Usng Sem-Emprcal Models to Desgn Tmber Platform Frame for Stablty Dr Robert Harstans Lecturer n Structural/Tmber Engneerng Centre for Tmber Engneerng, Naper Unversty Ednburgh, UK. Prof Abdy Kerman Professor and R&D Consultant n Tmber Engneerng Centre for Tmber Engneerng, Naper Unversty Ednburgh, UK. Summary Tmber platform frame s growng ts market share n the UK predomnately n the low cost, hgh volume estate market. These market pressures are nfluencng buldng layout parameters and n partcular the requrement for a large percentage of openngs n houses wth narrow frontages and long gables s problematc when consderng structural stablty. By developng sem-emprcal models the nfluence of buldng parameters, ste locaton and wall detalng on stablty were quantfed. These models were used to develop a smplfed desgn technque for determnng rackng resstance requrements and have formed the bass of desgn rules detaled n The Scottsh Buldngs Standards Agency: Domestc Techncal Handbook 7 (SBSA, 7). In ths paper the developed models have been combned wth materel cost nformaton to llustrate the fnancal mplcatons of buldng layout requrements and recommendatons are made to mprove system effcency. Introducton Tmber platform frame house constructon n the UK s growng as a result of beng a sustanable off-ste modern method of constructon (MMC) and accounts for % of the UK market (7% market share n Scotland) accordng to the UK Tmber Frame Assocaton (7). However, the growth of tmber platform frame s predomnately n the low cost, hgh volume estate market whch has resulted n a desre to buld detached propertes wth a hgh level of openng n the shorter sdes of the buldngs wth a neglgble amount of openng requred n the longer sdes (Grfths et al 5) a) Durng constructon b) Masonry clad Fgure Examples of UK tmber platform frame constructon (Fgure ). The purpose of ths research was to use sem-emprcal models developed n accordance wth Brtsh Standards Codes of Practce n combnaton wth materal cost nformaton to demonstrate the fnancal mpact of such practces on tmber platform frame buldng systems.
Stablty of Tmber Platform Frame Fgure Basc wnd speed Vb (ms - ) shear wall n UK tmber platform frame normally consst of vertcal studs (typcally 8 or 45mm deep by 89, 5 or 4mm wde) at 6mm centres sngle or double sheathed wth 9 or mm OSB wth an nternal facng of.5mm plasterboard wth an overall heght of.4m. From a structural perspectve the wall can be regarded as a cantlevered daphragm loaded at the top plate (Fgure ). Usng the sheathng as a bracng the appled force s transferred to the foundaton n a very A tmber platform frame buldng s subjected not only to vertcal loadngs, such as self weght and mposed load, but also horzontal loadngs caused by wnds or earthquakes. In the UK earthquakes are not normally experenced at a level hgh enough to mpnge on structural desgn. Wnd has a number of effects on a buldng. Its drect acton s to cause pressure on one or more of the faces and sucton on the others. In addton to the prncpal wnd loads, the wnd may also cause sucton or pressure on the nner faces of the buldng (Alsmarker, 995). The current method for determnng the wnd loads on buldng n the UK s n accordance wth BS 699-:997 Loadng for buldngs - Part : Code of practce for wnd loads. The basc wnd speed map of the UK s shown n Fgure. The appled wnd acton on a tmber platform frame buldng s ressted by the shear or rackng walls of the system. A a) Typcal wall unt b) Prncpal structural behavour Fgure Tmber frame shear wall (Alsmarker, 995) effectve manner (Alsmarker, 995). The sheathng wll be ether naled or screwed to the frame and the type and level of fxng s of prmary mportance as t transfers the rackng load to the sheathng.
Snce the connectons between framng members are nomnal at best, the sheathng connectors also play a crucal role n transmttng loads between framng members. Sem-Emprcal Model For a tmber platform frame system to perform optmally n terms of structural resstance to appled wnd acton the rackng resstance requrement must be equal to rackng panel resstance. Therefore, extensve parametrc studes were undertaken to derve two sem-emprcal models (equatons & ) whch would determne rackng resstance requrement and rackng panel resstance based on a range of varables whch corresponded to normal buldng locatons and wall panel materal and fxng specfcaton (Harstans, 7). Q L r A α QB α Σ Rackng Resstance Requrement =.V b ( PA e ln( β ) + PB e ) () L Where: β s the aspect rato ( 4) V b s the basc wnd speed n accordance wth BS 699-:997 n metres per second ( V b ms - ) α s the ste alttude to dstance from the sea rato (Table ) ΣL s the total length of the nternal rackng walls n metres. L s the length of the external wall the nternal wall s parallel to n metres. r s the rackng resstance of the nternal rackng walls n klo Newton per metre run. P A, Q A, P B & Q B = x H + y H + z Where: β s the aspect rato. H s the heght to the rdge n metres (not exceedng storeys or 5m) x, y & z are as defned n Table Table Equaton constants x & y Varable Duo Mono P or Q x y z x y z P A Front -. -.885.64 -.6 -.4647.946 P A Gable -.75 5.686-8.55.77..595 P B Front..756 -.49.6.969 -.596 P B Gable.57 -.8.9468 -.494.665 -.897 Q A Front..8.77 -..6.654 Q A Gable.6 -.5.997.7 -.5.49 Q B Front -..6.646 -..6.654 Q B Gable -.6.56 -.7 -.4.45.68 Note: Where constants are negatves they have been converted to nverse a prevous converson requred so that an exponental trend could be appled. () Table Alttude to dstance ratos Dstance from sea. D sea (km) Alttude, < < > s α m.9.8.8 < 5m..9.9 < m..9.87 < 5m.8.66.57 < m...9 < m 5. 4.6 4.7 < 4m 6. 5.5 5.4
= A + B () ln( s) + B Op + A ln( s) + B Op + A ln( s) Rackng Panel Resstance [ ] [ ] Where: s s the permeter nal spacng n mllmetres (5 s mm) A & B are as defned n Table 4. Op s the percentage of openng n the wall ( Op 7%). Note: Wall types are gven n Table. Table Masonry claddng arrangement type Type Type Type For masonry walls wth buttresses or returns not less than 55mm length and not greater than 9m centre to centre. For masonry walls wth buttresses or returns at one end of wall not less than 55mm length wth the other end wthout buttresses or returns less than 55mm length and wall length not greater than 4.5m For masonry walls wthout buttresses or returns or wth buttresses or returns of less than 55mm length. Table 4 Equaton constants A & B Type Sheathng Arrangement A B A B A B & Storey Double -..8.4 -.5-4.5.89 Sngle -..79.4 -.98-4.5.4 Double -.9.6. -.79 -.74 7. Sngle -.8.54. -.69 -.4.78 Double -.6.4.8 -.6 -..75 Sngle -.5.7.8 -.5 -.75 9. Storey Double -..77.5 -. -4.95 4. Sngle -.9.66. -.86-4.8 8. Double -.7.48.9 -.68 -..99 Sngle -.7.45.9 -.6 -..9 Double -.5.6.7 -.5 -.67 9.7 Sngle -.5.4.7 -.46 -.44 6.9 Notes: Sheathng to be a mnmum of 9mm OSB or 9.5mm plywood. The nternal face of the wall panels are assumed to be lned wth.5mm plasterboard whch s connected to the wall panels wth.65 mm dameter plasterboard nals at least 4mm long, maxmum spacng5 mm. For wall type desgnaton see Table As prevously stated, f optmum performance of the system s to be acheved n terms or structural resstance to appled wnd acton then: Rackng Resstance Requrement = Rackng Panel Resstance
Therefore the followng polynomal expresson can be solved for Op as follows: b ± b 4ac Op = (5) a Where a = A + B (6) ln( s) ln( s) b = A + B (7) c = ln( s) + B.V Q L r B Σ ln( β ) + PB e ) + (8) L QA α α b ( PA e Note; that Equaton 5 leads to only one realstc soluton,.e. percentage openng of < %. Usng the model the nfluence of buldng parameters and rackng panel sheathng arrangement and level of fxty were analysed examples of whch are contaned n Fgure 4. It s to be noted that where the plots return to zero and form a straght lne, falure of the system has occurred as no percentage of openng can be ncorporated n the wall. 8 7 6 5 4 Gable; nal spacng, s = 5mm; Sngle sheathed Gable; nal spacng, s = 5mm; Sngle sheathed Gable; nal spacng, s = 5mm; Double sheathed Gable; nal spacng, s = 5mm; Double sheathed.5 Front; nal spacng, s = 5mm; Sngle sheathed Front; nal spacng, s = 5mm; Sngle sheathed Front; nal spacng, s = 5mm; Double sheathed Front; nal spacng, s = 5mm; Double sheathed Gable; nal spacng, s = mm; Sngle sheathed Gable; nal spacng, s = mm; Sngle sheathed Gable; nal spacng, s = mm; Double sheathed Gable; nal spacng, s = mm; Double sheathed.5 Front; nal spacng, s = mm; Sngle sheathed Front; nal spacng, s = mm; Sngle sheathed Front; nal spacng, s = mm; Double sheathed Front; nal spacng, s = mm; Double sheathed.5 Allowable Percentage Openng % Allowable Percentage Openng % 6 5 4.5.5.5 4 Aspect rato a) Wall type : Duo ptch 5.5m rdge heght 6 5 4.5.5.5 4 Aspect rato b) Wall type : Mono ptch 5m rdge heght Fgure 4 Allowable percentage openng relatve to aspect rato, buldng heght, wall make-up and type. 4 Cost Implcatons Cost per percentage openng s consdered wth respect to panel make-up (sheathng arrangement and nal spacng). Shown n Fgure 5 s the rackng resstance and assocated cost (based on 6 fgures) of a range of commonly specfed rackng panels. Usng the nformaton contaned n Fgure 5 Cost per percentage of openng s determned:
Cost per % of openng = Cost per metre run of wall / total allowable % of openng Cost per % of openng s shown relatve to sheathng arrangement, aspect rato Beta (β) and nal spacng n Fgure 6 when consderng the front of the buldng. 8 Rackng resstance kn/m run 7 6 5 4 x Sh; nals 5mm c/c x Sh; nals mm c/c x Sh; nals 5mm c/c x Sh; nals mm c/c x Sh; nals 5mm c/c Panel type x Sh; nals mm c/c x Sh; nals 5mm c/c x Sh; nals mm c/c Cost of materal /m run a) Rackng panel resstances b) Rackng panel cost 5 5 5 x Sh; nals 5mm c/c x Sh; nals mm c/c x Sh; nals 5mm c/c x Sh; nals mm c/c x Sh; nals 5mm c/c Panel type x Sh; nals mm c/c x Sh; nals 5mm c/c x Sh; nals mm c/c Fgure 5 Resstance and cost for gven make-ups (Table for detals)..9.8.7.6.5.4 7 9 Front: Beta = sngle sheathed Front: Beta =.6 sngle sheathed Front: Beta = sngle sheathed Front: Beta = sngle sheathed 5 7 9 5 Front: Beta = 4 sngle sheathed Front: Beta = double sheathed Front: Beta =.6 double sheathed Front: Beta = double sheathed Front: Beta = double sheathed Front: Beta = 4 double sheathed Cost per percentage of openng per m run /%Op...8.6.4.. 5 75 5 5 75 a) Wall type : Duo ptch & 5.5m rdge heght.. Cost per percentage of Openng per m run /%Op 9. 8. 7. 6. 5. 4.... Cost per percentage of openng /%Op 5.. 5.. 5.. 5 75 5 5 75. 5 75 5 5 75 b) Wall type : Duo ptch & m rdge heght c) Wall type : Duo ptch & 5m rdge heght Fgure 6 Allowable percentage openng cost relatve to aspect rato, buldng heght, wall make-up and wall type From Fgure 5 & 6 the followng conclusons are drawn: It s shown that Wall Type provdes the most added shelter and as a result more economcal desgn s acheved.
It s more cost effectve to reduce the spacng between nals than add a secondary layer of sheathng and t s shown that at reduced nal spacng sngle sheathed panels provde a hgher degree of value n terms of level of openng. However, as nal spacng s ncreased there are occasons where a double sheathed panel s more cost effectve than a comparable sngle sheathed panel. It s demonstrated that as aspect rato, β, s ncreased the cost effectveness of the openngs s mproved. 5 Conclusons The developed model has been used to asses the fnancal and structural mplcatons of the archtectural layout on tmber platform frame buldngs, whch n normal UK house constructon requres a hgh level of percentage openng n the front and back of houses and a neglgble amount n the gable walls. From a fnancal perspectve t has been demonstrated that n order that the requred level of openng n the front of a house does not mpnge on system cost there are two vable optons avalable:. The percentage of openng can be reduced to a level whch s acceptable to negate the requrement for extra sheathng but can be acheved by means of reduced nal spacng.. The aspect rato of the system s ncreased wthout reducng the nternal area, as long as the gables are capable of carryng the ncreased load, allowng addtonal openng to be acheved wthout an ncrease n cost. The sem-emprcal models contaned n ths paper were derved and used to provde a smplfed desgn technque for determnng rackng resstance requrements publshed by the Scottsh Buldngs Standards Agency (7) n Structural Gudance for Small Buldngs: Techncal Handbook 7. 6 References [] Alsmarker, T. (995), Daphragms and Shear Walls, Tmber Engneerng Step, Lecture 4, ISBN 9 5645 8. [] Brtsh Standards Insttuton (BSI). (996). BS 568: Secton 6.: 996 Structural Use of Tmber, Part 6. Code of Practce for Tmber Frame Walls, Secton 6. Dwellngs Not Exceedng Four Storeys, ISBN 58 4969 7. [] Brtsh Standards Insttuton (BSI). () BS 568-:: Structural Use of Tmber Part : Code of practce for permssble stress desgn, materals and workmanshp, ISBN 58 4. [4] Brtsh Standards Insttuton (BSI). () BS EN 99--4:5 Eurocode : Actons on Structures - Part -4: General actons Wnd. ISBN 58 45959 4. [5] Brtsh Standards Insttuton (BSI). (). BS 699-:997: Loadngs for buldngs, Part : Code of practce for wnd loads, ISBN 58 7447. [6] Grffths, B., Blass, H. & Kallnser, B. (5) A Unfed Method for the Rackng Resstance of Tmber Framed Walls for Incluson n Eurocode 5, Internatonal Councl for Research and Innovaton n Buldng and Constructon, Workng Commsson W8 Tmber Structures, Meetng Thry-Eght, Karlsruhe, Germany August 5. [7] Harstans, R. (7) Optmsaton of Tmber Platform Frame Constructon PhD Thess, Naper Unversty, Ednburgh, Scotland, UK, EH 5DT. [8] Scottsh Buldngs Standards Agency (SBSA) (7) The Scottsh Buldng Standards Agency: Domestc Techncal Handbook 7, Denholm House, Almondvale Busness Park, Lvngston, EH54 6GA. [9] UK Tmber Frame Assocaton (UKTFA). (5) Tmber Frame Facts and Fgures, www.tmber-frame.org, UKTFA, The e-centre, Cooperage Way Busness Vllage, Alloa.