Design of Fibre Reinforced Polymer structures load combinations and partial factors to be used together with JRC document on Design of FRP with

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1 Design of Fibre einforce Polymer structures loa combinations an partial factors to be use together with JC ocument on Design of FP with Fiberline proucts Prepare by: Controlle by: John Dalsgaar Sørensen Carsten unk Plum Date: January 2016

2 Contents 1 Introuction Loa combinations in EN1990 an in DK NA EN Safety format for resistances an materials Design values of resistances an materials aterial partial factors... 8 Application to Fibre einforce Polymer (FP) structures eferences Annex A Backgroun for material partial factors Page 2 of 19

3 1 Introuction This report escribes the specification for application of the JC (2016) report for esign of FP loa bearing structures, incl. the loa combinations to be use an the basis for selecting material partial factors for esign accoring to the principles in the Eurocoes as escribe in EN 1990 (2002). Especially, loa combinations an the moel for material partial factors for obtaining esign values for resistances in the Danish national annex to the Eurocoes are escribe, DK NA EN Section 2 escribes the loa combinations an loa partial factors to be use following the Danish National Annex to EN1990. Section 3 escribes the moels for obtaining esign values for loa bearing capacities following the Danish National Annex to EN1990. Also escribe is the statistical basis for estimating material partial factors for esign of fibre reinforce polymer structures obtaine from tests with typical fibre reinforce polymer an calculation moels. Section escribes the specifications for use of the JC (2016) report for esign of FP structures in connection with the Eurocoes EN1990 an EN1991, an the corresponing Danish national annexes. Finally Annex A escribes the backgroun for the material partial factors in chapter. Page 3 of 19

4 2 Loa combinations in EN1990 an in DK NA EN1990 Generally all limit states in EN1990 (2002) have to be checke. However, only one esign situation for one limit state is consiere in this this report, namely ST for Persistent an transient esign situations: SLS Serviceability Limit States SLSs are not consiere in this report. ULS Ultimate Limit States In accorance with EN1990 (2002) the following ultimate limit states (ULS) have to be verifie: EU: ST: GEO: FAT: Loss of static equilibrium. EU is not consiere in this report. Internal failure or excessive eformation of the structure or structural members, incluing footings, piles, basement walls, etc., where the strength of construction materials of the structure governs. The following esign situations have to be checke: Persistent an transient esign situations. Acciental. These esign situations are not consiere in this report. Seismic. These esign situations are not consiere in this report. Failure or excessive eformation of the groun where the strengths of soil or rock are significant in proviing resistance. GEO is not consiere in this report. Fatigue failure of the structure or structural members. FAT is not consiere in this report. The esign value of the action effect E for ST can be etermine by the following three moels where "" inicates to be combine with when etermining action effects (e.g. eformations or cross-sectional forces): 1) Verification of eq. (6.10): ST (6.10): E ' ' G, Gk, " ",1k,1" ", where G, characteristic value of permanent loa from source no. k k,1 characteristic value of the ominating variable loa, characteristic value of non-ominating variable loa no. k G, partial factor for permanent loa from source no.,1 partial factor for the ominating variable loa, partial factor for non-ominating variable loa no. 0, loa combination factor for variable loa no. 2) Verification of both eq. (6.10a) an (6.10b): 1 0, k, Page of 19

5 ST (6.10a): ST (6.10b): where E ' ' G, Gk, " ",1 0,1k,1" ", 1 E ' ' G, Gk, " ",1k,1" ", 1 0, 0, k, k, reuction factor for unfavourable permanent actions G 3) Verification of both eq. (6.10a) an (6.10b), but no variable loas in eq. (6.10a): ST (6.10a): ST (6.10b): E ' ' G, G k E ' ' GGk, " ",1k,1" ", 0, 1 k, The recommene values for the partial factors in EN 1990, Annex A1 for builings are = 1.35 where unfavourable G,sup G,inf = 1.00 where favourable = 1.5 where unfavourable (0 where favourable) = 0.85 (so that x G, sup = 0.85x ) 0, see EN 1990, Annex A The recommene values for the partial factors in EN 1990, Annex A2 for briges are = 1.35 where unfavourable G,sup G,inf = 1.00 where favourable = 1.35 when represents unfavourable actions ue to roa or peestrian traffic (0 when favourable) = 1,5 when represents unfavourable actions ue to rail traffic, to groups of loas 11 to 31 (except 16, 17, 26 an 27), loa moels L71, SW/0 an HSL an real trains, when consiere as iniviual leaing traffic actions (0 when favourable) = 1.20 when represents unfavourable actions ue to rail traffic, to groups of loas 16 an 17 an SW/2 (0 when favourable) = 1.50 for other traffic actions an other variable actions = 0.85 (so that x G, sup = 0.85x ) In the Danish National annexes for builings DK NA EN1990 (2013) an briges EN 1990/A1 DK NA (2009) moel 3) is chosen because it gives a more uniform reliability level with respect to ifferent combinations of permanent an variable loas than using (6.10). The following loa combinations have to be checke in ULS accoring to the Danish National annex ST (6.10b): ST (6.10a): E ' ' GA, Gk, " " k,1" " 0, E ' ', G, GB k 1 k, For builings the following values are applie, see DK NA EN1990 (2013): partial factor for permanent loa in (6.10b) = 1.0 GA,sup GB,sup partial factor for permanent loa in (6.10a) = 1.2 partial factor for variable loa =1.5 Page 5 of 19

6 0, loa combination factors, see DK NA EN1990 For briges the following values are applie, see EN 1990/A1 DK NA (2009): ξ = 1.00 = 1.00 for permanent loa from structural elements, soil an groun water GA,sup GA,inf = 0.90 for permanent loa from structural elements GA,inf = 1.00 for permanent loa from soil an groun water = 1.0 for traffic loa on briges = 1.20 for heavy special transports on rail (SW2) = 1.0 for impose loas uring execution = 1.50 for al other variable loas (climatic loas etc.) GB,sup = 1.25 for permanent loa from structural elements GB,sup = 1.00 for soil an groun water (1.25 in cases where the structure is loae by soil or (groun) water) = 1.00 for permanent loa from structural elements, soil an groun water GB,inf Consieration of consequence classes are one by multiplying all unfavorable loas with the factor K FI, see Table 1. The consequence classes in the Danish national annex are efine in DK NA EN1990:2013. Consequence class Low CC1 eium CC2 High CC3 K FI Table 1. K FI - factor epening on consequence class. Accoring to DK NA EN 1990/A1:2009 for briges CC1 is not use for briges an CC2 is only applie in special cases. Page 6 of 19

7 3 Safety format for resistances an materials 3.1 Design values of resistances an materials In DK NA EN1990 (2013), annex E it is escribe how partial factors for materials an resistances are to be obtaine. The same material partial factors are applie for builings an briges. The escription follows the overall principles in EN1990 (2002) but gives a more etaile moel to etermine the material partial factors epening on the level of uncertainty measure by the coefficient of variation (COV). It is assume that uncertainties relate to strengths an resistances can be moelle by LogNormal istributions. This is in accorance with the recommenations in EN 1990 (2002) an JCSS Probabilistic oel Coe (2002). Characteristic values are etermine as 5%-quantiles following EN 1990 Annex D. In assessment of the material partial factors it is important to account for hien safety or bias in the calculation moels. Annex D in EN 1990 contains a metho to quantify this bias by comparing test results with the calculation moel. Three moels may be applie to etermine the esign value of the resistance. oel 1 an 2 are base on a calculation moel, whereas moel 3 is base on tests performe to obtain the resistance irectly. Note: the sub-partial factor 3 in DK NA EN1990 (2013) is not use, since the effect of control is assume to be accounte for by 2 an. oel 1 The esign value of the resistance ( X, ) is etermine by: (1) where ( X, ) calculation moel for resistance as function of strength parameters X an geometry X partial factor relate to uncertainty in calculation moel (moel uncertainty) - incluing uncertainty associate with the transfer from laboratory conitions to conitions in an actual structure esign value of geometrical parameters esign value of strength parameters If the calculation moel epens on more than one strength parameter then esign values are applie for each of the strength parameters. The esign value of the strength parameter, X is etermine by: X k X (2) m where moification factor for e.g. loa uration, temperature an scale effects, see below characteristic value of strength parameter X k m = : partial factor for strength parameter - incluing uncertainty associate with the transfer from laboratory conitions to conitions in an actual structure, see below Page 7 of 19

8 The partial factor relate to the resistance moel is etermine by: 1 2 (3) b where 1 epens on type of failure (with or without warning), see below 2 epens on the uncertainty relate to the calculation moel, see below b bias (aitional safety) relate to the calculation moel The following simplification can be applie for a calculation moel linear in the strength parameters: X k, () where 1 2 m (5) b oel 2 The esign value of the resistance is obtaine by: k (7) where k moification factor for e.g. loa uration, temperature an scale effects characteristic value of resistance etermine by k X, () partial factor etermine by 1 (8) b oel 3 The esign value of the resistance is obtaine by: k (7) where k moification factor for e.g. loa uration, temperature an scale effects characteristic value of resistance etermine by tests partial factor etermine by 1 (8) 3.2 aterial partial factors The sub-partial factors 2 an are calibrate corresponing to an annual reliability inex equal to.3 for builings an.8 for briges. It is note that the same material factors are use for builings an briges whereas the loa partial factors are ifferent ue to the ifferent reliability levels. Page 8 of 19

9 Table 2 shows the sub-partial factor, 1 which epens on the type of failure of the structure. No warning of failure refers to failure that occurs without prior warning (e.g. in the form of increase crack formation or eformation) an significant reuction of resistance immeiately after a failure (e.g. in the event of stability failure or brittle fracture). Warning of failure without resiual resistance refers to failure where a warning is given of exhauste resistance (e.g. in the form of increase crack formation or eformation) an the resistance is retaine for some time after the warning. Warning of failure with resiual resistance refers to failure where the resistance increases (e.g. as a result of strain harening) after a formal failure has occurre (e.g. in the event of the permissible strain being exceee). If the resiual resistance is utilize in the calculation moels, the failure type is to be taken as Warning of failure without resiual resistance. Type of failure 1 Warning of failure with resiual resistance Warning of failure without resiual resistance 0,90 1,00 1,10 Table Sub-partial factor epening on type of failure. No warning Table 3 shows the sub-partial factor 2 which epens on the coefficient of variation of the moel uncertainty relate to the calculation moel. The coefficient of variation can be establishe by comparing resistances etermine by testing the structural members an by applying the calculation moel, with the use of measure/given strength parameters an geometric imensions. As an exception, the coefficient of variation may be etermine as an estimate. The coefficient of variation inclues uncertainty associate with the transfer from laboratory conitions to conitions in an actual structure. Coefficient of variation of the 5 % 10 % 15 % 20 % 25 % calculation moel, V Table Sub-partial factor 2 for uncertainty of the calculation moel. Table shows the sub-partial factor epens on the coefficient of variation for the measure strength parameter or resistance. The coefficient of variation is to inclue the uncertainty associate with the transfer from laboratory conitions to conitions in an actual structure. Coefficient of variation for measure 5 % 10 % 15 % 20 % 25 % 30 % strength parameter or re- sistance, V r Table. - Sub-partial factor for measure strength parameter or resistance. Page 9 of 19

10 Application to Fibre einforce Polymer (FP) structures This section escribes the application of JC (2016), PAT II for esign of fibre reinforce polymer (FP) loa bearing structures in Denmark using FP structures from Fiberline. The esign is assume to be performe using the Eurocoes EN 1990 an EN1991 with Danish National Annexes. Chapter 2 escribes the loa combinations an partial factors for loas to be applie. For resistances an materials the safety format escribe above is applie. NOTE the following specifications can be consiere as a Fiberline annex for application of CEN (2016), PAT II for esign of FP structures, since specific requirements are inclue relate to Fiberline manufacturing processes. In general the following specifications only apply to pultrue components an relate connections/oints, an not to e.g. sanwich panels. aterial strength parameters an resistance of structural elements are assume to be moelle by LogNormal stochastic variables with characteristic values etermine accoring to EN 1990, Annex D. Chapter 1 shall be use. Chapter 2 shall be use with the following changes: Section 2.3.2: characteristic an esign values shall be etermine using DK NA1990 an section 3.1 above. Section 2.3.3: esign values of capacities shall be etermine using section 3.1 above. Section 2.3.: Table 2.1 is exchange with, see Annex A: Table 2.1 NA values of γ 2 ULS (strength) Local stability Global stability (3) an () can not be use (1) can not be use Section can not be use. Chapter 3 shall be use with the following aitions: A quality control system shall be establishe to verify the characteristic values of the materials use in esign an the coefficients of variation (COV) use in annex A for etermination of the material partial factors, see also chapter 9. Characteristic values an COVs for the following strength parameters shall be ocumente: o Tensile strength parallel an perpenicular o Compressive strength parallel an perpenicular o Pin-bearing strength parallel an perpenicular The quality control system shall at least ocument on a regular basis that the characteristic values an COV for the flexural strength are satisfactory an fulfils the assumptions in annex A using the statistical control requirements in EN1990, Annex D. Chapter shall be use. Page 10 of 19

11 Chapter 5 shall be use. Chapter 6 shall be use except sections 6.3, 6. an 6.5 Chapter 7 shall be use. Chapter 8 shall be use except section 8.. Aitional information to section 8.2 can be foun in Oppe (2009) Chapter 9 shall be use. Chapter 10 (Annex A) shall be use. Chapter 11 shall not be use. efer to annex A Chapter (Annex C-F) shall be use. Page 11 of 19

12 5 eferences DK NA EN1990 (2013) National Annex to Eurocoe: Basis of structural esign. Danish Stanar. JC (2016) L. Ascione, J.-F. Caron, P. Goonou, K. van IJselmuien, J. Knippers, T. ottram,. Oppe,. Gantriis Sorensen, J. Taby, L. Tromp: Prospect for new guiance in the esign of FP - Support to the implementation, harmonization an further evelopment of the Eurocoes. EU EN; oi: / EN 1990/A1 DK NA (2009) Nationalt Anneks til Eurocoe 0: Proekteringsgrunlag for bærene konstruktioner. Annex A2 Applications for briges. FBD 300 (2008) FBD300 - ecommene values for structural analysis DS INF 172 (2009) Sørensen, J.D., J. unch-anersen, S.O. Hansen, F.O. Sørensen, H.H. Christensen, P. Lin & A. Poulsen: Backgroun investigations in relation to the rafting of National Annexes to EN 1990 an EN 1991 eliability verification formats, combination of actions, partial coefficients, fatigue, snow loa, win loa, etc. Dansk Stanar, EN 1990 (2002) Eurocoe 0 Basis of Structural Design. Felmann,. &. Oppe (2007) Dreipunktbiegeversuche zur Überprüfung er -V Interaktion von glasfaserverstärkten Polymerprofilen. eport, WTH Aachen. JCSS (1996) Backgroun ocumentation Eurocoe 1 (ENV 1991) Part 1: Basis of Design. JCSS PC (2002) Probabilistic oel Coe. Oppe,. (2009) Zur Bemessung geschraubter Verbinungen von pultruierten faserverstärkten Polymerprofilen. Heft 66, Stahlbau WTH Aachen, Dissertation D82, Shaker Verlag, Plum, C.. (2015) Fiberline - Beregningsmoel WG kontra Trumpf. Note, ES-Consult, Selacek, Brozzetti, Hanswille, Lizner & Canisius (1996) elationship between Eurocoe 1 an the material oriente Eurocoes. IABSE Colloquium: Basis of Design an Actions on Structures. Delft. Trumpf, H. (2006) Stabilitätsverhalten ebener Tragwerke aus pultruierten faserverstärkten Polymerprofilen. Shaker Verlag, Aachen Page 12 of 19

13 Annex A Backgroun for material partial factors This annex escribes the backgroun for the material partial factors in Table 2.1 NA in chapter. Accoring to section 2.2 the following sub-material partial factors are to be chosen: If a calculation moel is applie to etermine the resistance: o If moel 1 is applie: b epening on calculation moel (etermine using EN 1990, Annex D) 1 epening on failure moe 2 epening on uncertainty relate to calculation moel epening on uncertainty relate to material parameters o If moel 2 is applie: b epening on calculation moel (etermine using EN 1990, Annex D) 1 epening on failure moe epening on uncertainty relate to calculation moel incl. uncertainty relate to material parameters If a calculation moel is not applie, but the resistance is etermine base on tests: o oel 3 is applie: 1 epening on failure moe This metho is not being use in the following. Table A1 an A2 show examples of mean values, 5% fractile values an corresponing COV (Coefficient Of Variation) values from FBD 300 (2008). Average values 5% fractile characteristic values COV aterial characteristics Unit Test stanar Top flange Bottom flange Top flange Bottom flange Top flange Bottom flange oulus-axial Tension Etx N/mm² EN ISO oulus-axial Compression Ecx N/mm² EN ISO *** oulus-transverse Tension - Ety N/mm² EN ISO oulus-transverse Compression Ecy N/mm² EN ISO *** Strength-axial Flexural ffx N/mm² EN ISO * 300 * 0,17 Strength-axial Tension ftx N/mm² EN ISO ,15 0,15 Strength-axial Compression fcx N/mm² EN ISO ,10 0,10 Strength-transverse Flexural ffy N/mm² EN ISO * 100 * 0,11 Strength-transverse Tension fty N/mm² EN ISO ,16 0,16 Strength-transverse Compression fcy N/mm² EN ISO ,08 0,08 Interlaminar shear strengthaxial tm N/mm² EN ISO ,08 0,08 In-plane shear moulus G ISO ** N/mm² Table A1. Average- an characteristic values for the local analysis flanges. ***) inicative numbers. Page 13 of 19

14 aterial characteristics Unit Test stanar Average values Outer Inner web web 5% fractile characteristic values Outer Inner web web Top flange COV Bottom flange oulus-axial Tension Etx N/mm² EN ISO oulus-axial Compression - Ecx N/mm² EN ISO oulus-transverse Tension - Ety *** N/mm² EN ISO oulus-transverse Compression Ecy *** N/mm² EN ISO *** Strength-axial Tension ftx N/mm² EN ISO ,15 0,15 Strength-axial Compression fcx N/mm² EN ISO ,1 0,1 Strength-transverse Tension fty *** N/mm² EN ISO ,17 0,11 Strength-transverse Compression fcy *** N/mm² EN ISO ,30 0,25 In-plane shear strength tm ** N/mm² AST D ,0 0,0 In-plane shear moulus G ** N/mm² AST D Table A2. Average- an characteristic values for the local analysis webs. *) These tests shall not be carrie out in accorance to "Test Program FB 300, 12. Dezember 2006". **) Tests mae at ISØ. ***) Tests mae at IA. ***) inicative numbers. These values inicate that in general COV for the material strength parameters are below 15-20% except Strength-transverse Compression fcy for webs. Table A3 shows examples of estimation of material partial factors for failure moes where the ominating failure moe is stability failure. The statistical ata are from Trumpf (2006). The Table shows the coefficient of variation relate to the calculation moel, V, the coefficient of variation relate to the material parameters in the calculation moel, V r an the bias b relate to the calculation moel. This means that these uncertainty measures are relate to the calculation moels escribe in Trumpf (2006). Local buckling Global buckling Flexural buckling Lateral-torsional buckling Web Flange Square profile I an U-profile Weak axis I an U-profile Strong axis I profile V 0,11 0,07 0,10 0,15 0,13 0,17 V r 0,13 0,10 0,18 0,13 0,28 0,17 b 1,08 1,31 1,26 1,30 1,69 1,15 1 1,10 1,10 1,10 1,10 1,10 1,10 2 1,11 1,07 1,10 1,15 1,13 1,17 1,23 1,20 1,28 1,23 1,38 1, ,50 1,1 1,55 1,56 1,72 1, b 1,39 1,08 1,23 1,20 1,01 1,2 Table A3. Uncertainties relate to calculation moels from Trumpf (2006) an associate material partial factors. Page 1 of 19

15 The following material partial factor is base on the following assumptions: The calculation moels in Trumpf (2006) or similar moels are use to estimate the characteristic loa bearing capacity (efine as a 5% quantile) using characteristic (5% quantiles) of the material strength parameters an the bias b is not accounte for when calculating the characteristic loa bearing The failure moe is brittle The material partial factor (incl. an aitional uncertainty factor 1.05) is applie to the characteristic loa bearing capacity Using the sub-partial factors in section 3.2: Local buckling: = 1.5 Global buckling: = 1.5 V 0,05 V r 0,06 b 0,95 1 1,00 2 1,05 1, , b 1,28 Table A. Uncertainties relate to calculation moels from Felmann & Oppe (2007) an associate material partial factors. Table A shows examples of estimation of material partial factors for failure moes where the ominating failure moes such as bening. The statistical ata are from Felmann & Oppe (2007). It is note that these uncertainty measures are relate to the calculation moels escribe in Felmann & Oppe (2007). The following material partial factor (incl. an aitional uncertainty factor 1.05) is base on the following assumptions: The calculation moels in Felmann & Oppe (2007) or similar moels are use to estimate the characteristic loa bearing capacity (efine as a 5% quantile) using characteristic (5% quantiles) of the material strength parameters an the bias b is not accounte for when calculating the characteristic loa bearing The failure moe is uctile The material partial factor is applie to the characteristic loa bearing capacity Using the sub-partial factors in section 3.2 the following partial factor for ULS (strength) is obtaine: = 1.35 The above material partial factors are relate to the computational moels in Trumpf (2006). However, these moels are ifferent from the moels in JC (2016). Figures A2-A5 show the ratios Page 15 of 19

16 T WG between the loa bearing capacities using the moels in Trumpf (2006) an the moels in JC (2016) evelope by TC250 WG. oel in Trumpf for Flexural buckling with α = 0.5 for Square profile, 0.75 for weak axis, 0.5 for strong axis: oel in JC/WG: Figure A2. T an WG for Flexural buckling: with α = 0.5 for Square profile, 0.75 for weak axis, 0.5 for strong axis for Trunpf moel, from Plum (2015). Page 16 of 19

17 Figure A3. T WG for Flexural buckling: with α = 0.5 for Square profile, 0.75 for weak axis, 0.5 for strong axis for Trunpf moel, from Plum (2015). oel in Trumpf Lateral-torsional buckling with α = 0.5: oel in JC/WG: Page 17 of 19

18 Figure A. T an WG for Lateral-torsional buckling with α = 0.5, from Plum (2015). Figure A5. T WG for Lateral-torsional buckling with α = 0.5, from Plum (2015). Base on the results in Figures A2 an A it is seen that the ratio T WG can approximately an on the safe sie be put equal to 0.9 except for the case with flexural buckling with I- an U-profiles, Strong axis where the ratio can be put to 0.8. This implies that the material partial factors to be moifie to Local buckling: = 1.65 Global buckling: = 1.65 Page 18 of 19

19 In a similar way to account for the sparse ocumentation for the uncertainties relate to the computational moel for ULS (strength) the partial factor is moifie to: = 1.5 resulting in the values in Table 2.1 NA. Page 19 of 19