Innovative Buckling Design Rules for Structural Hollow Sections FINAL WORKSHOP, Oslo, 6th June 2019 HOLLOSSTAB is an EU funded programme under RFCS, the.

Innovative Buckling Design Rules for Structural Hollow Sections FINAL WORKSHOP, Oslo, 6th June 2019
HOLLOSSTAB is an EU funded programme under RFCS, the Research Fund for Coal and Steel, under grant agreement

PROGRAMME 4. Development of GSRM Design Rules
1. Welcome and introduction 2. Trends for hollow sections 3. Physical and numerical test campaign 4. Development of GSRM Design Rules 5. Software: calculation core 6. Examples 7. Closing statement

OVERVIEW Design Steps & Routes

Cross-sectional Resistance
RHS/SHS – FEM parametric study General overview of the scatter-band – what is achieved “directly” by the GSRM definition? At first sight, relatively “compact” scatter band in the GSRM representation based on ideal- plastic reference resistances However, the differences are still pronounced  a lower-bound curve for all cases would underpredict many capacities by up to 50%  Differentiation of cases necessary SHS & RHS, S EN (cold-formed) SHS & RHS, S EN & EN 10219

RHS/SHS – FEM parametric study Differentiation: in-plane cases, N+My More compact scatter band Pure compression and pure bending are upper bounds a lower-bound curve for all is again not satisfactory, differences of 20-30% Lower half of “stocky” results only reaches Rpl at 𝜆 L~0.3 SHS & RHS, S EN 10219 SHS & RHS, S EN (hot-finished)

RHS/SHS – FEM parametric study Differentiation: bi-axial bending My + Mz -- N=0; Some particularly low values are found in bi-axial bending  Rpl implies large plastic strains, these cannot be reached at moderate local slenderness -fy +fy pl= Rpl/Rel can be >>1.5 SHS & RHS, S EN 10219 SHS & RHS, S EN (hot-finished)

RHS/SHS – FEM parametric study Different approach: Rref = Relastic - in-plane N+M cases Scatter seemingly wider, very high values of L are reached because of the difference between Rel and Rpl However, much clearer patterns emerge  description with “Winter- type formulae” possible Conveniently, the “standard cases” of pure compression and pure bending are near the lower bound of resistances S EN 10219 S EN 10210

RHS/SHS – Development of Design Proposals Elastic range – Winter format: 𝜒= 1 𝜆 1 − 𝐴 𝜆 2 Mechanical / physical effect: the stress distributions in (at least) two plates adjacent to the most compressed point in the section influence each other and the “overall” reduction of the cross- section  taken into account in the effective width method. GSRM must account for this effect as well.  introduction of L as function of both 𝜓 1 and 𝜓 2 see EC3-1-5: differentiation by stress state in each plate: (𝜒=)𝜌= 1 𝜆 1 − 𝐴 𝜆 2 𝑓(𝜓 1 ) A=0.11 𝑓(𝜓 2 ) A=0.18 𝐴=0,055∗ 3+𝜓 =0,22∗ 3+𝜓 4 A=0.22 𝜓 1 =1 𝜓 2 =−0,4 Euler

RHS/SHS – Development of Design Proposals Elastic range – Winter format: calibration, in plane cases (1=1,0) 𝜒= 1 𝜆 1 − 𝐴 𝜆 2 SHS & RHS EN 10210 SHS & RHS EN 10210 SHS & RHS EN 10219 note: EC3 pure compression “unsafe”

RHS/SHS – Development of Design Proposals Elastic range – Winter format: calibration 𝜒= 1 𝜆 1 − 𝐴 𝜆 2 𝑓(𝜓 2 )=0,225+0,025 ∗𝜓 2 cold-formed 𝜓 1 =1 𝜓 2 𝑓(𝜓 2 )=0,20+0,02 ∗𝜓 2 hot-finished 𝐴=𝑓(𝜓 2 )∗ 𝑓(𝜓 1 ) 𝑓(𝜓 1 )= 3+ 𝜓 or 𝜓 (finally chosen) very compact representation, very similar to the familiar representations in EC3 simple calculation of elastic quantities 𝜓 1 and 𝜓 2 SHS & RHS EN 10219

RHS/SHS – Development of Design Proposals Plastic range – simplified approach: interpolation between “anchor points” ALTERNATIVE:  Continuous Strength Method

RHS/SHS – Design Proposal – Summary: 𝑹 𝑳 = 𝝌 𝑳 ⋅ 𝑹 𝒆𝒍 𝝌 𝑳 = 𝟏+( 𝜶 𝒑𝒍 −𝟏)⋅ 𝝀 𝟎 − 𝝀 𝑳 𝝀 𝟎 −𝟎,𝟑 ≤ 𝜶 𝒑𝒍 for 𝝀 𝑳 ≤ 𝝀 𝟎 with: 𝛼 𝑝𝑙 = 𝑅 𝑝𝑙 𝑅 𝑒𝑙 ≤ 1,5 𝜆 0 = −𝐴 for 𝝀 𝑳 > 𝝀 𝟎 𝝌 𝑳 = (𝟏− 𝑨 𝝀 𝑳 𝑩 𝟐 )⋅ 𝟏 𝝀 𝑳 𝑩 𝟐 may be calculated as: Ψ 1 =𝑀𝐴𝑋( 𝑁 𝐴 + 𝑀 𝑊𝑦 − 𝑀 𝑊𝑧 𝑁 𝐴 + 𝑀 𝑊𝑦 + 𝑀 𝑊𝑧 ; 𝑁 𝐴 − 𝑀 𝑊𝑦 + 𝑀 𝑊𝑧 𝑁 𝐴 + 𝑀 𝑊𝑦 + 𝑀 𝑊𝑧 ) with: 𝐵 2 =1 ; 𝐴= ( ψ 2 ) ( 1+ψ 1 ) for hot-finished sections Ψ 2 =𝑀𝐼𝑁( 𝑁 𝐴 + 𝑀 𝑊𝑦 − 𝑀 𝑊𝑧 𝑁 𝐴 + 𝑀 𝑊𝑦 + 𝑀 𝑊𝑧 ; 𝑁 𝐴 − 𝑀 𝑊𝑦 + 𝑀 𝑊𝑧 𝑁 𝐴 + 𝑀 𝑊𝑦 + 𝑀 𝑊𝑧 ) 𝐴= ( ψ 2 ) ( 1+ψ 1 ) for cold-formed sections

Alternative: CSM-GSRM for SHS & RHS
Same material models & resistance functions as CHS/EHS For hot-rolled hollow sections: Equivalent to GSRM in slender range Displaying full set of CSM-GSRM design formulae for SHS & RHS Brief introduction –base curves calibrated for SHS & RHS & converging to existing CSM base curve for compression, resistance functions remain applicable For cold-formed hollow sections: Base curves for SHS & RHS: Same format Calibrated using SHS & RHS data

RHS/SHS – Design Proposal – Validation and comparison with GMNIA & EC3 GSRM GMNIA prEN (+Annex B)

RHS/SHS – Design Proposal – Validation and comparison with GMNIA & EC3 GMNIA vs GSRM GMNIA vs EC3 GSRM vs EC3

RHS/SHS – Design Proposal – Validation and comparison with GMNIA & EC3 GMNIA vs GSRM GMNIA vs EC3 GSRM vs EC3 EC3 class 4 EC3 class 3 EC3 class 4 EC3 class 1/2 EC3 class 4 EC3 class 1/2 EC3 class 3 (SEMI-COMP method) EC3 class 1/2 EC3 class 3 (SEMI-COMP method)

RHS/SHS – Design Proposal – Validation and comparison with GMNIA & EC3 GSRM vs GMNIA SUMMARY: GSRM design: Consistent accuracy = comparable average distance from „real“ (GMNIA) resistance across slenderness ranges and EC3 classes. Gains in strength compared to EC3 particularly in class 4 sections; consciously lower resistance in class 1/2 to compensate for lack of conservatism  could be easily compensated = “improved“ by raising 𝜆 pl and pl,max GSRM vs EC3

Local Buckling – Reliability Assessment
Step 1 Resistance function gr,t rt = gr,t(X1, X2, …, Xn) Experimental resistance re Data basis of experimental and numerical results re,i. Statistical information on basic variables Xj Mean value Xm and standard deviation sj of dimensions and material data. Step 2 Mean value of the correction factor b The factor b indicates the accuracy of the model in terms of mean value. Coefficient of variation of the error Vd The coefficient of variation Vd indicates the accuracy of the model in terms of variation of the difference. Step 3 Determine the sensitivity of the resistance function to variations of the input data – coefficient of variation Vrt 𝑉 𝑟𝑡,𝑖 2 = 1 𝑟 𝑡,𝑖 𝑋 𝑚 𝑗=1 𝑘 𝜕 𝑟 𝑡,𝑖 𝑋 𝑗 𝜕 𝑋 𝑗 𝜎 𝑗 2 𝜕 𝑟 𝑡,𝑖 𝑋 𝑗 𝜕 𝑋 𝑗 = 𝑟 𝑡,𝑖 𝑋 1 ,…,𝑋 𝑗 +∆ 𝑋 𝑗 ,…, 𝑋 𝑘 − 𝑟 𝑡,𝑖 𝑋 1 ,…,𝑋 𝑗 ,…, 𝑋 𝑘 ∆ 𝑋 𝑗 Step 4 Determine the design value of the resistance rd for each specimen 𝑟 𝑑,𝑖 𝑏, 𝑟 𝑡,𝑖 𝑋 𝑚 , 𝑉 𝛿 , 𝑉 𝑟𝑡,𝑖 Determine the partial factor for each specimen and as a mean value 𝛾 𝑀,𝑖 ∗ = 𝑟 𝑛𝑜𝑚,𝑖 𝑟 𝑑,𝑖 𝛾 𝑀 ∗ = 𝑖=1 𝑛 𝛾 𝑀,𝑖 ∗ 𝑛

Acceptance level for the partial factor (according to RFCS-SAFEBRICTILE) fa = gM*/gM,target

Local Buckling – Statistical evaluation
Statistical data of input variables – dimensions: For SHS and RHS sections For EHS sections For CHS sections Height h Width b Thickness t Corner radius r Mean value 100,0% 95,6% 99,6% Standard deviation 0,18% 0,23% 4,37% 11,6% Diameter D1 Diameter D2 Thickness t Mean value 100,0% 100,7% 101,1% Standard deviation 0,62% 1,26% 3,80% Diameter D Thickness t Mean value 100,0% 94,14% Standard deviation 0,18% 4,04%

Local Buckling – Statistical evaluation
Statistical data of input variables – material Data: For all types of section Steel Grade Statistical Value Yield Strength fy Ultimate tensile strength fu S355 and S420 Mean value 141,5% * nominal 110,7% Standard deviation 10,99% 4,78% S460 132,0% 114,4% 9,34% 5,00% S700 and S550 122,4% 118,1% 7,68% 5,21%

Partial factor obtained for design models for local buckling: For SHS and RHS sections For EHS sections For CHS sections gM* 1,067 gM=gM*/fa 0,999 gM* 1,018 gM=gM*/fa 0,946 gM* 1,124 gM=gM*/fa 1,043

Beam-Columns – Global Buckling
Starting point – General Shape of GSRM Global Buckling Curves Numerical results from parametric study, one section, various  and lengths Decrease of  with increase of , however the relative distance decreases with higher values of  With increasing  and the same physical length of the member, the “global” slenderness 𝜆 G decreases “Euler” is not exceeded, as expected N My

Starting point – Background of the EC3 column buckling formulae e0 Nb  Quadratic equation with well-known solution:

Starting point – Background of the EC3 column buckling formulae My/ “My,L“ N/ “NL“ 1,0 e0 Nb  Solution depends on a linearization of the cross-section capacity

Starting point – Background of the EC3 column buckling formulae What makes the “Ayrton-Perry“ formula accurate? ACCURACY can be achieved by calibration of , a, b parameters have a mechanical ”meaning“: - : imperfection, axial load eccentricity - a, b: CS interaction for the basic case of column buckling (only N or M + imperf.) a, b, c can be set to 1.0 => calibrate  alone for more complex cases (N+M), consideration of “true” (linearized) CS interaction necessary Real behaviour: - inelastic deformation path - distributed spread of plasticity - central CS not fully plastic Model: - always elastic - failure in one CS - linear interaction:

Bending Moment vs. Imperfection: two comparable types of ““ 1,0 1,0 elastic CS interaction of equivalent type  relative eccentricity L * elastic N/ “NL“ N/ “NL“ e0 Nb h N My 1,0 My/ “My,L“ 1,0 My/ “My,L“

Derivation of the GSRM Beam-Column formulae – in-plane case Some basic variable relations: 1,0 elastic CS interaction L * elastic N/ “NL“ RL*a h a N My My/ “My,L“ 1,0

Derivation of the GSRM Beam-Column formulae – in-plane case Derivation of y,y: similarly as before for y,EC3 1,0 elastic CS interaction L * elastic RL*a  again known solution: h a N My My/ “My,L“ 1,0

Derivation of the GSRM Beam-Column formulae – in-plane case Reintroduction of GSRM variables: representation y=0.00 general behaviour well captured y=0.25 y=0.50 y=1.00 y=2.00

Derivation of the GSRM Beam-Column formulae – in-plane case Additional effect for “plastic“ cross-sections, L>1.0 1,0 ….solution similar as before….. L * elastic, L >1 elastic 2nd order 1/LG elastic CS real behaviour (elasto-plastic) 1/L interpolation h “transition surface” & calibration with =0.5 for SHS/RHS 1,0

Derivation of the GSRM Beam-Column formulae – spatial cases In principle similar, but two main paths = buckling modes must be considered My,E NE Rel My,E NE FBz,z Mz,E Rpl L*Rel (case L>1,0) FBy,y Rcr,y Mz,E FBy,y Rtransition FBz,z Rcr,z N/ “NL“ e.g. FBz-z, My-moments remain mostly linear: Mz/ “Mz,L“ ….and similar changes with Cm factors… ….solution similar as before….. My/ “My,L“

Proposal for GSRM Beam-Column formulae – SHS / RHS

Validation of Rules for SHS/RHS – Comparisons with GMNIA results Class 1 SHS, in-plane loading Class 3 SHS, in-plane loading Behaviour is very consistently described For in-plane cases, the combined accuracy of L and G generally leads to quite accurate results Conservatism a bit more pronounced for HSS cold-formed sections, because of EC3 rule (𝛼EC3=0.49)  increase, as is done for HFS?  0.13  0.49  0.34? N My N My

Validation of Rules for SHS/RHS – Comparisons with GMNIA results Class 1 SHS, in-plane loading Class 3-4 RHS, spatial Cmy=0.6 normalization eliminates conservatism of L from representation N My N My;Mz ; N My;Mz ;

Validation of Rules for SHS/RHS Overview of GMNIA vs. GSRM Proposal vs. EC3 (=prEN SEMI-COMP) – uniaxial N+My GMNIA/GSRM GMNIA/EC3 EN10210 (hot-finished), S355-S770 N My

Validation of Rules for SHS/RHS Overview of GMNIA vs. GSRM Proposal vs. EC3 (=prEN SEMI-COMP) – uniaxial N+My GMNIA/GSRM GMNIA/EC3 EN10219 (cold-formed), S355-S770 N My

Validation of Rules for SHS/RHS Overview of GMNIA vs. GSRM Proposal vs. EC3 (=prEN SEMI-COMP) – biaxial N+My+Mz GMNIA/GSRM GMNIA/EC3 EN10210 (hot-finished), S355-S770 N My;Mz ;

Validation of Rules for SHS/RHS Overview of GMNIA vs. GSRM Proposal vs. EC3 (=prEN SEMI-COMP) – biaxial N+My+Mz GMNIA/GSRM GMNIA/EC3 EN10219 (cold-formed), S355-S770 N My;Mz ;

Design of CHS & EHS - Outline
Development of design rules for CHS/ EHS Follows same general format as SHS/ RHS Two design alternatives considered for cross- section design – GSRM and CSM-GSRM Hot-rolled Cold-formed

Cross-section design

GSRM design flowchart (cross-section)
GSRM cross-section design procedure: 1. Three key R factors for cross-section design: Rel – elastic section resistance Rpl – plastic section resistance Rcr,L – elastic local buckling resistance Recap the GSRM cross-section design flowchart Introduce key parameters – R, λL, χL CSM-GSRM GSRM GSRM CSM-GSRM CSM-GSRM

GSRM cross-section design procedure: 1. Three key R factors for cross-section design: Rel – elastic section resistance Rpl – plastic section resistance Rcr,L – elastic local buckling resistance 2. Local slenderness 3. GSRM or CSM-GSRM 4. Cross-section resistance CSM-GSRM GSRM CSM-GSRM

GSRM cross-section design procedure: 1. Three key R factors for cross-section design: Rel – elastic section resistance Rpl – plastic section resistance Rcr,L – elastic local buckling resistance 2. Local slenderness 3. GSRM or CSM-GSRM 4. Cross-section resistance Two design options available at cross-section level CSM-GSRM GSRM GSRM CSM-GSRM CSM-GSRM

GSRM cross-section design procedure: 1. Three key R factors for cross-section design: Rel – elastic section resistance Rpl – plastic section resistance Rcr,L – elastic local buckling resistance 2. Local slenderness 3. GSRM or CSM-GSRM 4. Cross-section resistance CSM-GSRM GSRM CSM-GSRM

Cross-section design – GSRM
Stocky GSRM for CHS & EHS – design formulae Slender Same definitions & formulae as GSRM for SHS & RHS Calibrated using CHS & EHS test & FE data Introduction of cross-section GSRM for CHS & EHS – simple extension of proposal for SHS & RHS Very brief – key concept and parameters will have been introduced previously by Andreas Compression – no spread of plasticity, bending some, N+M more

Cross-section design – GSRM
Stocky GSRM for CHS & EHS – design formulae Slender ψ = 1 for pure compression ψ = -1 for pure bending s2 s1 (max. comp.) s1 = How much of the resistance is from spread of plasticity and how much from strain hardening? Introduction of cross-section GSRM for CHS & EHS – simple extension of proposal for SHS & RHS Very brief – key concept and parameters will have been introduced previously by Andreas Points above 1 represent benefit from spread of plasticity and strain hardening. In compression, there is no spread of plasticity because the section is under uniform strain, but you do get strain hardening for the stockier cross-sections, while for the other cases – bending and combined M+N, you have both spread of plasticity and strain hardening. How much of the resistance is down to spread of plasticity and how much from strain hardening? How much plastic deformation is required to reach these resistances? These questions are not limited to the GSRM design method; also EC3. How much plastic deformation is required to reach these resistances? Ru/Rel values greater than unity represent spread of plasticity/ strain hardening

CSM-GSRM design concept
The continuous strength method (CSM) is a deformation based design approach that replaces cross-section classification and accounts for spread of plasticity and strain hardening in a controlled way Includes two key features CSM base curve defines how much strain a cross-section can tolerate before failure CSM material model to reflect the stress-strain behaviour of the material (hot-rolled and cold-formed steel in this case) Resistances derived from basic mechanics

CSM-GSRM design concept
Continuous Strength Method (CSM)-based design procedure: Benefits of CSM design concept: Mechanically consistent design approach Knowledge and control of required deformations Rational exploitation of spread of plasticity and strain hardening Local slenderness Section deformation capacity from base curves Material model incorporating strain hardening Cross-section resistance

CSM base curves for CHS & EHS
CSM ‘base curves’ defines maximum strain ecsm section can endure prior to failure as function of local slenderness Base curve is function of ψ to reflect response under N+M Ratio between N & M ψ = 1 for pure compression ψ = -1 for pure bending ψ: ratio of “minimum” stress (circled in red) to “maximum” stress (circled in blue), compression positive s2 s1 (max. comp.) s1 = N M Higher ψ Base curves Base curves for combined loading – transition based on ψ Definition of ψ: ratio of “minimum” stress (circled in red) to “maximum” stress (circled in blue), compression positive ecsm = CSM cross-section failure strain ey = yield strain

Base curves for CHS & EHS
Base curve formulation: εcsm/εy > 1, section failure by inelastic local buckling (Rb,L>Rel) Benefit can be taken from spread of plasticity and strain hardening Stocky sections Explain how base curves work for stocky & slender section Explain the parameters in the formulae – λ0 A, B1, B2

Base curve formulation: Explain how base curves work for stocky & slender section Explain the parameters in the formulae – λ0 A, B1, B2 B1 describes the shape of base curve in stocky range Transition based on ψ

Base curve formulation: At , εcsm/εy = 1, i.e. section fails at yield strain (Rb,L=Rel) for pure compression for pure bending marks transition between stocky and slender sections and is f(y) Explain how base curves work for stocky & slender section Explain the parameters in the formulae – λ0 A, B1, B2

Base curve formulation: Slender sections Explain how base curves work for stocky & slender section Explain the parameters in the formulae – λ0 A, B1, B2 εcsm/εy < 1, section failure by local buckling (Rb,L<Rel) Winter-curve format

Base curve formulation: Explain how base curves work for stocky & slender section Explain the parameters in the formulae – λ0 A, B1, B2 A, B2 describe the shape of base curve in slender range The stockier the cross-section, the higher the failure strain and the further along the stress-strain curve you could progress, allowing spread of plasticity and potentially strain hardening

Material models Hot-rolled steels:
The material models reflect the differences between hot rolled steel, with a clear yield plateau before strain hardening commences..

Material models Cold-formed steels:
Rounded stress-strain curve of cold-formed steels is represented by an elastic linear hardening model Cold-formed steels: And cold-formed steel, with strain hardening begins from the yield point and is represented by a linear hardening region

CSM-GSRM resistance functions
For hot-rolled hollow sections: For cold-formed hollow sections: Spread of plasticity Spread of plasticity Strain hardening Strain hardening Spread of plasticity CSM-GSRM resistance functions – originate from CSM resistance functions, but with R factors incorporated Explain the meaning of terms – one for spread of plasticity, one for strain hardening Rel and Rpl are the same for compression, so spread of plasticity term is zero for compression

CSM-GSRM for SHS & RHS Same material models & resistance functions as CHS/EHS For hot-rolled hollow sections: Equivalent to GSRM in slender range Displaying full set of CSM-GSRM design formulae for SHS & RHS Brief introduction –base curves calibrated for SHS & RHS & converging to existing CSM base curve for compression, resistance functions remain applicable For cold-formed hollow sections: Base curves for SHS & RHS: Same format Calibrated using SHS & RHS data

Accuracy of design proposal for CHS & EHS
Hot-rolled CHS (by load case): EC3 GSRM EC3 a bit conservative in the stocky range due to strain hardening, and in the slender range due to classification limits and effective area formulae EC3 a bit conservative in stocky range due to strain hardening, and in slender range due to classification limits and effective area formulae Improved predictions with GSRM

Hot-rolled CHS (by load case): EC3 CSM-GSRM Further improvements with CSM-GSRM

Hot-rolled CHS (by class): EC3 CSM- GSRM Toggle to show load cases / class Same results presented by cross-section classification

Cold-formed CHS (by class): EC3 CSM- GSRM Toggle to show load cases / class Similar results for cold-formed CHS – improvements in both the stocky and slender ranges

Hot-rolled EHS (by class): EC3 CSM-GSRM Toggle to show load cases / class Similar results for hot-rolled EHS – improvements in both the stocky and slender ranges

Cold-formed EHS (by class): EC3 CSM-GSRM Toggle to show load cases / class …And cold-formed EHS – improvements in both the stocky and slender ranges

Statistical results – CHS: Statistics EC3 Cold-formed Hot-rolled N M N+M All Mean 1.294 1.202 1.430 1.397 1.250 1.144 1.317 1.295 COV 0.142 0.090 0.154 0.159 0.163 0.092 0.136 GSRM 1.093 1.099 1.198 1.179 1.054 1.046 1.108 1.097 0.078 0.036 0.071 0.077 0.106 0.047 0.080 0.083 CSM-GSRM 1.084 1.088 1.171 1.155 1.065 1.050 1.101 0.042 0.029 0.070 0.072 0.096 0.081 FE capacity/design capacity Substantial improvements in CHS cross-section resistance predictions (around 20% on average) and substantial reduction in scatter (important for gM)

Statistical results – EHS: Statistics EC3 Cold-formed Hot-rolled N M N+M (uniaxial) N+M (biaxial) All Mean 1.356 1.248 1.565 1.480 1.473 1.294 1.188 1.477 1.394 1.393 COV 0.136 0.111 0.219 0.236 0.226 0.148 0.225 0.213 GSRM 1.140 1.126 1.187 1.122 1.151 1.101 1.062 1.120 1.051 1.085 0.094 0.053 0.082 0.052 0.075 0.128 0.057 0.095 0.071 0.091 CSM-GSRM 1.114 1.115 1.130 1.098 1.065 1.099 1.081 0.064 0.046 0.078 0.056 0.067 0.125 0.049 0.088 0.070 0.083 FE capacity/design capacity Even greater improvements for EHS!

Global buckling

GSRM design flowchart (member)
GSRM global buckling design procedure: 1. Three key R factors for global buckling design: Rel – elastic section resistance Rb,L – cross-section resistance Rcr,G – elastic global buckling resistance 2. Global slenderness 3. GSRM member buckling curves 4. Member buckling resistance Recap the GSRM member design flowchart Introduce key parameters – R, λG, χG

GSRM global buckling design procedure: 1. Three key R factors for global buckling design: Rel – elastic section resistance Rb,L – cross-section resistance Rcr,G – elastic global buckling resistance 2. Global slenderness 3. GSRM member buckling curves 4. Member buckling resistance We take our cross-section resistance and we combine it with our global critical load to define our global slenderness

GSRM global buckling design procedure: 1. Three key R factors for global buckling design: Rel – elastic section resistance Rb,L – cross-section resistance Rcr,G – elastic global buckling resistance 2. Global slenderness 3. GSRM member buckling curves 4. Member buckling resistance Recap the GSRM member design flowchart Introduce key parameters – R, λG, χG

GSRM global buckling design procedure: 1. Three key R factors for global buckling design: Rel – elastic section resistance Rb,L – cross-section resistance Rcr,G – elastic global buckling resistance 2. Global slenderness 3. GSRM member buckling curves 4. Member buckling resistance Member buckling resistance is global buckling reduction factor multiplied by cross-section resistance

Key parameters for CHS & EHS
Global slenderness: Local instability Allowance for spread of plasticity & strain hardening for stocky sections, and loss of effectiveness due to local buckling for slender sections λG incorporates χG – account for spread of plasticity & strain hardening for stocky sections, or local buckling for slender sections Global elastic instability

Member buckling design of CHS & EHS
Member buckling curves (Ayrton-Perry format): To reflect influence of extent of cross- section plastification on global stability Higher bLG N Higher ψ To reflect gradual influence of material strength on buckling curves N+M To allow for different global stability response under different loading conditions Peryy-Robertson with a couple of modifications: Firstly, the imperfection factor is a function of psi, to allow for the different stability response under the different loading conditions. In the low global slenderness range, benefit can be taken from the spread of plasticity and strain hardening because the loss of stiffness due to plasticity doesn’t have a detrimental effect on your global stability. However, as global slenderness increases, stability effects become more dominant, resistance is dependent on the elastic stiffness and the point at which that is lost (i.e. first yield). So, the beta LG factor is a transition factor allowing spread of plasticity and strain hardening in the stocky range to a first yield failure critierion in the slender range.

Hot-rolled CHS (by load case): EC3 GSRM

Hot-rolled CHS (by class): EC3 GSRM Inaccuracy in EC3 mainly from cross-section level EC3 more conservative for stocky members and slender cross-sections

Cold-formed CHS (by load case): EC3 GSRM

Cold-formed CHS (by class): EC3 GSRM Inaccuracy in EC3 mainly from cross-section level Again, EC3 more conservative for stocky members and slender cross-sections

Hot-rolled EHS (by load case): EC3 GSRM EC3: a bit scattered down the stocky end, more accurate in the slender range GSRM: Good for all cases except bi-axial bending. The problem here is one of spatial buckling, and you can get conservative results when you have a dominant moment in the major axis direction so failure will be in that direction, but the design method utilises the minimum Rcritical, global for minor axis buckling. This can be resolved using the approach Andreas mentioned. EC3 more conservative for stocky members and slender cross-sections; GSRM gives improved predictions for all cases, though bi-axial bending results remain scattered

Hot-rolled EHS (by class): EC3 GSRM EC3 a bit conservative in the class 4 range GSRM similarly results for all classes, but the biaxial bending cases are high

Cold-formed EHS (by load case): EC3 GSRM Similar results for cold-formed EHS members: GSRM gives improved predictions for all cases, though bi-axial bending results remain scattered

Cold-formed EHS (by class): EC3 GSRM Inaccuracy in EC3 mainly from cross-section level

Statistical results – CHS: FE capacity/design capacity Statistics EC3 Cold-formed Hot-rolled N N+M All Mean 1.218 1.184 1.205 1.118 1.114 COV 0.113 0.141 0.131 0.217 0.114 0.132 GSRM 1.072 1.074 1.066 1.050 1.069 0.034 0.031 0.032 0.026 0.041 Substantial improvements in CHS member design resistance predictions (around 10% on average) and reduction in scatter; improvements largely due to gains at cross-section level

Statistical results – EHS: FE capacity/design capacity Statistics EC3 Cold-formed Hot-rolled N N+My N+Mz N+My+Mz All Mean 1.240 1.163 1.214 1.280 1.243 1.160 1.094 1.150 1.207 1.170 COV 0.123 0.111 0.129 0.124 0.127 0.148 0.114 0.136 0.133 0.139 GSRM 1.076 1.095 1.065 1.166 1.120 1.054 1.098 1.067 1.168 1.117 0.030 0.028 0.087 0.077 0.027 0.043 0.040 0.096 0.086 Similar results for EHS at member level

THANK YOU!

Innovative Buckling Design Rules for Structural Hollow Sections FINAL WORKSHOP, Oslo, 6th June 2019 HOLLOSSTAB is an EU funded programme under RFCS, the.

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Innovative Buckling Design Rules for Structural Hollow Sections FINAL WORKSHOP, Oslo, 6th June 2019 HOLLOSSTAB is an EU funded programme under RFCS, the.

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Presentation on theme: "Innovative Buckling Design Rules for Structural Hollow Sections FINAL WORKSHOP, Oslo, 6th June 2019 HOLLOSSTAB is an EU funded programme under RFCS, the."— Presentation transcript:

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