Water vapour balance in a building moisture exposure for timber structures

Transcription

1 Jnt Wrkshp f COST Actns TU1 and E55 September , Ljubljana, Slvena Water vapur balance n a buldng msture expsure fr tmber structures Gerhard Fnk ETH Zurch, Swtzerland Jchen Köhler ETH Zurch, Swtzerland Summary It s a knwn fact that the surrundng clmate,.e. the ars relatve humdty and temperature and the crrespndng changes ver tme nfluence the lad bearng behavr f tmber structural elements. Every attempt t grasp the many dfferent ways hw wd and ts mechancal prpertes nteract wth ts surrundng clmate take bass n the understandng f the specal way tmber desrbs and adsrbs water,.e. hw msture equlbrum n wd s reached dependng nt nly n the state f relatve humdty and temperature but als n the crrespndng tme hstry f the clmate. In the present fact sheet mdels t descrbe hw ndr and utdr msture and temperature varatns may be descrbed. Keywrds Wd, Msture Cntent, Relatve Humdty, Temperature. Cntext and relevance Many falures and malfunctns f tmber structures are related t the specal way tmber r wd nteracts wth the surrundng clmate. Durng the rle f COST Actn t became apparent that present engneerng best practce, namely cdes and standards, d nt accunt fr the clmate tmber nteractn wth suffcent reslutn. The partcpants f WG II dd dscuss pssble ways t cnsder clmate durng desgn. The results f these dscussns are a number f fact sheets n nteractns f msture and wd wth a specal fcus n materal prpertes. The present paper descrbes hw msture expsure fr tmber structures may be represented. Water vapur balance n a buldng Relatve humdty ϕ s defned as the relatnshp between the exstng vapur cntent c and the ttal vapur cntent c s (Equatn (1)) whch can be retaned n the ar at a gven temperature. The relatnshp between saturated vapur cntent and temperature s 85

2 llustrated n Fgure 1. It can be seen that ncreasng temperature enables the ar s maxmal water absrptn. c ϕ = (1) c s Fgure 1: Saturated vapur cntent [2] Under fxed cndtns a balanced state f the relatve humdty s acheved. Assumng that the relatve humdty n a buldng (rm) s unfrmly dstrbuted and that nly external ar s nfltrated, the water vapur balance can be descrbed as a functn between the suppled M & S, prduced M & P and exhausted water vapur cntent M & E. Fgure 2: Schematc llustratn f the water vapur balance n a buldng 86

3 M + M = M (2) S P E M S s the suppled water vapur cntent. T S = ϕ s T (3) M LV c The ventlatn rate L s defned by the number f rm vlume exchanges per hur. It depends n the transmssblty f the cnstructn and the type f ventlatn. The relatnshp between the abslute temperatures T, T cnsders the crcumstance that ar expands durng warmng. M P s the prduced water vapur cntent. Ths part ncludes the water vapur prduced r remved by ar dryng n rm plus the vapur added by dryng r wthdrawn by cndensatn f the surface. M E s the exhausted water vapur cntent. M = LV ϕ c (4) E s Analgcal t the suppled water vapur cntent the exhausted water vapur cntent can be calculated. By nsertng equatn (3) and (4) n (2) fllws (5) T LV ϕ c + M = LV ϕ c (5) s P s T Dsslvng f equatn (5) t ϕ fllws t: ϕ c T M s P = ϕ + cs T LV cs (6) The lwer bundary value f the relatve humdty s under ntensve ventlatn rate L and cnstant rm temperature. L ϕ c T = ϕ c T (7) s s Applcatn Example In ths example the ndr humdty fr a vrtual hall n Zürch s calculated. Therefre the utdr temperature T and the utdr humdty ϕ are gven and all ther values are taken as: 87

4 T = 18 C M& = g h P L= 1 h 1 V = 2 8 = 6m 2 The prduced water vapur cntent M & P represents persns and the ventlatn rate L crrelates t an average value fr a clsed, slated hall. In Fgure 3 and Fgure 4 the results fr the year 8 and fr ne week n august 8 are shwn. 1 Relatve humdty [%] Temperature [ C] ϕ ϕ T T Tme [mnth] Fgure 3: Illustratn f temperatures and humdty n 8 88

5 1 1 ϕ ϕ Relatve humdty [%] Temperature [ C] Tme [day] T T Fgure 4: Illustratn f temperatures and humdty frm f August 8 It s demnstrated that there s a crrelatn between the utdr temperature and the relatve ndr humdty ver a year. Furthermre t s shwn, that the varatn f the ndr humdty s hgher than the varatn f the utdr humdty (see Fgure 3). If the temperatures T and T are smlar (summer tme) the ndr humdty ϕ depends n utdr humdty ϕ (see Fgure 4). Lmtatns The physcal nteractns presented n ths fact sheet are useful t estmate the ndr clmate varatns based n the utdr clmate hstry, the ndr vapur prductn and the rate f ar vlume exchange. In general, there exst prfund data bases fr the utdr clmate hstry, whereas the remanng factrs have t be estmated. The presented mdels are nly vald fr the estmatn f an average ndr clmate. The effect f clmate n the behavur f tmber structural element mght be very much depended n rather lcal clmate cndtns,.e. n the surface f elements (wth a temperature dfferent frm the ar temperature), n crners r wthn wall assembles. Outlk t further research The use f ndr and utdr clmate mdels fr the assessment f msture nduced stresses n tmber structural elements requres an apprprate reslutn and classfcatn f the requred nput data. As t s necessary fr the mdellng f lads, smlarly as e.g. fr the cnsderatn f snw lads, utdr clmate varatn classes shuld be dentfed based n 89

6 clmatc regns. Furthermre buldng classes fr the classfcatn f the rate f ar vlume exchange shuld be defned and a set f benchmark values fr the ndr vapur prductn shuld be dentfed dependng n the use f the buldng. References [1] Köhler J., Srensen J.D., Faber M.H. (5). Prbablstc Mdelng f Tmber Structures. Prceedngs f the nternatnal Cnference n Prbablstc Mdels n Tmber Engneerng. Arcachn, France. [2] Fscher H.-M., Jensch R., Klpfer H., Freymuth H., Rchter E., Petzld K. (1997). Lehrbuch der Bauphysk. Schall Wärme Feuchte Lcht Brand Klma. Stuttgart. [3] Hens H. (7). Buldng Physcs Heat, Ar and Msture. Fundamentals and Engneerng Methds wth Examples and Exercses. Berln.