A Comparison of Design, Construction and Dynamic Performance of Timber Floors in the UK and Finland

Transcription

1 Napier University Schoo of Engineering and the Buit Environment Centre for Timber Engineering Merchiston Campus 10 Cointon Road Edinburgh EH10 5DT 26 November 2007 Revised: June 2009 A Comparison of Design, Construction and Dynamic Performance of Timber Foors in the UK and Finand Scientific Report by Jan Weckendorf Short Term Scientific Mission of COST Action E55 -Modeing the performance of timber structures- Proposer: Host: Host Institution: Duration: Dr. Binsheng Zhang Dr. Tomi Toratti VTT Technica Research Centre of Finand October 2007

2 A Comparison of Design, Construction and Dynamic Performance of Timber Foors in the UK and Finand i Contents Page 1. Introduction Objectives 1 2. Design Guides for Controing Foor Vibrations Design in the UK and Finand Summary regarding design criteria 2 3. Investigation of Finnish and British Fooring Systems The Finnish foor The British foor Summary of construction practices 5 4. Investigation of Design Criteria Investigation of the Finnish fooring structure Investigation of the British fooring structure Summary of investigations Concusions and Recommendations for Future Work Acknowedgements References 14

3 A Comparison of Design, Construction and Dynamic Performance of Timber Foors in the UK and Finand 1 1. Introduction A Short Term Scientific Mission (STSM) of COST Action E55 - Modeing the performance of timber structures - has been undertaken for exchanging knowedge and experiences about the dynamic performances of timber fooring structures. Humans in residentia or office buidings can sense excessive foor vibrations, which produce a certain eve of discomfort. Unsatisfying vibrationa foor behaviours are serviceabiity issues. These issues are not satisfactoriy addressed in the current design standards. Furthermore, athough the estabishment of the Eurocodes provides harmonisation of design criteria within the member countries, this harmonisation is not reached for foor vibration design in different countries such as Finand and UK. The EC5 design criteria are either party modified (UK Nationa Annex) or competey superseded (Finnish Nationa Annex). Research in the area of foor vibrations has been continuousy carried out at Napier University in Edinburgh of Scotand and at VTT Technica Research Centre of Finand in Espoo, whereas different methods and techniques are used at the two institutes, which are focused on different aspects. The research that has aready been undertaken at VTT incudes investigating human discomfort due to vibrations of ight-weight foors and cassifying the structura foor performances. Fundamenta natura frequency, acceeration, veocity and dynamic dispacement of the fooring systems were the main parameters examined (Taja et a., 2002; Toratti et a., 2002, 2006). The research carried out at Napier University focuses on the effect of structura and non-structura modifications on the dynamic response of timber fooring systems. Natura frequencies, mode shapes, damping ratios and static defections are the parameters of main interest (Weckendorf et a., 2006, 2007). In brief, whie the research at VTT is especiay aimed to assess and cassify the foor performances, the research at Napier aims to identify contribution of individua structura and non-structura components on variation in the dynamic response. This has formed a strong basis for the undertaken STSM, for exchanging and enhancing the expertise with respect to different measurement and anaysis procedures, and design, construction and assessment methods. 1.1 Objectives The Memorandum of Understanding (MoU) of COST Action E55 states that "attributes such as high performance regarding reiabiity, serviceabiity and durabiity are generay not associated with timber as a buiding materia." One of the main objectives of the Action is to improve "the knowedge concerning the behaviour of timber structura eements". Excessive foor vibrations are serviceabiity issues. The described research projects wi provide a better understanding of the probems and show the effect of structura modifications on dynamic foor performances. The MoU further states, "However, whereas the codes and reguations for the design of concrete and stee have undergone a remarkabe modernisation over the ast two to three decades, codes and reguations for the design of timber structures are faing significanty behind." In this STSM it is specificay concentrated on the different design, assessment and construction methods in Finand and the UK due to the fact that reconsideration of the design rues with regard to foor vibrations is required. Contribution to design criteria is continuousy made by VTT and is aimed to be aso made by Napier University in the near future.

4 A Comparison of Design, Construction and Dynamic Performance of Timber Foors in the UK and Finand 2 2. Design Guides for Controing Foor Vibrations The Eurocodes have been estabished to serve as pan-european standards in form of harmonised design criteria within the member countries to buid a common basis for design, research and deveopment. The design of timber structures is covered in Eurocode 5 (EC5). The criteria associated with timber foor vibrations are part of the serviceabiity imit states (SLS) in EC5. Nationa Annexes to EC5 provide the modified or additiona design criteria by considering oca design aspects. The design rues in EC5 to contro timber foor vibrations are based on the research carried out by Ohsson (Ohsson, 1982, 1988). A foor having a fundamenta frequency above 8 Hz is considered to be a high-frequency foor, where "the resutant vibration is made up of a owfrequency semi-static component [ ] and a number of resonance dominated components [ ], which are of the same magnitude, or arger than, the semi-static component" (Ohsson, 1994). Limiting the unit point oad defection of the foor is beieved to satisfy the foor performance regarding the semi-static component. The resonance dominated components are to be controed by imiting the veocity response. Referring to the EC5 it is thus required that for foors with a fundamenta natura frequency greater than 8 Hz the defection under a unit point oad and the unit impuse veocity response of the foor are imited. Equations for cacuating the fundamenta natura frequency, unit impuse veocity response and the veocity imit are provided. A imit for the unit point oad defection and a method for cacuating the defection are not given. The EC5 does not provide guidance for ow-frequency foors. 2.1 Design in the UK and Finand To design the foors regarding their dynamic performance, the design rues of EC5 are adopted in the UK. Due to the ack of formua and imiting vaue regarding the defection criterion in EC5, guidance for determining the defection and its imit is introduced in the UK Nationa Annex (UK NA to EC5-1-1). Furthermore, the damping ratio for cacuating the design imit for the unit impuse veocity response in EC5 has been doubed in the UK NA. Competey new design criteria are estabished in the Finnish Nationa Annex (FI NA to EC5-1-1). After cassifying the foors as ow- or high-frequency foors at a threshod eve of 9 Hz, ony a defection imit appies for high-frequency foors. Guidance for ow-frequency foors is not given. Tabe 1 provides a comparison of the design guideines used in Finand and the UK. Tabe 2 shows the cacuation methods to be used and Tabe 3 shows the imiting vaues. For detais of the individua factors, see EC5, UK NA to EC5-1-1 and FI NA to EC Summary regarding design criteria There are certain imitations and uncertainties when foors are designed with respect to the EC5 criteria. First of a, it is distinguished between ow-frequency foors and high-frequency foors. Whereas design criteria are provided for high-frequency foors, guidance for the design of owfrequency foors is not given. The design thus needs to assure a fundamenta frequency that is above the given threshod for cassification. For the design of high-frequency foors, unit point oad defection and its imit need to be determined. Formuae for the cacuations of these and the

5 A Comparison of Design, Construction and Dynamic Performance of Timber Foors in the UK and Finand 3 corresponding imits are not incuded. The cacuation methods for the veocity response and its imit are questionabe since their vaidation is not easiy proven (Hu, et a., 2001; Zhang, 2004). Tabe 1: Comparison of foor cassification and design guidance Country UK (based on EC5) Low-frequency foor High-frequency foor Condition Guidance Condition Guidance f 1 8 Hz N/A f 1 > 8 Hz FI (NA) f 1 < 9 Hz N/A f 1 9 Hz 1) Limiting unit point oad defection w 2) Limiting unit impuse veocity response v Limiting unit point oad defection δ Tabe 2: Design equations for cacuating frequency, defection and veocity Country Fundamenta frequency Point oad defection Veocity response UK FI (NA) "For a rectanguar foor [...], simpy supported aong a four edges [...]" (EC5-1-1) f 1 f π ( EI) k w = 1 = ( ) 2 2 joist m for 2-side supported foors: f 1 π = 2 2 ( EI) m for 4-side supported foors: π = 2 2 ( EI ) 1+ 2 b m 2 + b 4 ( EI ) b ( EI ) dist EI 3 eq k amp 2 F 42 k ( EI) = min 3 F 48 s ( EI) δ δ v = ( n ) 4 40 m B Cassification of the structures as ow- and high-frequency foors and assessment of their dynamic performances differ in Finand and the UK as can be easiy seen from the design rues. There are two formuae provided in the FI NA to cacuate the fundamenta frequency. One is used for foors supported aong two edges and the other for foors supported aong four edges. The formua in the FI NA used for two-side supported foors is the one used in EC5 "for a rectanguar foor [...] simpy supported aong a four edges [...]." This comment in the EC5 is irritating since it creates the impression that the formua is rather to be used for foors supported aong four edges. However, this simpified formua may be more accurate for two side supported foors but is aso used for foors with supports aong four sides. The Finnish formua for foors with supports aong a sides considers stiffness in transverse direction, which is negected in the simpified equation. N/A

6 A Comparison of Design, Construction and Dynamic Performance of Timber Foors in the UK and Finand 4 It can be noted that the formuae for cacuating the defection are adopted from the genera defection equations for beams and pates but have been modified in the UK NA to account for factors such as oad distribution. Aso, detaied guidance on the design of more compex fooring structures is not given. The uncertainties of the formuations are more comprehensiby shown in the foowing section where simpe and compex structures from the UK and Finand are assessed by the avaiabe design criteria. Tabe 3: Design imits for frequency, defection and veocity Country Fundamenta frequency Point oad defection UK (NA) FI (NA) f 1 > 8 Hz f 1 9 Hz 1.8 mm/kn for 4000 mm 16500/ 1.1 mm/kn for > 4000 mm ( ) ( EI ) EI b min mm/kn for 6000 mm b 0.5 mm/kn for > 6000 mm An additiona 0.5 mm defection can be aowed in case of foating and raised foors Veocity response v b (f 1 ζ - 1) where ζ = 0.02 (EC5: ζ = 0.01) N/A 3. Investigation of Finnish and British Fooring Systems Before the STSM started, fooring structures had been buit and tested in aboratory conditions at VTT and Napier University. A Finnish and a British timber fooring system have been seected for a detaied anaysis using the cassification and assessment methods of EC5 and the Finnish and UK Nationa Annexes. The fooring structures are representing the typica construction styes in either country and are described beow. 3.1 The Finnish foor The Finnish test foor had dimensions of 6.0x4.3 m. LVL joists of 51x400 mm, spaced at 600 mm centres, were used for the structure. The ends were connected to LVL rim boards, which had the same dimensions as the joists. The foor was simpy supported on timber was aong a 4 sides and decked with 18 mm thick pywood boards which were connected to the joists using gue and screws. A 60 mm concrete screed was added on top of a 30 mm thick hard minera woo (ASL2) ayer that was paced on the pywood deck. The concrete screed had no structura connection to the fooring structure. LVL bockings, staggered between the main LVL foor beams at the third points of the span and gued to the deck, and tension bars beow the rows of bockings were used as transverse stiffeners. The pywood decking ayer and the tension bars are the ony continuous primary foor structura eements in the transverse direction. However, aso the concrete screed heped to distribute the oad in the direction perpendicuar to the joist direction. Figure 1 shows a Finnish test foor in construction, before isoation and concrete ayer were added, representing a typica Finnish fooring structure.

7 A Comparison of Design, Construction and Dynamic Performance of Timber Foors in the UK and Finand 5 Figure 1: Typica Finnish foor, simiar to the test foor described: constructed with main soid timber beams, bocking eements, tension bar and pywood deck 3.2 The British foor The British test foor had dimensions of 3.5x2.44 m. I-joists with a depth of 220 mm were spaced at 400 mm centres. The ends were fixed to Guam rim boards. The 19 mm thick chipboard decking ayers were fixed to the joists using screws at a spacing of 300 mm. The foor was supported on timber beams aong 2 edges, whereas the bottom fanges of the I-joists were connected to the supports using screws at the joist ends. Figure 2 shows the British test foor. 3.3 Summary of construction practices In Finand LVL or soid timber beams are usuay used for constructing fooring structures. Bockings as transverse stiffeners are recommended to be used. Furthermore, it is a standard procedure to use adhesives in addition to screws for fixing the pywood decking to the joists. A concrete screed is in some cases aid on top after hard minera woo isoation has been added. In the UK, I-joists are used nowadays to form the fooring structures. Adhesives are ony occasionay used for fixing the decking to the joists. Concrete screed is usuay not utiised for timber foors in the UK.

8 A Comparison of Design, Construction and Dynamic Performance of Timber Foors in the UK and Finand 6 Figure 2: Typica British foor buit with I-joists and chipboard deck for a defection test 4. Investigation of Design Criteria The Finnish and British fooring structures were examined with respect to the design rues of EC5 ony, EC5 with the UK NA and the FI NA. Comparisons were made for the measured and cacuated vaues incuding the imits and for the design to the nationay determined parameters (NDPs) and criteria. 4.1 Investigation of the Finnish fooring structure The Finnish fooring structure has been assessed at two different construction stages: before and after the concrete screed was added to the fooring system. Due to the pywood ayer being gued to the foor joists, fu composite action of pywood deck and joists was assumed. Since the EC5 does not give any advice for consideration of composite action and this effect may sometimes be negected for simpicity, the cacuations for the fundamenta natura frequencies have been repeated where composite action was not considered. For a other cacuations composite action was incuded. To determine the stiffness due to bocking and tension bars in the transverse direction, composite and non-composite I-sections have been assumed to be effective, where the tension bar acted as the bottom fange, the pywood deck as the top fange and the bocking as the web. For not overestimating the transverse stiffness, however, a width of 0 mm has been assumed for the web.

9 A Comparison of Design, Construction and Dynamic Performance of Timber Foors in the UK and Finand 7 From Figure 3, it can be seen that the predicted frequencies are significanty higher when fu composite effect is considered. It can aso be noted that the mass of the concrete drasticay reduces the fundamenta frequencies in a region that becomes critica for design. The predicted frequencies based on the design rue of the FI NA for foors supported aong four edges and of the simpified design rue of EC5 are very cose if ony the timber structure is considered and composite action negected. In the cases of the foor without concrete screed but with consideration of composite action and of the foor with concrete screed, the cacuations to the Finnish formua resut in higher fundamenta frequencies by up to 23 % compared to the cacuations to the EC5 formua. If the structure has no concrete screed, the fundamenta frequency is we above the threshods but over-predicted if fu composite effect between the deck and joists is assumed (Figure 3(a)). For the fooring structure with concrete screed, the predicted frequency under consideration of composite action and with respect to Finnish design is the ony one over-predicting the actua vaue (Figure 3(b)). From Figure 4 it can be noted that the predicted defection vaues are 52 % and 217 % arger than the measured vaues with respect to UK design. Using the Finnish criteria eads to cose prediction of the actua defection in absoute terms. Athough the added concrete screed has haved the actua foor defection in comparison with the foor without the concrete screed, the predicted defection remained unchanged among the two different structures with respect to the UK NA equation. The defections cacuated using the UK design rue are 73 % and 138 % higher than those determined from the Finnish formua. In a cases, the foors woud resut in satisfactory performances athough the imits show that the UK design criterion is much more generous since the aowabe defection is more than doube as much compared to the imit regarding Finnish design. The veocity criterion is not part of the Finnish design guide but is incuded in EC5 and the UK NA. From Figure 5 it can be noted that the aowance with respect to the UK NA is much higher than the one to the EC5. The addition of the concrete screed consideraby reduced the veocity response and the imits. However, the veocity response is not a critica criterion in this exampe.

10 A Comparison of Design, Construction and Dynamic Performance of Timber Foors in the UK and Finand 8 Frequency f 1 [Hz] Design to Finnish NA Design to EC5 inc. UK NA no composite action fu composite action (a) Without concrete screed f 1, meas = Hz FI NA threshod EC5 threshod Frequency f 1 [Hz] Design to Finnish NA Design to EC5 inc. UK NA no composite action fu composite action (b) With concrete screed f 1, meas = Hz FI NA threshod EC5 threshod Figure 3: Measured and predicted fundamenta frequencies with respect to the design threshods in Finand and UK for the Finnish foor

11 A Comparison of Design, Construction and Dynamic Performance of Timber Foors in the UK and Finand 9 Defection w [mm] ] Design to Finnish NA Design to EC5 inc. UK NA (a) Without concrete screed UK NA imit FI NA imit w meas = 0,25 mm Defection w [mm] ] Design to Finnish NA Design to EC5 inc. UK NA (b) With concrete screed UK NA imit FI NA imit w meas = 0,12 mm Figure 4: Measured and predicted point oad defections with respect to the design imits in Finand and the UK for the Finnish foor

12 A Comparison of Design, Construction and Dynamic Performance of Timber Foors in the UK and Finand Veocity response v [(m/s)/(ns)] ] Design to EC5 and UK NA (a) Without concrete screed UK NA imit EC5 imit Design to EC5 and UK NA Veocity response v [(m/s)/(ns)] ] UK NA imit EC5 imit 0.00 (b) With concrete screed Figure 5: Predicted veocity responses and imits with respect to EC5 and the UK NA for the Finnish foor

13 A Comparison of Design, Construction and Dynamic Performance of Timber Foors in the UK and Finand Investigation of the British fooring structure The deck of the British fooring structure was fixed to the joists using screws, which means that a certain degree of composite action was achieved. The fundamenta frequencies were cacuated by assuming no composite action first and then an appropriate eve of composite action due to the screw-fixing. In a other cacuations composite action was accounted for. The degree of composite action has been cacuated using the guideines in EC5 ( B.2 in EC5). The formuae for cacuating the natura frequencies of the British foor were the same for Finand and the UK since this foor was supported aong two edges ony so that there are no differences in frequency predictions (see Tabe 2). Figure 6 shows that a cacuated natura frequencies ie we above the threshod eves, but it must be mentioned that the fooring structura eements were sighty oversized. However, no matter whether composite action was considered, the measured fundamenta natura frequency was over-predicted by up to 22 %. Frequency f 1 [Hz] Design to Finnish NA Design to EC5 inc. UK NA no composite action fu composite action f 1, meas = Hz FI NA threshod EC5 threshod Figure 6: Measured and predicted fundamenta frequencies with respect to the design threshods in Finand and UK for the British timber foor From Figure 7 it can be seen that the design to the FI NA provides reativey accurate prediction of the unit point oad defection, the design to UK NA underestimates the actua foor defection. Whereas the measured and predicted defection vaues are we beow the UK imit and woud thus be regarded to be acceptabe, they are we above the Finnish imit and thus regarded to be unacceptabe in Finand. Figure 8 shows that the veocity response is not critica for design in this exampe. However, it can be ceary noted that the corresponding imit to the UK NA is far more generous than the one to EC5.

14 A Comparison of Design, Construction and Dynamic Performance of Timber Foors in the UK and Finand Design to Finnish NA Design to EC5 inc. UK NA UK NA imit Defection w [mm] ] w meas = 1.30 mm FI NA imit Figure 7: Measured and predicted point oad defections with respect to the design imits in Finand and the UK for the British timber foor Veocity response v [(m/s)/(ns)] ] Design to EC5 and UK NA UK NA Limit EC5 Limit Figure 8: Predicted veocity responses and imits with respect to EC5 and the UK NA for the British timber foor

15 A Comparison of Design, Construction and Dynamic Performance of Timber Foors in the UK and Finand Summary of investigations For the cassification of a fooring system as high-frequency foor in Finand, the fundamenta natura frequency needs to be above a threshod that is more than 12 % above the EC5 (and thus UK) requirement. The design then reies on a static defection criterion where the aowabe defection is usuay beow the UK imit, possiby consideraby. In the EC5 and the UK NA, a veocity response criterion is incuded additionay. The simpified formua in EC5 for cacuating the fundamenta natura frequency of the foor supported aong a four edges gives simiar predictions as the precise formua of the FI NA for the pure timber structure if negecting the composite action. Otherwise, using the Finnish formua eads to resuts, which can be notaby higher than those from the simpified formua. The measured unit point oad defections of the two investigated Finnish fooring structures are overestimated by at east 73 % with respect to the UK design equation. In one case, the prediction using the Finnish formua is sighty beow the actua vaue, in the other case sighty above. Both criteria yied predictions cose to the measurement for the UK timber foor, but the defection is under-predicted to the UK NA and may thus not be on the safe side. The veocity imit to the UK NA is more generous than that to the EC5 and is 65 % % higher in the exampes shown. The conducted cacuations revea that it is a compex task to make accurate assumptions for determining the transverse stiffness if, beside the decking ayers, transverse stiffening eements are used. Simpe guidance for estimating the crosswise stiffness is neither provided in the Eurocode nor propery defined in the Nationa Annexes of Finand and the UK. The exampes aso demonstrate that it is uncear whether composite action shoud be accounted for in the cacuation of the fundamenta natura frequency. 5. Concusions and Recommendations for Future Work The research undertaken for the STSM shows the differences in the design, construction and assessment methods in Finand and the UK. Overa it can be observed that the Finnish design rues are stricter than those of the UK, the atter being even more generous than the criteria in EC5. Whereas a three fooring types investigated show satisfactory performances with regard to the UK design rues, one of the systems woud be cassified as unacceptabe to the Finnish standards. Nevertheess, neither in UK nor in Finand can the dynamic parameters be predicted accuratey in a cases, which coud resut in miscassification of fooring structures. Reconsideration of the design rues and guidance for accuratey determining the crosswise stiffness as we as recommendations regarding consideration of composite effects are needed. Future research is aso needed to show whether different construction practices justify different design methods in different countries. The procedures for more accuratey cacuating the foor performances, threshods and imits need to be further harmonised. Furthermore, parametric studies on the veocity response criterion as currenty used in the UK are required to assess whether this design rue is redundant or needs modification due to a reativey high imiting vaue, which may satisfy this criterion easiy in common cases. This may then need further reconsideration of the given set of design criteria regarding dynamic foor performances in the EC5 to produce appropriate guidance for the UK NA.

16 A Comparison of Design, Construction and Dynamic Performance of Timber Foors in the UK and Finand Acknowedgements The Short Term Scientific Mission at VTT Technica Research Centre of Finand was very vauabe since it provided the opportunity for meeting experts in the fied of dynamic performances of fooring structures and obtaining access to test data and iterature not avaiabe in the UK and eventuay aowed a comparison of design rues, construction practices and assessment methods of Finand and the UK. The mission offered thus good networking opportunities, widened the knowedge and produced resuts, which are vauabe for research in the fied of ight-weight foor vibrations. In particuar, the proposa for this STSM by Dr. Binsheng Zhang, the very kind and supporting supervision of the host Dr. Tomi Toratti, the hep of VTT scientists, the provision of materia and faciities from VTT and the kind support of the COST committee given for the accompishment of this STSM are a gratefuy acknowedged. Further acknowedgment is due to James Jones and Sons Ltd., which provided the materias for the UK test foor. 7. References British Standards Institution (2004), BS EN : Eurocode 5 [EC5-1-1] - Design of timber structures - Part 1-1: Genera - Common rues and rues for buidings. British Standards Institution (2004), The UK Nationa Annex to EN [UK NA to EC5-1-1]: Design of timber structures - Part 1-1: Genera - Common rues and rues for buidings. COST Action E55 Committee (2006), Memorandum of Understanding, Brusses, Begium. Hu L., Chui Y.H. and Onysko D.M. (2001), Vibration serviceabiity of timber foors in residentia construction, Progress in Structura Engineering and Materias. Ohsson S. (1982), Foor Vibrations and Human Discomfort, PhD thesis, Chamers University, Sweden. Ohsson S. V. (1988), Springiness and Human Induced Foor Vibrations - A design guide, Swedish Counci for Buiding Research, Sweden. Ohsson S. V. (1994), Foor vibration - A serviceabiity probem, Proceedings of the Austraasian Structura Engineering Conference, Sydney, Austraia. Taja A., Toratti T. and Jaervinen E. (2002), Lattioiden värähteyt - Suunnitteu ja kokeeinen arviointi, VTT Technica Research Centre of Finand, Espoo, Finand. Toratti T., Taja A. and Jaervinen E. (2002), Cassification of human induced foor vibrations in buidings: A wood-concrete composite foor exampe, The 7 th Word Conference on Timber Engineering (WCTE), Shah Aam, Maaysia. Toratti T. and Taja A. (2006), Cassification of human induced foor vibrations, Journa of Buiding Accoustics, Essex, UK, Weckendorf J., Zhang B., Kermani A., Dodyk R. and Reid D. (2006), Assessment of vibrationa performance of timber foors, The Word Conference on Timber Engineering (WCTE), Portand, Oregon, USA. Weckendorf J., Zhang B., Kermani A. and Reid D. (2007), Vibrationa behaviour of timber foors experimenta investigations, The 3rd PRoBE Conference, Gasgow Caedonian University, Gasgow, UK. VTT Technica Research Centre of Finand (2007), The Finnish Nationa Annex to EN [FI NA to EC5-1-1]: Puurakenteiden suunnitteu - Osa 1-1:Yeiset säännöt ja rakennuksia koskevat säännöt. Zhang B. (2004), Parametric study on the design of timber foor joists to Eurocode 5 and Nationa Annex, Technica document for BSI Technica Committee B/525/5, TRADA, UK.