for structural steel can be obtained

either by:

a) adopting fy = Reh and fu = Rm from the product standard, or

b) using the values from EC3 Table 3.1.

EC3 Table 3.1: Nominal values of yield strength fy and ultimate tensile strength fu for hot rolled structural steel

Material thickness ≥ 3 mm [EC3-1-1: Clause 1.1.2]

However, the Singapore National Annex set slightly stricter requirements. The nominal values of the fy and

fu for structural steel should be those obtained from the product standards, such as EN 10025-1.

Further information on the yield and ultimate strength for structural steel is also given in BC 1: 2012.


August 2012 4

EC3 Table 3.1 (continued): Nominal values of yield strength fy and ultimate tensile strength fu for structural hollow sections

Material thickness ≥ 3 mm [EC3-1-1: Clause 1.1.2]

2.2 DUCTILITY REQUIREMENTS [EC3-1-1: Clause 3.2.2]

A minimum ductility is required to prevent brittle and sudden failure. The recommended values are:


August 2012 5

a) fu ≥ 1,10fy

b) elongation at failure ≥ 15%

c) εu ≥ 15εy

2.3 MATERIAL COEFFICIENTS [EC3-1-1: Clause 3.2.6]

Modulus of elasticity, E E = 210000 N/mm2

Shear modulus, G

Poisson’s ratio in elastic range, ν ν = 0,3

Coefficient of linear thermal expansion, α α = 12 × 10-6 per K (for T ≤ 100°C)

2.4 MATERIAL PARTIAL FACTORS

The partial factors, γMi, have been determined such that

γM0 = 1,00 [EC3-1-1: Clause 6.1] γM0 = 1.00 [NA to SS EN 1993-1-1]



γM2 = 1.25 [NA to SS EN 1993-1-8]


γM3,ser = 1,10 [EC3-1-8: Clause 2.2] γM3,ser = 1.10 [NA to SS EN 1993-1-8]



γM6,ser = 1,00 [EC3-1-8: Clause 2.2] γM6 = 1.00 [NA to SS EN 1993-1-8]


2.5 SYMBOLS

E Modulus of elasticity

fy Yield strength of structural steel

fu Ultimate strength of structural steel

G Shear modulus

α Coefficient of linear thermal expansion

εy Strain at yield strength (= fy / E)

εu Strain at ultimate strength

γM0 Partial factor for resistance of cross-sections whatever the class is

γM1 Partial factor for resistance of members to instability assessed by member checks

γM2 Partial factor for resistance of cross-sections in tension to fracture

ν Poisson’s ratio in elastic range

281000)1(2

mmNEG ≈+

=ν


August 2012 6

CHAPTER 3 – SECTION CLASSIFICATION 3.1 INTRODUCTION [Clause EC3-1-1: Clauses 5.5.1 & 5.5.2]

The role of cross section classification is to identify the extent to which the resistance and rotation capacity

of the cross sections is limited by its local buckling resistance.

Four classes of sections are defined as follows:

a) Class 1 sections are those which can form a plastic hinge with the rotation capacity required from plastic

analysis without reduction of the resistance.

b) Class 2 sections are those which can develop their plastic moment resistance, but have limited rotation

capacity because of local buckling.

c) Class 3 sections are those in which the stress in the extreme compression fibre of the steel member

assuming an elastic distribution of stresses can reach the yield strength, but local buckling is liable to

prevent development of the plastic moment resistance.

d) Class 4 sections are those in which local buckling will occur before the attainment of yield stress in one

or more parts of the cross-section.

A section is classified according to the highest (least favourable) class of its compression parts.

3.2 CLASSIFICATION [EC3-1-1: Table 5.2]

The limiting proportions for Class 1, 2 and 3 compression parts should be obtained from EC3 Table 5.2. Any

compression part which fails to satisfy the limits for Class 3 should be taken as Class 4.

Tables 5.2 (1) and 5.2 (2): I-, H-, Box-sections, C-channels, Built-up sections

Table 5.2 (3): Angles, Tubular-sections

Example: I-Beam under bending

Web: Table 5.2 (1), “Part subject to bending”, Classification based on c/t

Flange: Table 5.2 (2), “Part subject to compression”, Classification based on c/t

Example: H-Column under compression

Web: Table 5.2 (1), “Part subject to compression”, Classification based on c/t

Flange: Table 5.2 (2), “Part subject to compression”, Classification based on c/t


August 2012 7

Example: Beam-Column

Web: Table 5.2 (1), “Part subject to bending and compression”, Classification based on c/t

Flange: Table 5.2 (2), “Part subject to bending and compression”, Classification based on c/t

EC3 Table 5.2 (sheet 1 of 3): Maximum width-to-thickness ratios for compression parts


August 2012 8



August 2012 9


3.3 CLASS 4 SECTIONS [EC3-1-1: Clauses 5.5.2(2) & 6.2.2.5]

The effective cross-section properties of Class 4 sections should be based on the effective widths of the

compression parts. The effective widths may be used to make allowances for reductions in resistance due to

the effects of local buckling. Reference is to be made to EC3-1-5: Clause 5.2.2.


August 2012 10

CHAPTER 4 – RESTRAINED BEAMS 4.1 SHEAR [EC3-1-1: Clause 6.2.6]

The design value of the shear force, VEd, must be smaller than the design shear resistance Vc,Rd.

4.1.1 Shear Resistance [EC3-1-1: Clause 6.2.6.2].

The plastic design shear resistance Vpl,Rd, in the absence of torsion.

The shear area, Av, can be taken as follows [EC3-1-1: Clause6.2.6.3]:

a) Rolled I- & H-sections, load parallel to web

Av = A – 2btf + (tw + 2r)tf ≥ ηhwtw

b) Rolled channel actions, load parallel to web

Av = A – 2btf + (tw + r)tf

c) Rolled T-section, load parallel to web

Av = 0,9(A – btf)

d) Welded I-, H- and box sections, load parallel to web

Av = ηΣ(hwtw)

e) Welded I-, H-, channel and box sections, load parallel to flanges

Av = A – Σ(hwtw)

f) Rolled rectangular hollow sections of uniform thickness, load parallel to depth

Av = Ah / (b + h)

g) Rolled rectangular hollow sections of uniform thickness, load parallel to width

Av = Ab / (b + h)

h) Circular hollow sections and tubes of uniform thickness

Av = 2A / π

η may be conservatively taken as 1,0.

Vc,Rd can be equal to Vpl,Rd for plastic design, or Vel,Rd for elastic design

4.1.2 Shear Buckling [EC3-1-1: Clause 6.2.6.6].

Shear buckling need not be considered if:

ηε72≤

w

w

th

where, yf

235=ε

0,1VV

Rd,c

Ed ≤

0,,

)3(

M

yvRdplRdc

fAVV

γ==


August 2012 11

4.2 BENDING MOMENT [EC3-1-1: Clause 6.2.5]

The design value of the bending moment, MEd, must be smaller than the design resistance for bending Mc,Rd.

4.2.1 Bending Resistance (Low Shear)

Section is considered low shear when VEd < 0,5Vpl,Rd [EC3-1-1: Clause 6.2.8]

The design resistance for bending, Mc,Rd, in the absence of torsion.

For Class 1 or 2 cross sections

For Class 3 cross sections


Where Wel,min and Weff,min corresponds to the fibre with the maximum elastic stress

4.2.2 Bending Resistance (High Shear) [EC3-1-1: Clause 6.2.8]

Section is considered high shear when VEd > 0,5Vpl,Rd

The equations used for calculating bending resistance is the same as that for low shear except that

the yield strength will be reduced using (1 – ρ) fy

4.2.3 Allowances for Fastener (Bolt) Holes [EC3-1-1: Clause 6.2.5(4)]

Fastener holes in the tension flange may be ignored provided that for the tension flanges:

Fastener holes (except for oversize and slotted holes) in compression zone of the cross-section may

be ignored provided that they are filled by fasteners.

0,1MM

Rd,c

Ed ≤

0M

yplRd,plRd,c

fWMM

γ==

0M

ymin,elRd,elRd,c

fWMM

γ==

0M

ymin,effRd,c

fWM

γ=

0M

yf

2M

unet,f fAf9,0Aγ

≥γ

2

Rd,pl

Ed 1V

V2⎟⎟⎠

⎞⎜⎜⎝

⎛−=ρ


August 2012 12

4.3 VERTICAL DEFLECTION [EC3-1-1: Clause 7.2.1, EC0: Annex A1.4.3]

The definitions of vertical deflections are defined in Figure A1.1.

Deflections are based on unfactored actions in service. The SG National Annex is assuming deflections due

to permanent actions can be countered by pre-cambering; hence, w1 and w2 would be zero, so wtot would be

equal to w3 which should be less than the permissible limit given below.

The serviceability deflection limit depends on the criterion being used:

a) To avoid unsightly appearance, a value of L/200 (L/180 for cantilevers) might be used after making

allowances for any pre-camber.

b) For against cracking of plaster finishes, a value of L/360 is adopted.

c) For crane gantry girders, a value of L/600 is used.

4.4 DESIGN PROCEDURE

a) Section Classification [EC3-1-1: Clause 5.5.2]

b) Analysis structure to obtain factored moment MEd and shear VEd

c) Calculate Vc,Rd [EC3-1-1: Clause 6.2.6]

d) Check Vc,Rd ≥ VEd

e) Check whether beam is under low shear, VEd < 0,5Vpl,Rd, or high shear

f) Calculate Mc,Rd [EC3-1-1: Clause 6.2.5]

g) Check Mc,Rd ≥ MEd

h) Check deflection [EC3-1-1: Clause 7.2.1]


August 2012 13

4.5 SYMBOLS

A Cross-sectional area

Af Tension flange area

Av Shear area

b Overall breadth of section


h Overall depth of section

hw Depth of web of section

Mc,Rd Design resistance for bending (Can be plastic or elastic bending resistance)

Mel,Rd Design elastic bending resistance

Mpl,Rd Design plastic bending resistance

MEd Design value of bending moment (Applied moment due to factored loading)

r Root radius of section

tf Flange thickness of section

tw Web thickness of section

Vc,Rd Design shear resistance (Can be plastic or elastic shear resistance)

Vpl,Rd Design plastic shear resistance

VEd Design value of shear force (Applied shear force due to factored loading)

Wpl Plastic section modulus

Wel,min Minimum elastic section modulus

Weff,min Minimum effective section modulus

η Shear area factor (η = 1.0 from UK NA).


August 2012 14

CHAPTER 5 – UNRESTRAINED BEAMS (LATERAL TORSIONAL BUCKLING) 5.1 BUCKLING RESISTANCE OF MEMBERS IN BENDING [EC3-1-1: Clause 6.3.2]

A laterally unrestrained member subject to major axis bending should be verified against lateral-torsional

buckling as follows:

5.1.1 Buckling Resistance [EC3-1-1: Clause 6.3.2.1]

The design buckling resistance moment of a laterally unstrained beam, Mb,Rd, should be taken as:

Wy = Wpl,y For Class 1 or 2 cross sections

Wy = Wel,y For Class 3 cross sections

Wy = Weff,y For Class 4 cross sections

Where, χLT is the reduction factor for lateral torsional buckling.

5.1.2 Lateral Torsional Buckling Curves – General Case [EC3-1-1: Clause 6.3.2.2]

The non-dimensional slenderness λLT should be taken as:

Use Table 6.4 to determine the relevant buckling curve (a, b, c or d) to use. The value of χLT is

determined using slenderness λLT and the appropriate buckling curve in Table 6.3:

but χLT ≤ 1,0

0,1MM

Rd,b

Ed ≤

1M

yyLTRd,b

fWM

γχ=

2LT

2LTLT

LT1

λ−Φ+Φ=χ

])2,0(1[5,02LTLTLTLT λλα +−+=Φ

cr

yyLT

MfW

=λ

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡−++⎟⎟

⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛= gg

z

t

z

w

w

zcr zCzC

EIGIkL

II

kk

kLEI

CM 22

22

22

2

2

1 )()(

)( ππ


August 2012 15

EC3 Table 6.3: Recommended values for imperfection factors for lateral torsional buckling curves

EC3 Table 6.4: Recommended values for lateral torsional buckling curves for cross-sections using equation (6.56)

For λLT ≤ λLT,0 or for MEd/Mcr ≤ λLT,02, lateral torsional buckling effects may be ignored and only cross-

sectional checks are necessary.

5.1.3 Lateral Torsional Buckling Curves – rolled or equivalent welded sections Case [EC3-1-1:

Clause 6.3.2.3]

LTB curves for rolled or equivalent welded sections case are described through the following

equation:

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

≤

≤

−+=

2T

LT

LT

2LT

2LTLT

LT 10.1

but1

Lλχ

χ

λβφφχ

where ])(1[5.0 2

LTLT,0LTLTLT λβλλαφ +−+=

value)maximum( 4,0LT,0 =λ

value)(minimum 0,75=β

The definitions LTλ , αLT and Mcr are as for the general case but the selection of LTB curve should be based on Table 6.5 of EN 1993-1-1.

EC3 Table 6.5: Recommended values for lateral torsional buckling curves for cross-sections using equation (6.57)

Cross-section Limits Buckling curve

Rolled I sections h/b ≤ 2 b

h/b > 2 c

Welded sections h/b ≤ 2 c

h/b > 2 d


August 2012 16

SS EN 1993-1-1: 2010, Table 6.5 should be replaced with the following table:

Cross-section Limits Buckling curve

Rolled I- and H- sections, and hot-finished hollow

sections

h/b ≤ 2 b

2.0 < h/b ≤ 3.1 c

h/b > 3.1 d

Angles (for moments in the major principal plane) d

Welded sections and cold-formed hollow sections h/b ≤ 2 c

2.0 < h/b ≤ 3.1 d

5.1.4 Elastic Critical Moment for Lateral Torsional Buckling

The elastic critical moment Mcr can be calculated from the following formula derived form the

buckling theory:

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡−++⎟⎟

⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛= gg

z

t

z

w

w

zcr zCzC

EIGIkL

II

kk

kLEICM 2

222

22

2

2

1 )()()( π

π

4

)( 2fz

w

tDII

−=

For normal support conditions at the ends (fork supports), k = kw = 1,0. When the transverse load is

applied in the shear centre, C2zg = 0. The Mcr equation can be simplified to:

z2

t2

z

w2

z2

1cr EIGIL

II

LEI

CMπ

+π

=


August 2012 17

Values of C1 for cases with transverse loading (for k = 1,0)

For end moment loading C1 may be obtained from using the following table:

ψ +1,00 +0,75 +0,50 +0,25 0,00 –0,25 –0,50 –0,75 –1,00

C1 1,00 1,14 1,31 1,52 1,77 2,05 2,33 2,57 2,55

Values of C1 for cases with end moments (for k = 1.0)

Alternatively, C1 may be obtained from using the equation below:

21 52.040.188.1 ψψ +−=C but C1 ≤ 2.70

5.2 SIMPLIFIED METHOD FOR BEAMS WITH RESTRAINTS [EC3-1-1: Clause 6.3.2.4]

5.2.1 SLENDERNESS OF EQUIVALENT COMPRESSION FLANGE

Members with discrete lateral restraint to the compression flange are not susceptible to LTB if:

The slenderness of the equivalent compression flange satisfied:

Edy,

Rdc,c0

1zf,

ccf M

Mi

Lk λλ

λ ≤=


August 2012 18

Where, M1

yyRdc, γ

fWM =

1.0

2359.939.93

0,0

1

+=

===

LTC

yy ffE

λλ

επλ

kc is a slenderness correction factor for moment distribution between restraints; see Table 6.6 of EC3-1-1

EC3 Table 6.5: Correction factor kc

5.2.2 BUCKLING RESISTANCE

If the slenderness of the compression flange fλ exceeds the limit given in the forgoing equation, the

design buckling resistance moment is taken as:

Rdc,Rdb,Rdc,Rdb, but MMMKM fl ≤= χ

The modify factor kfl = 1.0, for hot rolled I-sections; kfl = 1.0, for welded I-sections with h/b ≤ 2; kfl = 0.9, for other sections. χ is the reduction factor of the equivalent compression flange determined using the non-dimensional slenderness fλ from the buckling curve ‘c’ (Figure 6.4 of EC 3-1-1; see page 24) .


5.3.1 DESIGN PROCEDURE WITH GENERAL METHOD



August 2012 19

b) Analysis structure to obtain factored moment MEd

c) Calculate Mcr [EC3-1-1: Clause 6.3.2.2]

d) Calculate λLT [EC3-1-1: Clause 6.3.2.2]

e) Use Table 6.4 to determine buckling curve to use [EC3-1-1: Table 6.4]

f) Use Table 6.3 to determine αLT to use [EC3-1-1: Table 6.3]

g) Calculate ϕ LT and χ LT [EC3-1-1: Clause 6.3.2.2]

h) Calculate Mb,Rd [EC3-1-1: Clause 6.3.2.1]

i) Check Mb,Rd ≥ MEd

5.3.2 DESIGN PROCEDURE WITH SIMPLIFIED METHOD

a) Section classification [EC3-1-1: Clause 5.5.2]

b) Determine effective (buckling) length Lc

c) Calculate if,z and Wyfy (Mc,Rd)

d) Slenderness correction factor kc and C [EC3-1-1: Clause 6.2.4.1]

e) Determine slenderness λ [EC3-1-1: Clause 6.2.4.1]

f) Determine buckling reduction factor χ

g) Design buckling resistance Mb,Rd = kflχMc,Rd[EC3-1-1: Clause 6.2.4.2]


August 2012 20

5.4 SYMBOLS

C1 Coefficient depending on the loading and end restraint conditions

C2 Coefficient depending on the loading and end restraint conditions

D Overall depth of beam section

E Modulus of elasticity of structural steel


G Shear modulus of structural steel

k Effective length factor and refers to end rotation on plan (k ≥ 1,0)

kc Slenderness correction factor for moment distribution between restraints

kfl Modification factor accounting for the conservation of the equivalent compression flange method

kw Effective length factor and refers to end warping (kw = 1,0)

if,z Radius of gyration of the equivalent compression flange composed of the compression flange plus

1/3 of the compressed part of web, about the minor axis of the section

It Torsion constant of section

Iw Warping constant of section

Iz Second moment of area of the section in the minor axis

L Beam length between points which have lateral restraints

Mb,Rd Design buckling resistance moment

Mcr Elastic critical moment for lateral-torsional buckling

MEd Design value of bending moment (Applied moment due to factored loading)

tf Thickness of flange

Wpl,y Plastic section modulus about the y-y axis

Wel,y Elastic section modulus about the y-y axis

Weff,y Effective section modulus about the y-y axis

zg Distance between point of load application and the shear centre

αLT Imperfection factor in accordance to Tables 6.3 and 6.4

β reduction parameter (β = 0.75, minimum value)

χ Reduction factor of the equivalent compression flange

χLT Reduction factor for lateral torsional buckling

λLT Non-dimensional slenderness for lateral torsional buckling

λLT,0 Plateau length of the lateral torsional buckling curves (max. value = 0,4) [Clause 6.3.2.3]


August 2012 21

CHAPTER 6 – TENSION MEMBERS 6.1 TENSION [EC3-1-1: Clause 6.2.3]

The design value of the tension force, NEd, must be smaller than the design resistance of the cross-section for

uniform tension Nt,Rd.

The design resistance of the cross-sections for uniform tension, Nt,Rd, should be taken as the smaller of:

a) the design plastic resistance of the gross cross-section

b) the design ultimate resistance of the net cross-section at holes for fasteners

6.2 NET AREA [EC3-1-1: Clause 6.2.2.2]

The net area of a cross-section should be taken as its gross area less appropriate deductions for all holes and

other openings.

The deduction for a single fastener (bolt) hole should be the gross cross-sectional area of the hole in the

plane of its axis.

6.2.1 Non-Staggered Holes

The total area to be deducted for fastener holes should be the maximum sum of the sectional areas of

the holes in any cross-section perpendicular to the member axis (see failure plane 2 in Figure 6.1)

0,1NN

Rd,t

Ed ≤

0M

yRd,t

AfN

γ=

2M

unetRd,t

fA9,0N

γ=

0net tndAA −=


August 2012 22

6.2.2 Staggered Holes

Where the fastener holes are staggered, the total area to be deducted for fasteners should be the

greater of:

a) the deduction of non-staggered holes

b)

EC3 Figure 6.1: Staggered holes and critical fracture lines 1 and 2

EC3 Figure 6.2: Angles with holes in both legs


b) Section Classification [EC3-1-1: Clause 5.5.2]

c) Analysis structure to obtain factored load NEd

d) Calculate Anet [EC3-1-1: Clause 6.2.2.2, Figures 6.1 and 6.2]

e) Calculate Nt,Rd [EC3-1-1: Clause 6.2.3]

f) Check Nt,Rd ≥ NEd

⎟⎟⎠

⎞⎜⎜⎝

⎛− ∑ p4

sndt2

0 ⎟⎟⎠

⎞⎜⎜⎝

⎛−−= ∑ p4

sndtAA2

0net

0net tndAA −=


August 2012 23

6.4 SYMBOLS

A Gross cross-sectional area

Anet Net cross-sectional area

d0 Diameter of hole


fu Ultimate strength of structural steel

NEd Design value of tension force (Applied tension force due to factored loading)

Nt,Rd Design resistance of the cross-section for uniform tension

n Number of holes

p Spacing of the centres of the same two holes measured perpendicular to the member axis

s Spacing of the centres of the same two holes measured parallel to the member axis

t Thickness of tension section


August 2012 24

CHAPTER 7 – COMPRESSION MEMBERS 7.1 COMPRESSION (NO BUCKLING) [EC3-1-1: Clause 6.2.4]

The design value of the compression force, NEd, must be smaller than the design resistance of the cross-

section for uniform compression Nc,Rd.

The design resistance of the cross-sections for uniform compression, Nc,Rd, should be determined as follows:

For Class 1, 2 or 3 cross sections


Fastener (Bolt) holes (except for oversize and slotted holes) may be ignored in compression members

provided that they are filled by fasteners.

7.2 BUCKLING RESISTANCE OF COMPRESSION MEMBERS [EC3-1-1: Clause 6.3.1]

The design value of the compression force, NEd, must be smaller than the design buckling resistance of the

compression member, Nb,Rd.

7.2.1 Buckling Resistance [EC3-1-1: Clause 6.3.1.1]

The design buckling resistance of the compression member, Nb,Rd, should be taken as:



where χ is the reduction factor for the relevant buckling mode.

0,1NN

Rd,c

Ed ≤

0,1NN

Rd,b

Ed ≤

1M

yRd,b

AfN

γ

χ=

1M

yeffRd,b

fAN

γ

χ=

0M

yRd,c

AfN

γ=

0M

yeffRd,c

fAN

γ=


August 2012 25

7.2.2 Buckling Curves [EC3-1-1: Clause 6.3.1.2]

The non-dimensional slenderness λ should be taken as:



[EC3-1-1: Clause 6.3.1.3] – Class 1, 2 and 3 only

Use EC3 Table 6.2 to determine the relevant buckling curve (a0, a, b, c or d) to use. The value of χ is

determined using slenderness λ, appropriate buckling curve and either calculation or graphical

method.

a) Calculation method

but χ ≤ 1,0

EC3 Table 6.1: Imperfection factors for buckling curves

Buckling curve a0 a b c d

Imperfection factor α 0,13 0,21 0,34 0,49 0,76

Graphical method

EC3 Figure 6.4: Buckling curves

22

1

λ−Φ+Φ=χ

])2,0(1[5,02

λλα +−+=Φ

cr

y

NAf

=λ

cr

yeff

NfA

=λ

2cr

2

cr LEIN π

=


August 2012 26

EC3 Table 6.2: Selection of buckling curve for a cross-section


August 2012 27

7.2.3 Slenderness for Flexural Buckling [EC3-1-1: Clause 6.3.1.3)



For Class 1, 2 and 3 sections, substitute λ1 into λ equation to find

For λ ≤ 0,2 or for NEd/Ncr ≤ 0,04, the buckling effects may be ignored and only cross-sectional

checks are necessary.



b) Structural analysis to obtain design value NEd

c) Calculate Ncr [EC3-1-1: Clause 6.3.1.3]

d) Calculate λ [EC3-1-1: Clause 6.3.1.2]

e) Use Table 6.2 to determine buckling curve to use [EC3-1-1: Table 6.2]

f) Use Table 6.1 to determine α to use [EC3-1-1: Table 6.1]

g) Calculate ϕ and χ [EC3-1-1: Clause 6.3.1.2]

h) Steps f) and g) can be replaced by using Figure 6.4 to find χ [EC3-1-1: Figure 6.4]

i) Calculate design buckling resistance Nb,Rd [EC3-1-1: Clause 6.3.1.1]

j) Check Nb,Rd ≥ NEd

1

cr

cr

y 1i

LNAf

λ==λ

1

eff

cr

cr

yeff

λAA

iL

NfA

λ ==

y1 f

Eπ=λ

2cr

2

cr LEIN π

=


August 2012 28

7.4 SYMBOLS

A Cross-sectional area

Aeff Effective cross-sectional area

E Modulus of elasticity


i Radius of gyration of section

I Second moment of area of the section in the buckling plane considered

Lcr Buckling length in the buckling plane considered (Effective length)

Nb,Rd Design buckling resistance of the compression member

Nc,Rd Design resistance of the cross-section for uniform compression

Ncr Elastic critical force for the relevant buckling mode based on the gross sectional properties

NEd Design value of compression force (Applied compression force due to factored loading)

α Imperfection factor in accordance to Tables 6.1 and 6.2

χ Reduction factor for the relevant buckling mode

λ Non-dimensional slenderness for compression buckling


August 2012 29

CHAPTER 8 – WEB BEARING AND BUCKLING 8.1 TRANSVERSE FORCE [EC3-1-5: Clause 6.1.2]

The transverse forces applied on the flanges to web of rolled beams and welded girders can be distinguished

by three different types as follows:

a) Through the flange and resisted by shear forces in the web, see Figure 6.1 (a);

b) Through one flange and transferred through the web directly to the other flange, see Figure 6.1 (b).

c) Through one flange adjacent to an unstiffened end, see Figure 6.1 (c)

(a) (b) (c)

EC3-1-5 Figure 6.1: Buckling coefficients for different types of load application

8.2 Design resistance to transverse forces [EC3-1-5: Clause 6.2.1]

For unstiffened or stiffened webs the design resistance to local buckling under transverse forces should be

taken as:

1M

weffywRd

tLfF

γ=

Where, effL is the effective length for resistance to transverse forces:

yfeff lL χ=

8.2.1 Length of stiff bearing [EC3-1-5: Clause 6.3.1]

The length of stiff bearing ss on the flange should be taken as the distance over which the applied

load is effectively distributed at a slope of 1:1, as shown in Figure 6.2. However, ws hs ≤ .

EC3-1-5 Figure 6.2: Length of stiff bearing


August 2012 30

8.2.2 Reduction factor Fχ for effective length for resistance [EC3-1-5: Clause 6.4.1]

The reduction factor Fχ should be taken as:

0.15.0

≤=F

F λχ

where cr

ywwyF F

ftl=λ

w

wFcr h

tEkF3

9.0=

For webs without longitudinal stiffeners Fk should be obtained from Figure 6.1.

8.2.3 Effective loaded length [EC3-1-5: Clause 6.5.1.2)

The effective loaded length yl should be calculated as follows:

1) For types a) and b) in Figure 6.1, yl should be obtained using:

)1(2 21 mmtsl fsy +++=

But yl ≤ distance between adjacent transverse stiffeners

2) For type c) yl should be taken as the smallest value obtained from the follow equations:

2

2

1

2m

tlmtll

f

efey +⎟

⎟⎠

⎞⎜⎜⎝

⎛++=

21 mmtll fey ++=

where cshf

Etl swyw

wFe +≤=

2

2κ

wyw

fyf

tfbf

m =1

2

2 02.0 ⎟⎟⎠

⎞⎜⎜⎝

⎛=

f

w

th

m if 5.0>Fλ

02 =m if 5.0<Fλ


August 2012 31


a) Load type and buckling coefficients Fk [EC3-1-5: Clause 6.1.2]

b) Calculate Fcr [EC3-1-5: Clause 6.4.1]

c) Assuming Fλ and calculate m1, m2 [EC3-1-5: Clause 6.5.1]

d) Calculate le [EC3-1-5: Clause 6.5.3]

e) Calculate ly based on different load types. [EC3-1-5: Clause 6.5.2]

f) Check Fλ [EC3-1-5: Clause 6.4.1]

g) Calculate χF ≤ 1.0 [EC3-1-5: Clause 6.4.1]

h) Calculate Leff [EC3-1-5: Figure 6.2.1]

i) Calculate FRd [EC3-1-5: Clause 6.2.1]

j) Check FRd ≥ FEd [EC3-1-5: Clause 6.6.1]

8.4 SYMBOLS

fyw The yield strength of the web

fyf The yield strength of the flange

FRd Design buckling resistance under transverse forces

FEd Design value of transverse load

kF Buckling coefficient

ly Effective loaded length

Leff The effective length of web

ss Length of stiff bearing

tw The thickness of the web

χF Reduction factor due to local buckling

APPENDIX I - FORMULAE FOR BEAM DEFLECTION


August 2012 32

Loading and Support conditions Maximum deflection & Position

EI

FL3

3=δ (B)

EIwL8

4=δ (B)

EIwL

3845 4

=δ (C)

)(6

222 xbLLEIFbx

x −−=δ (0≤x≤a)

⎥⎦⎤

⎢⎣⎡ −+−−= xbLxax

bL

LEIFb

x )()(6

2233δ (a≤x≤

L)

EIFL48

3=δ (C)

EIFL

38481.6 3

=δ (C)

EIwL

384

4=δ (C)

EIFL

192

3=δ (C)

BA

L

F

wA B

L

wA B

LC

baBA

L

F

C

xx

BA

L/2 L/2

F

C

L/3 L/3L/3C

A B

F /2 F /2

CL

BAw

C

F

L/2L/2

A B


August 2012 33

APPENDIX II – TABLES OF DIMENSIONS AND GROSS SECTION PROPERTIES

Dimensions

Designation Area Depth Width Thickness Root Depth Ratios For Dimensions For Detailing

Size Mass of of of Radius Between Local Per Section Section Section Fillets Buckling End Metre Flange Web Flange Web Clearance Notch A h b tf tw r d cf/tf cw/tw C N n

mm kg/m cm2 mm mm mm mm mm mm mm mm mm

1016 x 305

487 620 1036.1 308.5 54.1 30.0 30.0 867.9 2.02 28.9 17 149 84

438 557 1025.9 305.4 49.0 26.9 30.0 867.9 2.23 32.3 15 149 79

393 500 1016.0 303.0 43.9 24.4 30.0 868.2 2.49 35.6 14 149 74

349 445 1008.1 302.0 40.0 21.1 30.0 868.1 2.76 41.1 13 150 70

314 400 1000.0 300.0 35.9 19.1 30.0 868.2 3.08 45.5 12 150 66

272 347 990.1 300.0 31.0 16.5 30.0 868.1 3.60 52.6 10 152 61

249 317 980.2 300.0 26.0 16.5 30.0 868.2 4.30 52.6 10 152 56

222 283 970.3 300.0 21.1 16.0 30.0 868.1 5.31 54.3 10 152 51

914 x 419 388 494 921.0 420.5 36.6 21.4 24.1 799.6 4.79 37.4 13 210 61

343 437 911.8 418.5 32.0 19.4 24.1 799.6 5.48 41.2 12 210 56

914 x 305

289.1 368 926.6 307.7 32.0 19.5 19.1 824.4 3.91 42.3 12 154 51

253.4 323 918.4 305.5 27.9 17.3 19.1 824.4 4.48 47.7 11 154 47

224.2 286 910.4 304.1 23.9 15.9 19.1 824.4 5.23 51.8 10 154 43

200.9 256 903.0 303.3 20.2 15.1 19.1 824.4 6.19 54.6 10 154 39

838 x 292

226.5 289 850.9 293.8 26.8 16.1 17.8 761.7 4.52 47.3 10 149 45

193.8 247 840.7 292.4 21.7 14.7 17.8 761.7 5.58 51.8 9 149 40

175.9 224 834.9 291.7 18.8 14.0 17.8 761.7 6.44 54.4 9 149 37

762 x 267

196.8 251 769.8 268.0 25.4 15.6 16.5 686.0 4.32 44.0 10 136 42

173 220 762.2 266.7 21.6 14.3 16.5 686.0 5.08 48.0 9 136 38

146.9 187 754.0 265.2 17.5 12.8 16.5 686.0 6.27 53.6 8 136 34

133.9 171 750.0 264.4 15.5 12.0 16.5 686.0 7.08 57.2 8 136 32

686 x 254

170.2 217 692.9 255.8 23.7 14.5 15.2 615.1 4.45 42.4 9 131 39

152.4 194 687.5 254.5 21.0 13.2 15.2 615.1 5.02 46.6 9 131 36

140.1 178 683.5 253.7 19.0 12.4 15.2 615.1 5.55 49.6 8 131 34

125.2 159 677.9 253.0 16.2 11.7 15.2 615.1 6.51 52.6 8 131 31

yy

z

z

d

tf

r

b

twh

C

N

n


August 2012 34

Section Properties

Section Size

Surface Second Radius Elastic Plastic Buckling Torsional Warping Torsional Area Moment of Modulus Modulus parameter Index Constant Constant

per of Area Gyration Metre Axis Axis Axis Axis Axis Axis Axis Axis y-y z-z y-y z-z y-y z-z y-y z-z U X Iw IT

mm m2 cm4 cm4 cm cm cm3 cm3 cm3 cm3 dm6 cm4

1016 x 305

3.19 1021427 26728 40.6 6.57 19717 1733 23200 2800 0.867 21.1 64.4 4299

3.17 909913 23454 40.4 6.49 17739 1536 20762 2469 0.868 23.1 56.0 3185

3.14 807696 20503 40.2 6.40 15900 1353 18539 2168 0.868 25.5 48.4 2330

3.13 723138 18467 40.3 6.44 14347 1223 16592 1941 0.872 27.9 43.3 1718

3.11 644218 16239 40.1 6.37 12884 1083 14851 1713 0.872 30.7 37.7 1264

3.10 553981 14011 40.0 6.36 11190 934 12826 1470 0.873 35.0 32.2 835

3.08 481313 11761 39.0 6.09 9821 784 11350 1245 0.861 39.9 26.8 582

3.06 407968 9553 38.0 5.81 8409 637 9807 1020 0.850 45.7 21.5 390

914 x 419

3.44 719638 45441 38.2 9.59 15627 2161 17665 3341 0.885 26.7 88.86 1734

3.42 625782 39159 37.8 9.46 13726 1871 15477 2890 0.883 30.1 75.78 1193

914 x 305

3.01 504188 15598 37.0 6.51 10883 1014 12570 1601 0.867 31.9 31.21 926

2.99 436306 13302 36.8 6.42 9501 871 10942 1371 0.866 36.2 26.37 626

2.97 376415 11237 36.3 6.27 8269 739 9535 1163 0.861 41.3 22.08 422

2.96 325255 9424 35.7 6.07 7204 621 8351 982 0.854 46.8 18.36 291.4

838 x 292

2.81 339704 11360 34.3 6.27 7985 773 9155 1212 0.870 35.0 19.29 513.7

2.79 279176 9067 33.6 6.06 6642 620 7640 974 0.862 41.6 15.20 305.8

2.78 246022 7800 33.1 5.90 5893 535 6808 842 0.856 46.5 12.99 221.4

762 x 267

2.55 239957 8175 30.9 5.71 6234 610 7167 959 0.869 33.2 11.33 404.3

2.53 205282 6850 30.5 5.58 5387 514 6198 807 0.864 38.1 9.39 267.2

2.51 168502 5456 30.0 5.40 4470 411 5156 647 0.858 45.2 7.40 159.0

2.51 150692 4788 29.7 5.30 4018 362 4644 570 0.854 49.8 6.46 119

686 x 254

2.35 170327 6631 28.0 5.53 4916 518 5631 811 0.872 31.8 7.42 307.6

2.34 150356 5784 27.8 5.46 4374 455 5000 710 0.871 35.5 6.42 219.6

2.33 136268 5184 27.6 5.39 3987 409 4558 638 0.868 38.7 5.72 168.7

2.32 117993 4383 27.2 5.24 3481 347 3994 542 0.862 43.9 4.80 116


August 2012 35

Dimensions

Designation Area Depth Width Thickness Root Depth Ratios For Dimensions For Detailing

Size Mass of of of Radius Between Local Per Section Section Section Fillets Buckling End Metre Flange Web Flange Web Clearance Notch A h b tf tw r d cf/tf cw/tw C N n


610 x 305 238 303 635.8 311.4 31.4 18.4 16.5 540.0 4.14 29.3 11 157 48 179 228 620.2 307.1 23.6 14.1 16.5 540.0 5.51 38.3 9 157 40

149.1 190 612.4 304.8 19.7 11.8 16.5 540.0 6.60 45.8 8 157 36

610 x 229

139.9 178 617.2 230.2 22.1 13.1 12.7 547.6 4.34 41.8 9 119 35 125.1 158 612.2 229.0 19.3 11.9 12.7 548.2 4.97 46.1 8 119 32 113 144 607.6 228.2 17.3 11.1 12.7 547.6 5.54 49.3 8 119 30

101.2 129 602.6 227.6 14.8 10.5 12.7 547.6 6.48 52.2 7 119 28

610 x 178 92 117 603.0 178.8 15.0 10.9 12.7 547.6 4.75 50.2 7 94 28 91 116 602.5 178.4 15.0 10.6 12.7 547.1 4.75 51.6 7 94 28

81.9 104 598.7 177.9 12.8 10.0 12.7 547.7 5.57 54.8 7 94 26

533 x 312

270.8 346 577.1 317.8 37.6 21.1 12.7 476.5 3.61 22.6 13 158 50 218.8 279 560.3 317.8 29.2 18.3 12.7 476.5 4.69 26.0 11 160 42 181.6 231 550.7 314.7 24.4 15.2 12.7 476.5 5.62 31.3 10 160 37 150.3 192 542.5 312.2 20.3 12.7 12.7 476.5 6.75 37.5 8 160 33

533 x 210

138.4 176 549.1 213.9 23.6 14.7 12.7 476.5 3.68 32.4 9 110 36 122 155 544.5 211.9 21.3 12.7 12.7 476.5 4.08 37.5 8 110 34 109 139 539.5 210.8 18.8 11.6 12.7 476.5 4.62 41.1 8 110 32 101 129 536.7 210.0 17.4 10.8 12.7 476.5 4.99 44.1 7 110 30 92.1 117 533.1 209.3 15.6 10.1 12.7 476.5 5.57 47.2 7 110 28 82.2 105 528.3 208.8 13.2 9.6 12.7 476.5 6.58 49.6 7 110 26

533 x 165 84.8 108 534.9 166.5 16.5 10.3 12.7 476.5 3.96 46.3 7 88 29 74.4 95 529.1 165.9 13.5 9.7 12.7 476.7 4.84 49.1 7 88 26 65.5 84 524.8 165.1 11.4 8.9 12.7 476.6 5.74 53.6 6 88 24

457 x 191

105.7 135 469.1 193.9 20.6 12.6 10.2 407.5 3.91 32.3 8 101 31 98.3 125 467.2 192.8 19.6 11.4 10.2 407.6 4.11 35.8 8 101 30 89.3 114 463.4 191.9 17.7 10.5 10.2 407.6 4.55 38.8 7 101 28 82 104 460.0 191.3 16.0 9.9 10.2 407.6 5.03 41.2 7 101 26

74.3 95 457.0 190.4 14.5 9.0 10.2 407.6 5.55 45.3 7 101 25 67.1 86 453.4 189.9 12.7 8.5 10.2 407.6 6.34 48.0 6 101 23

457 x 152

82.1 105 465.8 155.3 18.9 10.5 10.2 407.6 3.29 38.8 7 82 29 74.2 94 462.0 154.4 17.0 9.6 10.2 407.6 3.66 42.5 7 82 27 67.2 86 458.0 153.8 15.0 9.0 10.2 407.6 4.15 45.3 7 82 25 59.8 76 454.6 152.9 13.3 8.1 10.2 407.6 4.68 50.3 6 82 24 52.3 67 449.8 152.4 10.9 7.6 10.2 407.6 5.71 53.6 6 82 21

406 x 178

84.8 108 417.3 180.8 18.2 10.9 10.2 360.5 4.11 33.1 7 95 28 74.2 95 412.8 179.5 16.0 9.5 10.2 360.4 4.68 37.9 7 95 26 67.1 86 409.4 178.8 14.3 8.8 10.2 360.4 5.23 41.0 6 95 25 60.1 77 406.4 177.9 12.8 7.9 10.2 360.4 5.84 45.6 6 95 23 54.1 69 402.6 177.7 10.9 7.7 10.2 360.4 6.86 46.8 6 95 21


August 2012 36

Section Properties

Section

Size Surface Second Radius Elastic Plastic Buckling Torsional Warping Torsional

Area Moment of Modulus Modulus parameter Index Constant Constant per of Area Gyration Metre Axis Axis Axis Axis Axis Axis Axis Axis y-y z-z y-y z-z y-y z-z y-y z-z U X Iw IT


610 x 305

2.45 209472 15837 26.3 7.23 6589 1017 7486 1574 0.886 21.3 14.463 785.2 2.41 153025 11409 25.9 7.07 4935 743 5547 1144 0.886 27.7 10.15 340.1 2.39 125877 9308 25.7 7.00 4111 611 4594 937 0.886 32.7 8.17 200

610 x 229

2.11 111778 4505 25.0 5.03 3622 391 4142 611 0.875 30.6 3.99 216.4 2.09 97542 3872 24.8 4.95 3187 338 3639 528 0.872 34.5 3.40 149.1 2.08 87319 3434 24.6 4.88 2874 301 3281 469 0.870 38.0 2.99 111.3 2.07 75780 2915 24.2 4.76 2515 256 2881 400 0.864 43.1 2.52 77

610 x 178

1.88 64577 1436 23.4 3.50 2142 161 2511 258 0.848 42.8 1.242 71.0 1.88 63879 1426 23.5 3.51 2120 160 2480 256 0.850 43.2 1.23 68.6 1.87 55891 1207 23.2 3.40 1867 136 2195 218 0.843 48.5 1.04 49

533 x 312

2.36 197263 20156 23.9 7.63 6836 1268 7810 1956 0.890 15.9 14.67 1279.7 2.33 151141 15648 23.3 7.49 5395 985 6115 1518 0.884 19.8 11.03 642.2 2.31 123290 12691 23.1 7.41 4478 807 5033 1239 0.885 23.4 8.79 373.6 2.29 100688 10305 22.9 7.33 3712 660 4144 1011 0.885 27.8 7.03 216

533 x210

1.90 86088 3864 22.1 4.68 3136 361 3613 568 0.873 25.0 2.668 250.3 1.89 76043 3388 22.1 4.67 2793 320 3196 500 0.877 27.6 2.32 178.4 1.88 66822 2943 21.9 4.60 2477 279 2828 436 0.875 30.9 1.99 126.3 1.87 61519 2692 21.9 4.57 2292 256 2612 399 0.874 33.2 1.82 101.0 1.86 55228 2389 21.7 4.51 2072 228 2360 356 0.872 36.5 1.60 75.7 1.85 47539 2008 21.3 4.38 1800 192 2059 300 0.864 41.6 1.33 51.5

533 x 165

1.69 48632 1275 21.2 3.44 1818 153 2107 243 0.862 35.5 0.857 73.8 1.68 40862 1032 20.8 3.30 1545 124 1800 199 0.852 41.3 0.69 47.3 1.67 35044 859 20.5 3.20 1336 104 1561 166 0.847 47.0 0.57 32

457 x 191

1.67 48829 2511 19.0 4.32 2082 259 2387 405 0.877 24.4 1.263 145.7 1.67 45727 2347 19.1 4.33 1957 243 2232 379 0.881 25.7 1.18 121.3 1.66 41015 2089 19.0 4.29 1770 218 2014 338 0.880 28.3 1.04 90.7 1.65 37051 1871 18.8 4.23 1611 196 1831 304 0.877 30.9 0.92 69.2 1.64 33319 1671 18.8 4.20 1458 176 1653 272 0.877 33.9 0.82 51.8 1.63 29380 1452 18.5 4.12 1296 153 1471 237 0.872 37.9 0.71 37.1

457 x 152

1.51 36589 1185 18.7 3.37 1571 153 1811 240 0.873 27.4 0.591 89.2 1.50 32674 1047 18.6 3.33 1414 136 1627 213 0.873 30.1 0.52 65.9 1.50 28927 913 18.4 3.27 1263 119 1453 187 0.869 33.6 0.45 47.7 1.49 25500 795 18.3 3.23 1122 104 1287 163 0.868 37.5 0.39 33.8 1.48 21369 645 17.9 3.11 950 85 1096 133 0.859 43.9 0.31 21

406 x 178

1.52 31560 1798 17.1 4.08 1513 199 1725 309 0.881 24.4 0.716 92.5 1.51 27310 1546 17.0 4.04 1323 172 1501 267 0.882 27.6 0.61 62.8 1.50 24331 1365 16.9 3.99 1189 153 1346 237 0.880 30.5 0.53 46.1 1.49 21596 1203 16.8 3.97 1063 135 1199 209 0.880 33.8 0.47 33.3 1.48 18722 1021 16.5 3.85 930 115 1055 178 0.871 38.3 0.39 23


August 2012 37

Dimensions

Designation Area Depth Width Thickness Root Depth Ratios For Dimensions For Detailing Size Mass of of of Radius Between Local

Per Section Section Section Fillets Buckling End Metre Flange Web Flange Web Clearance Notch A h b tf tw r d cf/tf cw/tw C N N

mm kg/m cm2 mm mm mm mm mm mm mm mm Mm

406 x 140 46 59 403.2 142.2 11.2 6.8 10.2 360.4 5.13 53.0 5 78 21 39 50 398.0 141.8 8.6 6.4 10.2 360.4 6.69 56.3 5 78 19

356 x 406

633.9 808 474.6 424.0 77.0 47.6 15.2 290.2 2.25 6.1 26 198 92 551 702 455.6 418.5 67.5 42.1 15.2 290.2 2.56 6.9 23 198 83 467 595 436.6 412.2 58.0 35.8 15.2 290.2 2.98 8.1 20 198 73 393 501 419.0 407.0 49.2 30.8 15.2 290.2 3.51 9.4 17 198 64

339.9 433 406.4 403.0 42.9 26.6 15.2 290.2 4.03 10.9 15 198 58 287.1 366 393.6 399.0 36.5 22.6 15.2 290.2 4.74 12.8 13 198 52 235.1 299 381.0 394.8 30.2 18.4 15.2 290.2 5.73 15.8 11 198 45

356 x 368

201.9 257 374.6 374.7 27.0 16.5 15.2 290.2 6.07 17.6 10 189 42 177 226 368.2 372.6 23.8 14.4 15.2 290.2 6.89 20.2 9 189 39

152.9 195 362.0 370.5 20.7 12.3 15.2 290.2 7.92 23.6 8 189 36 129 164 355.6 368.6 17.5 10.4 15.2 290.2 9.37 27.9 7 189 33

356 x 171

67.1 85 363.4 173.2 15.7 9.1 10.2 311.6 4.58 34.2 7 92 26 57 73 358.0 172.2 13.0 8.1 10.2 311.6 5.53 38.5 6 92 23 51 65 355.0 171.5 11.5 7.4 10.2 311.6 6.25 42.1 6 92 22 45 57 351.4 171.1 9.7 7.0 10.2 311.6 7.41 44.5 6 92 20

356 x 127 39.1 50 353.4 126.0 10.7 6.6 10.2 311.6 4.63 47.2 5 70 21 33.1 42 349.0 125.4 8.5 6.0 10.2 311.6 5.82 51.9 5 70 19

305 x 305

282.9 360 365.3 322.2 44.1 26.8 15.2 246.7 3.00 9.2 15 158 59 240 306 352.5 318.4 37.7 23.0 15.2 246.7 3.51 10.7 14 158 53

198.1 252 339.9 314.5 31.4 19.1 15.2 246.7 4.22 12.9 12 158 47 158.1 201 327.1 311.2 25.0 15.8 15.2 246.7 5.30 15.6 10 158 40 136.9 174 320.5 309.2 21.7 13.8 15.2 246.7 6.11 17.9 9 158 37 117.9 150 314.5 307.4 18.7 12.0 15.2 246.7 7.09 20.6 8 158 34 96.9 123 307.9 305.3 15.4 9.9 15.2 246.7 8.60 24.9 7 158 31

305 x 165 54 69 310.4 166.9 13.7 7.9 8.9 265.2 5.15 33.6 6 90 23

46.1 59 306.6 165.7 11.8 6.7 8.9 265.2 5.98 39.6 5 90 21 40.3 51 303.4 165.0 10.2 6.0 8.9 265.2 6.92 44.2 5 90 19

305 x 127 48.1 61 311.0 125.3 14.0 9.0 8.9 265.2 3.52 29.5 7 68 23 41.9 53 307.2 124.3 12.1 8.0 8.9 265.2 4.07 33.2 6 68 21 37 47 304.4 123.3 10.7 7.1 8.9 265.2 4.60 37.4 6 68 20

305 x 102 32.8 42 312.7 102.4 10.8 6.6 7.6 275.9 3.73 41.8 5 58 18 28.2 36 308.7 101.8 8.8 6.0 7.6 275.9 4.58 46.0 5 58 16 24.8 32 305.1 101.6 7.0 5.8 7.6 275.9 5.76 47.6 5 58 15

254 x 254

167.1 213 289.1 265.2 31.7 19.2 12.7 200.3 3.48 10.4 12 133 44 132 168 276.3 261.3 25.3 15.3 12.7 200.3 4.36 13.1 10 133 38

107.1 136 266.7 258.8 20.5 12.8 12.7 200.3 5.38 15.6 8 133 33 88.9 113 260.3 256.3 17.3 10.3 12.7 200.3 6.38 19.4 7 133 30 73.1 93 254.1 254.6 14.2 8.6 12.7 200.3 7.77 23.3 6 133 27


August 2012 38

Section Properties Section

Size Surface Second Radius Elastic Plastic Buckling Torsional Warping Torsional

Area Moment of Modulus Modulus parameter Index Constant Constant per of Area Gyration Metre Axis Axis Axis Axis Axis Axis Axis Axis y-y z-z y-y z-z y-y z-z y-y z-z U X Iw IT


406 x 140

1.34 15685 538 16.4 3.03 778 76 888 118 0.871 38.9 0.207 19.0 1.33 12508 410 15.9 2.87 629 58 724 91 0.858 47.5 0.16 11

356 x 406

2.52 274845 98126 18.4 11.02 11582 4629 14235 7108 0.843 5.5 38.78 13723.6 2.47 226939 82671 18.0 10.85 9962 3951 12076 6058 0.841 6.1 31.13 9240.4 2.42 183004 67834 17.5 10.68 8383 3291 10002 5034 0.839 6.9 24.31 5808.6 2.38 146673 55369 17.1 10.51 7001 2721 8228 4155 0.837 7.9 18.93 3553.7 2.35 122543 46854 16.8 10.40 6031 2325 6999 3544 0.836 8.8 15.48 2342.8 2.31 99876 38678 16.5 10.28 5075 1939 5812 2949 0.835 10.2 12.33 1440.6 2.28 79085 30994 16.3 10.17 4151 1570 4687 2383 0.834 12.1 9.54 811.5

356 x 368

2.19 66262 23689 16.1 9.60 3538 1264 3972 1920 0.844 13.4 7.156 557.5 2.17 57118 20530 15.9 9.54 3103 1102 3455 1671 0.844 15.0 6.09 381.5 2.16 48590 17554 15.8 9.49 2685 948 2965 1435 0.844 17.0 5.11 250.5 2.14 40246 14612 15.6 9.43 2264 793 2479 1199 0.844 19.9 4.18 153

356 x 171

1.38 19463 1362 15.1 3.99 1071 157 1211 243 0.886 24.4 0.412 55.7 1.37 16038 1108 14.9 3.91 896 129 1010 199 0.882 28.8 0.33 33.4 1.36 14136 968 14.8 3.86 796 113 896 174 0.881 32.1 0.29 23.8 1.36 12066 811 14.5 3.76 687 95 775 147 0.874 36.8 0.24 16

356 x 127

1.18 10172 358 14.3 2.68 576 57 659 89 0.871 35.2 0.105 15.1 1.17 8250 280 14.0 2.58 473 45 543 70 0.863 42.2 0.08 9

305 x 305

1.94 78872 24635 14.8 8.27 4318 1529 5105 2342 0.855 7.7 6.35 2033.8 1.91 64203 20315 14.5 8.15 3643 1276 4247 1951 0.854 8.7 5.03 1271.3 1.87 50904 16300 14.2 8.04 2995 1037 3440 1581 0.853 10.2 3.88 734.0 1.84 38747 12570 13.9 7.90 2369 808 2680 1230 0.851 12.5 2.87 378.0 1.82 32815 10700 13.7 7.83 2048 692 2297 1053 0.851 14.2 2.39 248.9 1.81 27673 9060 13.6 7.77 1760 589 1958 895 0.850 16.2 1.98 161.0 1.79 22249 7308 13.4 7.69 1445 479 1592 726 0.850 19.3 1.56 91

305 x 165

1.26 11696 1063 13.0 3.93 754 127 846 196 0.889 23.6 0.234 34.8 1.25 9899 896 13.0 3.90 646 108 720 166 0.891 27.1 0.19 22.2 1.24 8503 764 12.9 3.86 560 93 623 142 0.889 31.0 0.16 14.7

305 x 127

1.09 9575 461 12.5 2.74 616 74 711 116 0.873 23.3 0.102 31.8 1.08 8196 389 12.4 2.70 534 63 614 98 0.872 26.5 0.08 21.1 1.07 7166 335 12.3 2.67 471 54 539 85 0.872 29.7 0.07 15

305 x 102

1.01 6501 194 12.5 2.15 416 38 481 60 0.866 31.6 0.044 12.2 1.00 5366 155 12.2 2.08 348 31 403 48 0.859 37.4 0.03 7.4 0.99 4455 123 11.9 1.97 292 24 342 39 0.846 43.4 0.03 4.8

254 x 254

1.58 29998 9870 11.9 6.81 2075 744 2424 1137 0.851 8.5 1.635 626.4 1.55 22529 7531 11.6 6.69 1631 576 1869 878 0.850 10.3 1.19 318.6 1.52 17511 5928 11.3 6.59 1313 458 1484 697 0.848 12.4 0.90 172.4 1.50 14268 4858 11.2 6.55 1096 379 1224 575 0.850 14.5 0.72 102.3 1.49 11407 3908 11.1 6.48 898 307 992 465 0.849 17.3 0.56 58


August 2012 39

Dimensions

Designation Area Depth Width Thickness Root Depth Ratios For Dimensions For Detailing Size Mass of of of Radius Between Local

Per Section Section Section Fillets Buckling End Metre Flange Web Flange Web Clearance Notch A h b tf tw r d cf/tf cw/tw C N n


254 x 146 43 55 259.6 147.3 12.7 7.2 7.6 219.0 4.92 30.4 6 80 20 37 47 256.0 146.4 10.9 6.3 7.6 219.0 5.73 34.8 5 80 19

31.1 40 251.4 146.1 8.6 6.0 7.6 219.0 7.26 36.5 5 80 16

254 x 102 28.3 36 260.4 102.2 10.0 6.3 7.6 225.2 4.04 35.7 5 58 18 25.2 32 257.2 101.9 8.4 6.0 7.6 225.2 4.80 37.5 5 58 16 22 28 254.0 101.6 6.8 5.7 7.6 225.2 5.93 39.5 5 58 14

203 x 203

99.7 127 228.6 210.3 23.8 14.5 10.2 160.6 3.68 11.1 9 108 34 86.1 110 222.2 209.1 20.5 12.7 10.2 160.8 4.29 12.7 8 108 31 71 90 215.8 206.4 17.3 10.0 10.2 160.8 5.09 16.1 7 108 28 60 76 209.6 205.8 14.2 9.4 10.2 160.8 6.20 17.1 7 108 24 52 66 206.2 204.3 12.5 7.9 10.2 160.8 7.04 20.4 6 108 23

46.1 59 203.2 203.6 11.0 7.2 10.2 160.8 8.00 22.3 6 108 21

203 x 133 30 38 206.8 133.9 9.6 6.4 7.6 172.4 5.85 26.9 5 74 17 25.1 32 203.2 133.2 7.8 5.7 7.6 172.4 7.20 30.2 5 74 15

203 x 102 23.1 29 203.2 101.8 9.3 5.4 7.6 169.4 4.37 31.4 5 58 17

178 x 102 19.0 24 177.8 101.2 7.9 4.8 7.6 146.8 5.14 30.6 4 58 16

152 x 152

37 47 161.8 154.4 11.5 8.0 7.6 123.6 5.70 15.5 6 83 19 30 38 157.6 152.9 9.4 6.5 7.6 123.6 6.98 19.0 5 83 17 23 29 152.4 152.2 6.8 5.8 7.6 123.6 9.65 21.3 5 83 14

22.3 28 152.1 152.1 6.6 5.8 6.4 126.1 10.11 21.7 5 83 13 152 x 89 16 20 152.4 88.7 7.7 4.5 7.6 121.8 4.48 27.1 4 52 15

127 x 76 13 17 127.0 76.0 7.6 4.0 7.6 96.6 3.74 24.2 4 46 15

102 x 102 24 31 107.0 100.0 12.0 7.9 6.0 71.0 3.34 9.0 6 56 18 21 26 102.0 102.0 9.4 8.0 6.0 71.2 4.36 8.9 6 57 15

19.4 25 105.7 103.1 8.8 7.1 6.4 75.3 4.73 10.6 6 58 15


August 2012 40

Section Properties

Section Size

Surface Second Radius Elastic Plastic Buckling Torsional Warping Torsional Area Moment of Modulus Modulus parameter Index Constant Constant

per of Area Gyration Metre Axis Axis Axis Axis Axis Axis Axis Axis y-y z-z y-y z-z y-y z-z y-y z-z U X Iw IT


254 x 146

1.08 6544 677 10.9 3.52 504 92 566 141 0.891 21.2 0.10 23.9 1.07 5537 571 10.8 3.48 433 78 483 119 0.890 24.3 0.09 15.3 1.06 4413 448 10.5 3.36 351 61 393 94 0.880 29.6 0.07 8.6

254 x 102

0.90 4005 179 10.5 2.22 308 35 353 55 0.874 27.5 0.028 9.6 0.90 3415 149 10.3 2.15 266 29 306 46 0.866 31.5 0.02 6.4 0.89 2841 119 10.1 2.06 224 23 259 37 0.856 36.4 0.02 4.1

203 x 203

1.25 11330 3695 9.4 5.39 991 351 1152 537 0.852 9.0 0.387 211.8 1.24 9449 3128 9.3 5.34 850 299 977 456 0.850 10.2 0.32 136.8 1.22 7618 2537 9.2 5.30 706 246 799 374 0.853 11.9 0.25 80.2 1.21 6125 2065 9.0 5.20 584 201 656 305 0.846 14.1 0.20 47.2 1.20 5259 1778 8.9 5.18 510 174 567 264 0.848 15.8 0.17 31.8 1.19 4568 1548 8.8 5.13 450 152 497 231 0.847 17.7 0.14 22

203 x 133

0.92 2896 385 8.7 3.17 280 57 314 88 0.881 21.5 0.04 10.3 0.91 2340 308 8.6 3.10 230 46 258 71 0.877 25.6 0.03 6.0

203 x 102 0.79 2105 164 8.5 2.36 207 32 234 50 0.888 22.5 0.015 7.0

178 x 102 0.74 1356 137 7.5 2.37 153 27 171 42 0.888 22.6 0.010 4.4

152 x 152

0.91 2210 706 6.8 3.87 273 91 309 140 0.848 13.3 0.040 19.2 0.90 1748 560 6.8 3.83 222 73 248 112 0.849 16.0 0.03 10.5 0.89 1250 400 6.5 3.70 164 53 182 80 0.840 20.7 0.02 4.6 0.89 1209 387 6.5 3.69 159 51 176 78 0.838 21.5 0.02 4

152 x 89 0.64 834 90 6.4 2.10 109 20 123 31 0.890 19.6 0.005 3.6

127 x 76 0.54 473 56 5.4 1.84 75 15 84 23 0.895 16.3 0.002 2.9

102 x 102

0.59 587 200 4.4 2.55 110 40 129 61 0.844 8.1 0.005 13.5 0.59 456 167 4.2 2.53 89 33 104 50 0.827 9.6 0.00 7.8 0.60 474 161 4.4 2.55 90 31 103 48 0.836 10.8 0.00 6

Overview of Eurocode 3

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