F From BS5950 to t EC3 Chiew Sing-Ping School of Civil and Environmental Engineering Nanyang Technological University, Singapore
Selected Topics for Verification • Material – ductility & toughness • Basis of design – combination of actions • Structural analysis – imperfections & second-order second order effects • Member design – beam & column b kli buckling g & buckling g • Web bearing • Shear buckling & plate girder • Hollow section joints
Ductility Requirement • Trend is to use higher grade and better quality steel in modern design codes. • EC3 has additional ductility requirements compared d tto BS5950 (CL (CL. 3 3.2.2) 2 2) iin tterms off stress ratio, elongation and strain ratio. • It is okay for hot-rolled steel but will be difficult for steel for cold cold-forming forming and cold-formed cold formed section.
D tilit Requirement Ductility R i t Normal Strength Steel
High Strength Steel
( fy < 460 N/mm2)
((460 < fy < 700 N/mm2)
• fu/fy ≥ 1.10
( fu/fy ≥ 1 1.15 15 ffor plastic l ti analysis) l i )
• elongation at failure not less than 15% • ε u ≥ 15 εy ( εy is the yield strain, t i εy= fy/ E)
• fu/fy ≥ 1.05 ( EC3-1-12) • fu/fy ≥ 1.10 ( UK NA to EC3-1-12) • elongation g at failure not less than 10% • εu ≥ 15 εy
Stress Strain Curve with Distinct Yield Stress-Strain fu fyUpper S Stress
fyLower
εy
εu
Strain
Stress Strain Curve with Distinct Yield Stress-Strain fu fyUpper S Stress
fyLower amount of plastic deformation represented by shaded area under the curve
εy
εu
Strain
Problem 1 – Steel for Cold Forming g Some product standards only have requirements on the nominal yield and tensile strengths, or their minimum values. The stress ratio calculated according to these nominal values cannot comply with the EC3 ductility requirement. Standard AS1397 AS 1595 EN 10149-2 EN 10326 ISO 4997
Grade G450 G500 G550 CA 500 S 550MC S 600MC S 650MC S 700MC S550GD CH550
Nominal yield strength (MPa) 450 500 550 500 550 600 650 700 550 550
Nominal tensile strength (MPa) 480 520 550 510 600 650 700 750 560 550
Stress ratio 1.07 1.04 1.00 1.02 1.09 1 08 1.08 1.08 1.07 1.02 1 00 1.00
AS 1397: Steel sheet and strip – hot-dip zinc-coated or aluminium/zinc-coated AS 1595: Cold-rolled, unalloyed, steel sheet and strip EN 10149-2: Hot-rolled flat products made of high yield strength steel for cold forming EN 10326: Continuously hot-dip coated strip and sheet of structural steels ISO 4997: Cold-reduced carbon steel sheet of structural quality * steel for profile metal decks and purlins
Problem 2 – Cold Formed Sections Most standards only have requirements on the range of tensile strength and min. min yield strength only. only It is possible for these steel to face problem with EC3 ductility requirement, for e.g. S355J2H in BS EN10219: fy>355 MPa and 470 MPa
Stress (MPa) 600.0
500 0 500.0
500.0
400.0
400.0
300.0
300.0
200.0
200.0
100.0
100.0
0.0
0.0 0.0
10.0
20.0
30.0
40.0 Elongation (%)
C ld f Cold-formed d S355J2H RHS
0.0
10.0
20.0
30.0
40.0 Elongation (%)
H tf Hot-formed d S355J2H RHS
Mechanical Properties p due to Cold Working g
Typical Curve with no distinct Yield Point
Stre ess
- gain in yield and loss in ductility due to cold working Rm Rp Rt
Agt
A
At
Strain
Toughness Requirement • To prevent sudden brittle fracture failure, both adopted a simple i l d deemed-to-satisfy dt ti f d i design approach h by b ensuring the maximum permitted thickness value is satisfied by choosing a steel quality grade with adequate notch toughness, taking into account factors such as service temperature, temperature thickness, thickness steel grade, grade member shape and detail, stress level and strain rate. • Unlike BS5950, BS5950 EC3-1-10 EC3 1 10 allows an alternative design for brittle fracture using fracture mechanics in addition to the above. above
Maximum Permissible Thickness Value Steel
S275
S355
Quality Grade JR J0 J2 M,N ML,NL JR J0 J2 M,N ML,NL
EC3 (σEd= 0.75 fy) (t)
EC3 (σEd = 0.5 fy) (t)
BS5950 (σEd )> 0.3 fy) (t)
10 (20)°C
0°C
10 (20)°C
0°C
20°C
0°C
55 75 110 135 185 40 60 90 110 155
45 65 95 110 160 35 50 75 90 130
80 115 155 180 200 65 95 135 155 200
70 95 130 155 200 55 80 110 135 180
71 103 148 178 250 50 72 104 124 179
50 71 103 124 178 35 50 72 86 124
Notes: (1) The units for the thickness values are mm. (2) Th The hi highest h t reference f ttemperature t th thatt EC3 allowed ll d is i 100C. C (3) This comparison is done under generally welded and high stress condition
Basis – Combination of Actions • •
Load partial factors for ultimate limit state for various load combinations are given in Table 2 of BS5950. Fundamental combination of actions can be determined from Eqns. 6.10, 6.10a or 6.10b of EN1990.
∑ γG,k Gk, j + γ p P + γQ,1Qk,1 + ∑ γQ,iψθ,iQk,i
j ≥1
Permanent actions
•
i >1
Action due to Leading variable prestressing action
Non-leading variable actions
From SS NA of EN1990 ψ0 = 0.5 for the wind load; ψ0 = 0.7 for the imposed load; γG = 1.35 for unfavorable permanent action; γQ = 1.50 1 50 ffor lleading di or non-leading l di variable i bl action ti .
(6.10)
Combination of Actions Combination
Design Action BS5950
EN1990
Dead & imposed
1.4Gk + 1.6Qk
1.35Gk + 1.5Qk
Dead & wind
1.4Gk + 1.4Wk
1.35Gk + 1.5Wk
Dead, imposed & wind
1.2Gk + 1.2Qk+ 1.2Wk
1.35Gk + 1.05Qk+ 1.50Wk or 1.35Gk + 1.50Qk+ 0.75Wk
Gk = permanent action; Qk = imposed variable action; Wk = wind variable action Example: Gk = 20 kN; Qk = 10 kN; Wk = 8 kN Combination
Design Action BS5950
EN1990
Dead & imposed
44.0 kN
42.0 kN
Dead, imposed & wind
45.6 kN
49.5 kN or 48.0 kN
Structural Analysis - Imperfections Imperfections must always be accounted for in analysis: • Global imperfections for frames and bracing systems, such as global initial sway imperfections Φ=Φ0αhαm in EC3 • Local imperfections p for members The effects of local imperfections in members are generally incorporated within the formulae given for buckling resistance for members members.
Frame Imperfection p in BS5950 BS5950 uses the notional horizontal force (NHF) concept to allow ll for f frame f imperfection i f ti such h as llack k off fframe verticality ti lit F3
φ F3
F3
F2
φ F2
F2
φ F1
F1
= φ
F1
1 in i 200 = 0.5% 0 %
Global Imperfection p in EC3 EC3 uses the same concept but called it ‘equivalent horizontal force (EHF)’ to allow for initial sway imperfection (lack of verticality) in frame
Combination of Actions Combination
Design Action BS5950
EC3
Dead & imposed
1.4Gk + 1.6Qk + NHF
1.35Gk + 1.5Qk + EHF
D d & wind Dead i d
1 4Gk + 1.4W 1.4G 1 4Wk* (no ( NHF)
1 35Gk + 1.5W 1.35G 1 5Wk + EHF
Dead, imposed & wind
1.2Gk + 1.2Qk+ 1.2Wk* (no NHF)
1.35Gk + 1.05Qk+ 1.50Wk + EHF or 1.35Gk + 1.50Qk+ 0.75Wk+ EHF
In BS5950, minimum Wk is 1% of factored dead load; this is to provide a minimum level of robustness but why no NHF when the wind is blowing?
Structural Analysis y - Terminology gy • First-order analysis: Equilibrium equations are written in terms of the geometry of the undeformed structure, geometrical non-linearity not considered y Equilibrium q equations q are • Second-order analysis: written in terms of the geometry of the deformed structure, g geometrical non-linearity y considered • Elastic analysis: Material properties is assumed to be elastic ((and often linear)) • Inelastic analysis: Inelastic material properties included in the analysis
Types of Structural Analysis First-order, second-order, elastic and inelastic analyses • First order elastic anal analysis: sis excluded e cl ded all nonlinearit nonlinearity, represents conditions under normal service loads very well • Second order elastic analysis: Effects of finite deformation considered. It produces good representation of destabilizing influences such as the P-Δ P Δ effects • First order inelastic analysis: Geometrical nonlinearity ignore but inelastic regions allowed to be form gradually or abruptly (e.g. onset of plastic hinge) • Second order inelastic analysis: Both geometrical and material nonlinearity are considered. Enable you to trace the behavior of the structure up to ultimate state and failure
Level of Non-Linearity y
Ref: Figure 8.1 8 1 of Matrix Structural Analysis, Analysis 2nd Edition, Edition William McGuire McGuire, Richard H H. Gallagher and Ronald D D. Ziemian Ziemian, John Wiley & Sons, 2000
BS5950 vs. EC3 BS5950
EC3
First-order elastic analysis (initial geometry and influence of deformation not considered))
First-order analysis
First-order plastic analysis (small axial forces & no instability effects) Second-order elastic analysis (can use simplified methods such as amplified moment or sway effective length methods for sway sensitive frames where 4 < λcr < 10) Other advanced analyses (generally not covered)
Elastic global analysis Plastic global analysis Using first-order analysis, if: αcr ≥ 10 for elastic analysis αcr ≥ 15 for plastic analysis αcr = Fcr/Fed, Fcr is the elastic critical g load buckling Second-order analysis (influence of geometrical deformation taken into account) Allowed more advanced analyses
Second-Order Second Order Effects in BS5950 The frame P-big Δ effect is allowed for in BS5950 using either one of the following 2 methods: • Amplified sway method - the sway moments are multiplied by an amplification factor factor, or • Effective length method - the actual sway effective lengths from the charts in Annex E are used. The column P-small δ effect is allowed for in BS5950 indirectly through the use of the cross cross-product product terms in more exact method method. Note: Although EC3 also allows amplified sway moment or effective length approach, less guidance is given. Unlike BS5950 which facilitates hand calculations, EC3 focuses on global second-order analysis by computer using geometric stiffness matrix approach approach. .
Second-Order Second Order Effects in BS5950 Simplified method:
Exact method:
Amplified the sway moments FC m x M x m y M y + + ≤1 py Z y py Z x PC
In-plane buckling
S Sway effective ff length from f Annex E Fc mLT M LT m y M y + + ≤1 Pcy Mb pyZ y
Lateral-torsional buckling
Moments about minor axis only: Fc m y M y + M cy Pcy
⎛ ⎞ ⎜1 + Fc ⎟ ≤ 1 ⎜ P ⎟ cy ⎠ ⎝
In-plane buckling
cross-product cross product term m yx M y Fc + 0.5 ≤1 Pcx M cy
Out-of-plane buckling
Moment about major axis only: Fc m x M x + Pcx M cx
⎛ F ⎜⎜1 + 0.5 c Pcx ⎝
m M Fc + 0.5 LT LT ≤ 1 Pcy Mb
⎞ ⎟⎟ ≤ 1 ⎠
In-plane buckling
Out-of-plane buckling
Member Design – LTB Resistance BS5950
EC3
Rigorous method: Mb = PbSx for class 1 & 2 Mb = PbZx Mb = PbSx,eff for class 3 Mb = PbZx,eff for class 4
General method:
For non-uniform moment or unequal end d moment: t Mx ≤ Mb/mLT and Mx ≤ Mcx where Pb determined by λLT = u v (βw)0.5LE/ry
M b ,Rd = χ LT Wy χ LT =
fy γ M1
1 Φ LT +
Φ 2LT
(
−
but
2 λ LT
)
2 Φ LT = 0,5⎡1 + α LT λ LT − 0,2 + λ LT ⎤ ⎢⎣ ⎥⎦
χ
LT
≤ 1,0 10 λ LT =
Wy f y M cr
where αLT is imperfection factor depending on which buckling curves (Figure 6.4 of EC3)
Member Design g – Compressive p Resistance BS5950
EC3
Pc = pcAg
for class 1, 2 & 3
Pc = pcsAeff
for class 4
χAf y
N b , Rd =
for class 1, 2 & 3
γ M1
N b ,Rd =
χA eff f y
for class 4
γ M1
where the compressive strength pc is χ is the reduction factor for the relevant based on the strut curve, slenderness λ buckling mode 1 & design strength py χ= λ = L/r
r = (I/A)0.5
There are 4 strut curves in BS5950 BS5950.
Φ + Φ2 − λ
2
but χ ≤ 1,0
(
)
2 Φ = 0,5⎡1 + α λ − 0,2 + λ ⎤ ⎢⎣ ⎥⎦
λ=
Aeff f y N cr
where α is imperfection factor depending on buckling curves (EC3 has 5 curves).
Elastic Critical Values missing in EC3 • EC3 offers no formulae and gives no guidance on how to calculate Ncr and Mcr. • Reference to other Published Documents (PD) is required required.
N cr =
π 2 EI Lcr
2
M cr = C1
π EI z ⎛ I w 2
Lcr
2
L GI T ⎜⎜ + ⎝ I Z π EI z 2 cr 2
⎞ ⎟⎟ ⎠
0.5
where h Lcr is i the h effective ff i llength h and d C1 is i the h correction i ffactor ffor non-uniform and unequal end moments. Unlike BS5950, EC3 does not provides any tables for effective length factors and equivalent uniform moment factors.
Web Bearing g and Buckling g BS5950-1 requires two independent checks for web bearing and buckling. However, EC3 presents a single check to deal with these two failure modes for the web subjected to a transverse force. However, unlike BS5950, EC3 does not take unrestrained flange g into account ((flange g free to sway y or rotate). )
Flange free to sway sideways
Flange rotation relative to the web
Web Bearing g and Buckling g BS5950
EC3
W b bearing: Web b i Pbw = (b1 + nk) k) tp t yw
Resistance R i t off web b against i t transverse force in which their compression flange is adequately restrained in the lateral direction:
Web buckling: for unstiffened web & αc> 0.7d
Px =
25εt
(b1 + nkk )d
Pbw
FRd =
For unstiffened web & αc< 0.7d
Px =
α e + 0.7d
25εt
1.4d
(b1 + nk )d
For unrestrained flange
0.7d Pxr = Px LE
Pbw
f yw Leff t w
γ M1
where Leffff is the effective length for resistance against transverse force: Leffff = χ f l y t w3 Fcr = 0.9k F E hw
χF =
0 .5
λF =
λF
≤ 1 .0
l y t w f yw Fcr
Web Bearing g and Buckling g EC3 has no equations to calculate stiff bearing length except saying the length of stiff bearing on the flange should be taken as the distance over which the applied load is effectively distributed at a slope of 1:1, and Ss should not be larger than hw. (EC3-1-5, clause 6.3.1)
BS5950-1
EC3-1-5
The Straits Times, 3 August 2004
Shear Buckling g and Plate Girder BS 5950-1 • Web with depth-to-thickness ratio d/t > 62ε is susceptible to shear buckling. • Shear buckling resistance Vb of the thin web is taken as the simple shear buckling resistance Vw given by: Vb = Vw = d t qw where d t qw
is the depth of the web; is the web thickness is the shear buckling strength of the web
Shear Buckling g and Plate Girder EC3-1-5
72
ε should be checked for • Web with hw/t greater than η resistance to shear buckling.
• The design resistance for shear buckling is taken as: ηfyw hw t Vb,Rd = Vbw ,Rd + Vbf ,Rd ≤ (5.1) 3γM1 in which the contribution from the web and flanges are: Vbw ,Rd = Vbf ,Rd =
χw fyw hw t 3γ M1 bf tf2fyf cγ M1
⎛ ⎛ M ⎞2 ⎞ ⎜1 − ⎜ Ed ⎟ ⎟ ⎟ ⎟ ⎜ ⎜M f , Rd ⎠ ⎠ ⎝ ⎝
(5.2) (5.3)
Shear Buckling g Resistance Stiffener spacing ratio, a/d (a/hw) = 1, fy = 275 N/mm2
she ear stren ngth qw (N/mm2)
180
0.6×275=165
EC3 rigid end post TFA
160
qw (BS5950-2000)TFA
140
EC3 non-rigid end post TFA
120
qcr (BS5950-1990) No TFA
100 80
71 61 55.7
60 40
28
20 80
0 0
50
87 7 87.7 100
114 150
200
web bd depth-to-thickness th t thi k ratio ti d/t (hw/t)
250
300
Tension Field Action shear buckling of thin web is allow to occur under the applied shear forces Tension e s o Field e d Action c o ((TFA)) when elastic critical shear buckling resistance is exceeded
Tension field action is mobilized in both BS5950 and EC3 to realize much higher g shear buckling g resistance of the thin web
Why y the fuss over Hollow Section Joint?
Hollow section joints can be very flexible because they are unstiffened! Designing unstiffened welded hollow section joints is a skilled task and must be done at member design stage.
Potential Failure Modes
Mode A: Plastic failure of the chord face
Mode C: Tension failure of the web member
Mode B: Punching shear failure of the chord face
Mode D: Local buckling of the web member
Potential Failure Modes
Mode E: Overall shear failure of the chord Mode F: Local buckling of the chord walls
Mode G: Local buckling g of the chord face
Verification Topic Material
BS5950
D tilit Ductility Toughness
√
Basis - combination of actions Structural analysis
Imperfections p Second-order effects
M b b Member buckling kli (b (beam & column) l ) Web bearing & buckling Shear buckling & Plate girder Hollow section jjoints
√ √ √ √
EC3
√ √ √ √ √
√
Final Concluding Remarks • BS5950-1 BS5950 1 was last amended in 2008; it will still be adequate and safe for use in the short term. • Migrating to EC3 is definite in the long term term. • EC3 is more comprehensive but its terminology, symbols b l and d values l are very diff differentt and d multiple lti l documents are needed. • Re-training is absolutely necessary in view of time g of change g involving g many y frame and magnitude design codes and documents. on the run’ run . • Engineers will have to learn ‘on
