Experimental study on the ultimate strength of R/C curved beam

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1 Fraur Mhani Conr and Conr Sruur - High Prforman, Fibr Rinford Conr, Spial Loading and Sruural Appliaion- B. H. Oh, al. (d) 2 Kora Conr Iniu, ISBN Exprimnal udy on h ulima rngh R/C urvd bam T. Tamura & H. Muraa Tokuyama Collg Thnology, Syunan, Japan ABSTRACT: Th ulima rngh a urvd R/C bam i invigad xprimnally. A urvd R/C bam i laifid a a aially indrmina ruur aording o h ruural boundary ondiion and i ubjd o a orion momn. Th orion momn gnra diagonal nil rak on h onr urfa, hn h bam i ubjd o a lo orion. An appropria arrangmn rbar i hrfor rommndd undr uh ondiion. Hovr, h ulima orion rngh an R/C mmbr dpnd on a ombinaion vral faor, o a univral hory hould b ablihd for h urvd RC bam. Paramr adopd hr ar h radiu urvaur, axial for, and har pan raio. Thn h influn ho paramr on h fraur bhavior h R/C urvd bam a obrvd. From h xprimnal rul, i a onfirmd ha h radiu urvaur and axial for aff h fraur bhavior h R/C urvd bam. INTRODUCTION In rn yar, h urvd bam ha bn adopd for larg-al onr ruur uh a highay inrhang or a pr-r onr ruur. A urvd bam riv h orion momn in ordr o kp h balan h for in h hol ruur again h prpndiular load, a hon in Figur. During an xrnal for, uh a an arhquak, a urvd ruur i ubjd o a ombind for ha i ompod h axial for, h bnding momn, h har for, and h orion. Whn h urvaur a urvd bam i mall, h ulima rngh may b abl o ihand h influn h orion momn. Tha i, h ulima rngh h mmbr in uh a a i didd in ihr h ulima momn or h ulima har rngh. On h ohr hand, ulima har rngh a rinford onr mmbr go up du o h axial ompriv for. In h a a urvd bam, h influn h axial ompriv for for ulima har rngh i no lar. Th auhor hav udid h ulima rngh a rinford onr mmbr ubjd o h bnding momn, h har for, and h axial for. Th rlaionhip bn ulima har rngh and an axial for h bam a larifid. Morovr, rarh on h urvd bam a don fouing on h urvaur. Figur. Curvd bam. In hi rarh, h fraur propri a rinford onr urvd bam a udid xprimnally a o h influn axial for and har pan dph raio. 2 EXPERIMENTAL PROGRAM 2. Spimn Figur 2 ho h bam. Thr ar hr yp pimn o diu in rm h rlaionhip bn ah faor and h urvaur. Nin pimn r providd. All h pimn for xprimn had h am dimnion. To dformd bar (D3) r plad a h nil rinformn and h ompriv rinformn. Alo, on round bar a arrangd a h nr h ro-ion o inrodu h axial for. Elvn irrup (Φ6) r plad a 5m inrval. Th marial propri boh h main and har rbar ar hon in Tabl. Tabl 2 ho h marial propri h onr.

2 J D ( h, T h D3 φ8 φ6 2 5 x5=5 5 h rlaiv humidiy h and 8 mpraur T (Bažan & Najjar 972). Th (a) moiur Sraigh bam ma R balan rquir R=4 (b) Curvd bam R 8 R=2 Panazopoulo & Mill 995). I i raonabl o () Curvd bam R2 aum ha h vaporabl ar i a funion Figur rlaiv 2. Cro-ion humidiy, h, a dgr urvd bam. hydraion,, and Tabl = ag-dpndn. Marial propri orpion/dorpion rbar. iohrm (Norling Mjonll 997). Undr hi aumpion and Rbar by ubiuing Equaion ino Equaion 2 on obain Rbar yp D φ 6 Elai modulu E (GPa) h Tnil rngh + ( Df u h) (MPa) = & & + 58 & n (3) h h Yild r σ y (MPa) hr Tabl 2. Marial /h i h lop h orpion/dorpion propri onr. iohrm (alo alld moiur apaiy). Th Conr govrning quaion (Equaion 3) mu b ompld by appropria boundary and iniial ondiion. Elai Th modulu rlaion bn E h (GPa) amoun 24.9 vaporabl Compriv ar and rngh rlaiv humidiy f (MPa) i alld 29.6 adorpion Tnil rngh f (MPa) 2.84 iohrm if maurd ih inraing rlaiviy humidiy and dorpion iohrm in h oppoi a. Ngling hir diffrn (Xi al. 994), in 2.2 h folloing, T apparau orpion and produr iohrm ill b ud ih Th rfrn oulin o boh h orpion i hon and dorpion in Figur ondiion. 3, and h By apparau h ay, i if hon h in hyri Figur 4. Th h apparau moiur i ompod iohrm ould an b oil akn prur ino auaor aoun, onrolld o diffrn by an rlaion, lro-hydrauli vaporabl ar rvo v mhanim. rlaiv humidiy, Boh mu upporing b ud poin aording ar o fixd h for ign vrial h variaion and horizonal h dirion rlaiviy and humidiy. roaion Th a hon hap in Figur h 5. orpion In h a iohrm h for mmbr HPC i inflund bing ubjd by many o axial paramr, for, h pially axial omprion ho ha influn i fir xn inrodud and ra ino boh h nd hmial h raion bam via and, a longiudinal in urn, jak drmin and i hld por onan ruur and afr por rahing iz diribuion h xpd (ar-o-mn ompriv r raio, a mn hon hmial in Figur ompoiion, 6. Nx, h SF ranvr onn, load uring ar im providd and mhod, by a ranvr mpraur, auaor mix addiiv, ha an inrodu.). In h h liraur load ino variou o poin formulaion by h loading an b bam. found o Th drib ranvr h orpion load inra iohrm oninuouly normal unil onr h bam (Xi fail al. undr 994). a Hovr, diplamn in h onrolld prn ym. papr h mi-mpirial xprion propod by Norling Mjornll (997) i adopd bau i 4 () Th proporionaliy fiin D(h,T) i alld moiur prmabiliy and i i a nonlinar funion ha h variaion in im h ar ma pr uni 8 volum onr (ar onn ) b qual o h divrgn h moiur flux J (2) Th ar onn an b xprd a h um h vaporabl ar (apillary ar, ar vapor, and adorbd ar) and h non-vaporabl (hmially bound) ar n (Mill 966, dgr ilia fum raion,, i.. = (h,, ) xpliily During aoun h loading for, h n voluion rak ar hydraion markd raion h fa and SF h bam onn. a ah Thi loading orpion ag. iohrm Dial gaug rad ar plad a h loading poin and h nr h pan o maur h dflion h bam. Thn h bam rain i maurd by ir rain gaug a h nr h nil rinformn and ( h,, ) = G (, ) + h op h bam. ( g ) h (4) 3 EXPERIMENTAL RESULTS ( g ) h K (, ) 3. Ulima rngh () Rul abou h rlaionhip bn har hr h fir rm (gl iohrm) rprn h pan o dph raio and urvaur phyially bound (adorbd) ar and h ond Tabl 3 ho h xprimnal ondiion and rm (apillary iohrm) rprn h apillary rul. Figur 7 ho h rlaionhip bn ulima rngh and h har pan o dph raio ar. Thi xprion i valid only for lo onn SF. Th fiin G (a/d). Whn h har pan rprn h amoun o dph raio a 2.5, in ar pr uni volum hld in h gl por a % all urvaur, h ulima rngh n up almo rlaiv humidiy, and i an b xprd (Norling imilarly. Th raon for hi phnomnon i ha h Mjornll 997) a orion momn h urvd bam bam mall in h a a har pan o dph raio 2.5. G (, ) = k + k (5) Axial For Fix vg vg Load Figur 3. Oulin a urvd bam. Load hr k vg and k vg ar marial paramr. From h maximum amoun ar pr uni volum ha an fill all por (boh apillary por and gl por), on an alula K a on obain K (, ) = 2.2 Tmpraur voluion Figur 4. T apparau and bnding a urvd bam. No ha, a arly ag, in h hmial raion aoiad ih mn hydraion and SF raion ar xohrmi, h mpraur fild i no uniform for non-adiabai ym vn if h nvironmnal mpraur i onan. Ha onduion an b dribd in onr, a la for mpraur no xding C (Bažan & Kaplan 996), by Fourir la, hih rad hr q i h ha flux, T i h abolu Figur mpraur, 5. Supporing and poin. λ i h ha onduiviy; in hi g Fix g G (6) Th marial paramr k vg and k vg and g an b alibrad by fiing xprimnal daa rlvan o fr (vaporabl) ar onn in onr a variou ag (Di Luzio & Cuai 29b). q = λ T (7) Proding FraMCoS-7, May 23-28, 2

3 Figur 6. A jak for axial nil omprion. Tabl 3. T ondiion and rul (). Spimn N a/d Pmax Fraur (KN) (KN) mod R-N B R-N B R2-N BS R-N BS R-N BS R2-N BS N: Axial for, a/d: Shar pan dph raio Pmax: Ulima rngh B: Bnding failur, BS: Bnding-har failur Maximum Shar pan dph raio Figur 7. Rlaionhip bn ulima rngh and a/d. R R R2 (2) Rul abou h rlaionhip bn axial omprion and urvaur Tabl 4 ho h xprimnal ondiion and rul. Figur 8 ho h rlaionhip bn ulima rngh and axial ompriv rngh. Whn h axial ompriv for a applid o h raigh lin bam, h ulima rngh n up 5%. Whn h urvaur a mall, an inra 3% h ulima rngh a n. Hovr, hn h urvaur a big, h ulima rngh drad 34%. Tabl 4. T ondiion J = and Drul ( h, T ) (2). h Spimn N a/d Pmax Fraur (KN) Th proporionaliy (KN) mod fiin D(h,T) moiur prmabiliy and i i a nonlina R-N h rlaiv 2.7 humidiy B h and mpraur R-N-32 & 3.2 Najjar 972) Th B moiur ma balan R2-N BS R-N ha 3.2 h variaion 28. in im S h ar ma R-N volum onr (ar BS onn ) b q R2-N divrgn 3.2. h moiur S flux J N: Axial for, a/d: Shar pan dph raio Pmax: Ulima rngh S: Shar failur Th ar onn an b xprd a 8 h vaporabl ar (apillary a 6 vapor, and adorbd ar) and h non- 4 (hmially bound) ar n (Mil 2 Panazopoulo & Mill 995). R I i ra aum ha h vaporabl ar R i a fu 8 rlaiv humidiy, h, dgr R2hydraion 6 dgr ilia fum raion,, i.. = 4 = ag-dpndn orpion/dorpion 2 (Norling Mjonll 997). Undr hi aum by ubiuing.2 Equaion ino Equai obain Axial r (kn/m2) Figur 8. Rlaionhip bn ulima rngh and axial omprion. h = & + & + h h Maximum From hi phnomnon, hr /h alhough i h h lop axial h ompriv for a iohrm mall, h (alo influn alld moiur h axial apa orpion/ for i ignifian govrning in h a quaion a urvd (Equaion bam. 3) mu b by appropria boundary and iniial ondii 3.2 Load dflion Th rlaionhip bn h amoun ar and rlaiv humidiy i alld Figur 9 ho h iohrm load dflion if maurd rlaionhip ih a inraing h nr all bam. humidiy In h urvd and dorpion bam, ouid iohrm diplamn bom a. largr Ngling han h hir inid diffrn dipla- (Xi al. in h mn. h folloing, orpion iohrm ill b rfrn o boh orpion and dorpion () Eff har By pan-o-dph h ay, raio if h hyri h A a har pan dph iohrm raio ould 3.2, b h akn maximum ino aoun, diplamn bam rlaion, larg in vaporabl h a ar larg v urva- rlaiv humi o ur. Hovr, a b a har ud aording pan dph o raio h ign 2.5, h h varia maximum diplamn rlaiviy bam humidiy. mall in Th h hap a h larg urvaur. iohrm for HPC i inflund by many p pially ho ha influn xn and (2) Eff axial hmial omprion raion and, in urn, drm In a raigh bam, ruur hn h and axial por omprion iz diribuion a (arraio, diplamn hmial bam ompoiion, mall. SF applid, h maximum Wih a mall urvaur uring im bam, and h mhod, maximum mpraur, diplamn a xndd.). In graly. h liraur Hovr, variou ih formulaio a mix larg urvaur bam, found h o drib maximum h diplamn orpion iohrm bam mall ih onr h maximum (Xi load. al. 994). Hovr, in h papr h mi-mpirial xprion pro Norling Mjornll (997) i adopd b Proding FraMCoS-7, May 23-28, 2

4 J (, () Inid 5 Ouid Th proporionaliy fiin D(h,T) i alld moiur prmabiliy and i i a nonlinar funion h rlaiv humidiy h and mpraur T (Bažan & Najjar 972). Th moiur ma balan rquir ha h variaion in im h ar ma pr uni volum 5 onr (ar onn ) b qual o h divrgn h moiur flux J 2 3 4(2) Dflion (mm) Th ar onn (a) an R-N-32 b xprd a h um h vaporabl ar (apillary ar, ar vapor, and adorbd ar) and h non-vaporabl (hmially bound) ar n (Mill Inid 966, Panazopoulo 5 & Mill 995). I i raonabl Ouid o aum ha h vaporabl ar i a funion rlaiv humidiy, h, dgr hydraion,, and dgr ilia fum raion,, i.. = (h,, ) = ag-dpndn orpion/dorpion iohrm (Norling 5 Mjonll 997). Undr hi aumpion and by ubiuing Equaion ino Equaion 2 on obain h Dflion (mm) = & + & + & n (3) h h (b) R-N-32 hr /h i h lop h orpion/dorpion iohrm (alo alld moiur apaiy). Inid Th govrning 5 quaion (Equaion 3) mu Ouid b ompld by appropria boundary and iniial ondiion. Th rlaion bn h amoun vaporabl ar and rlaiv humidiy i alld adorpion iohrm if maurd ih inraing rlaiviy humidiy and dorpion iohrm in h oppoi a. Ngling 5 hir diffrn (Xi al. 994), in h folloing, orpion iohrm ill b ud ih rfrn o boh orpion and dorpion ondiion. By h ay, if h hyri 2 3h moiur 4 iohrm ould b akn Dflion ino aoun, (mm) o diffrn rlaion, vaporabl ar v rlaiv humidiy, mu b ud aording o () h R2-N-32 ign h variaion h Figur 9. Rlaionhip bn load and dflion. rlaiviy humidiy. Th hap h orpion iohrm for HPC i inflund by many paramr, 3.3 pially Ulima ho rak ha a influn xn and ra h hmial raion and, in urn, drmin por () Rul abou h rlaion bn har pan o ruur and por iz diribuion (ar-o-mn dph raio and urvaur raio, mn hmial ompoiion, SF onn, Figur ho h fraur a all bam. uring im and mhod, mpraur, mix addiiv, A a har pan dph raio 3.2, h mmbr.). In h liraur variou formulaion an b faild during bnding, xp h mmbr ih h found o drib h orpion iohrm normal larg urvaur. Hovr, a a har pan dph raio onr (Xi al. 994). Hovr, in h prn 2.5, o orion rak influning h orion papr h mi-mpirial xprion propod by momn r obrvd. Norling Mjornll (997) i adopd bau i D h T h xpliily aoun for h voluion hydraion raion and SF onn. Thi orpion Inid iohrm rad 5 Ouid h, 5 ( g ) h K (, ) Dflion (mm) hr h fir rm (d) (gl R-N-25 iohrm) rprn h phyially bound (adorbd) ar and h ond rm (apillary iohrm) rprn h apillary ar. Thi xprion i valid only for lo onn SF. 5 Th fiin G rprn h amoun ar pr uni volum hld in h gl por a % rlaiv humidiy, and i an b xprd (Norling Mjornll 997) a G (, ) = k + k (5) 5 vg vg Inid hr k Ouid vg and k vg ar marial paramr. From h maximum amoun ar 2pr uni 3volum ha 4 an fill all por (boh apillary Dflion por (mm) and gl por), on an alula K a on obain () R-N-25 (, ) = G (, ) + ( g ) h 5, K ( ) = g G Inid Ouid Th marial paramr k vg and k vg and g an b alibrad by fiing xprimnal daa rlvan o fr (vaporabl) ar onn in onr a 5 variou ag (Di Luzio & Cuai 29b). 2.2 Tmpraur voluion No ha, a arly Dflion ag, in (mm) h hmial raion aoiad ih mn hydraion and SF raion (f) R2-N-25 Figur ar xohrmi, 9. Rlaionhip h bn mpraur load and fild dflion. i no uniform for non-adiabai ym vn if h nvironmnal mpraur (2) Rul i abou onan. h rlaionhip Ha onduion bn an axial b omprion dribd in and onr, urvaur la for mpraur no In xding a h C mmbr (Bažan ubjd & Kaplan o axial 996), omprion, Fourir i a la, obrvd hih rad ha h yp R bam and yp by R bam fail during har ih diagonal rak. q = λ T Hovr, hn h mall urvaur R bam a (7) ubjd o h axial omprion, h rak ourrd hr ovr q i a h id ha ara. flux, I a T obrvd i h abolu ha h bam mpraur, finally and faild λ during i h ha omprion onduiviy; a h in onr ompriv hi ara. g (4) (6) Proding FraMCoS-7, May 23-28, 2

5 5 5 Inid Ouid J D ( h, T h Th proporionaliy fiin D(h,T) moiur prmabiliy and i i a nonlina h rlaiv humidiy h and mpraur & Najjar 972). Th moiur ma balan ha (a) h R-N-32 variaion in im h ar ma volum onr (ar onn ) b q divrgn h moiur flux J Dflion (mm) 5 (g) R-N Inid Ouid Dflion (mm) 5 5 (h) R-N2-32 Inid Ouid Dflion (mm) (i) R2-N2-32 Figur 9. Rlaionhip bn load and dflion. 4 CONCLUSIONS Th fraur propri h rinford onr urvd bam r udid xprimnally a o h influn h axial for and h har pan dph raio. Bad on h rul, h folloing onluion an b dran: Th ar onn an b xprd a h vaporabl ar (b) R-N-32 (apillary a vapor, and adorbd ar) and h non- (hmially bound) ar n (Mil Panazopoulo & Mill 995). I i ra aum ha h vaporabl ar i a fu rlaiv humidiy, h, dgr hydraion dgr ilia fum raion,, i.. = = ag-dpndn orpion/dorpion (Norling Mjonll 997). Undr hi aum by ubiuing Equaion ino Equai () R2-N-32 obain h = h h & + & + hr /h i h lop h orpion/ iohrm (alo alld moiur apa govrning (d) R-N-25 quaion (Equaion 3) mu b by appropria boundary and iniial ondii Th rlaion bn h amoun ar and rlaiv humidiy i alld iohrm if maurd ih inraing humidiy and dorpion iohrm in h a. Ngling hir diffrn (Xi al. h folloing, orpion iohrm ill b rfrn o boh orpion and dorpion By () h R-N-25 ay, if h hyri h iohrm ould b akn ino aoun, o rlaion, vaporabl ar v rlaiv humi b ud aording o h ign h varia rlaiviy humidiy. Th hap h iohrm for HPC i inflund by many p pially ho ha influn xn and hmial raion and, in urn, drm ruur and por iz diribuion (arraio, (f) mn R2-N-25 hmial ompoiion, SF uring im and mhod, mpraur, mix Figur. Fraur a..). In h liraur variou formulaio found o drib h orpion iohrm onr (Xi al. 994). Hovr, in h papr h mi-mpirial xprion pro Norling Mjornll (997) i adopd b Proding FraMCoS-7, May 23-28, 2

6 J D ( h, T h () Th proporionaliy fiin D(h,T) i alld moiur prmabiliy and i i a nonlinar funion h rlaiv humidiy h and mpraur T (Bažan & Najjar 972). Th moiur ma balan rquir ha h variaion in (g) im R-N2-32 h ar ma pr uni volum onr (ar onn ) b qual o h divrgn h moiur flux J (2) Th ar onn an b xprd a h um h vaporabl ar (apillary ar, ar vapor, and adorbd (h) ar) R-N2-32 and h non-vaporabl (hmially bound) ar n (Mill 966, Panazopoulo & Mill 995). I i raonabl o aum ha h vaporabl ar i a funion rlaiv humidiy, h, dgr hydraion,, and dgr ilia fum raion,, i.. = (h,, ) = ag-dpndn orpion/dorpion iohrm (Norling Mjonll 997). Undr hi aumpion and by ubiuing Equaion ino Equaion 2 on obain (i) R-N2-32 Figur. Fraur a. h = & + & + & n (3) h h () Whn h har pan o dph raio hang, h ra hang h ulima rngh h urvd bam hr i lo /h o i ha h lop h raigh h orpion/dorpion bam. (2) iohrm In a urvd (alo bam alld ih moiur a mall urvaur, apaiy). h Th ulima govrning rngh quaion bom (Equaion larg 3) hn mu axial b ompld omprion by appropria a applid. boundary and iniial ondiion. (3) Th Hovr, rlaion in bn hi xprimnal h amoun udy, vaporabl for h urvd ar and bam rlaiv ih larg humidiy urvaur, i alld h ulima adorpion iohrm if maurd ih inraing rlaiviy humidiy and dorpion iohrm in h oppoi a. Ngling hir diffrn (Xi al. 994), in h folloing, orpion iohrm ill b ud ih rfrn o boh orpion and dorpion ondiion. By h ay, if h hyri h moiur iohrm ould b akn ino aoun, o diffrn rlaion, vaporabl ar v rlaiv humidiy, mu b ud aording o h ign h variaion h rlaiviy humidiy. Th hap h orpion iohrm for HPC i inflund by many paramr, pially ho ha influn xn and ra h hmial raion and, in urn, drmin por ruur and por iz diribuion (ar-o-mn raio, mn hmial ompoiion, SF onn, uring im and mhod, mpraur, mix addiiv,.). In h liraur variou formulaion an b found o drib h orpion iohrm normal onr (Xi al. 994). Hovr, in h prn papr h mi-mpirial xprion propod by Norling Mjornll (997) i adopd bau i xpliily rngh aoun bam for mall h hn voluion axial omprion hydraion a raion applid. and SF onn. Thi orpion iohrm rad I i imporan for rolving dign problm for urvd rinford onr bam ha hr i a lo rlaionhip bn h urvd bam and axial omprion. ( h,, ) = G (, ) + In ordr o rolv h problm, many mor ( g ) h xprimn ar ndd in fuur. In rn yar, (4) rinford onr mmbr hav bn ubjd o orion and analyzd by numrial ( g imulaion. ) h To K (, ) ahiv mor aura analyi, mor xprimnal udi ar nary. hr h fir rm (gl iohrm) rprn h REFERENCES phyially bound (adorbd) ar and h ond rm (apillary iohrm) rprn h apillary Kadonaga, ar. Thi T., xprion Shigmau, T., i Tamura, valid only T., and for Hara, lo T., onn 24. Sudy SF. Th on R/C fiin Mmbr Subjd G rprn o Torion, h Bnding amoun and ar Axial pr Tnion, uni volum Third Inrnaional hld in h Confrn gl por on a Advan % in Sruural Enginring and Mhani, Soul, Kora, rlaiv CDROM. humidiy, and i an b xprd (Norling Tamura, Mjornll T., 997) Shigmau, a T., Hara, T., and Maruyama, K., 995. A Sudy Propod Dign Equaion for h Shar Srngh R/C Bam Subjd o Axial Tnion, Pro. G ( JSCE,, ) = No. k 52/V-28, + k (5) vg vg Tamura, T., Shigmau, T., Hara, T., and Nakano, S., 99. Exprimnal Analyi Shar Srngh Rinford hr Conr k vg and Bam k vg Subjd ar marial o Axial paramr. Tnion, Pro. From JCI, h maximum Vol. 2, amoun ar pr uni volum ha an Taaka, fill all por T., Shigmau, (boh apillary T., Tamura, por T., and and gl Hara, por), T., 22. on Sudy on har rngh h R/C urvd bam, Th ond inrnaional a on obain an alula K onfrn on advan in ruural nginring and mhani, CDROM. Tukuda, H., Shigmau, T., and Tamura, T., 27. Sudy on g R/C mmbr ubjd o orion and axial for, Fourh + G Inrnaional Sruural Enginring and Conruion Confrn, Vol., pp (6) K (, ) = g Th marial paramr k vg and k vg and g an b alibrad by fiing xprimnal daa rlvan o fr (vaporabl) ar onn in onr a variou ag (Di Luzio & Cuai 29b). 2.2 Tmpraur voluion No ha, a arly ag, in h hmial raion aoiad ih mn hydraion and SF raion ar xohrmi, h mpraur fild i no uniform for non-adiabai ym vn if h nvironmnal mpraur i onan. Ha onduion an b dribd in onr, a la for mpraur no xding C (Bažan & Kaplan 996), by Fourir la, hih rad q = λ T (7) hr q i h ha flux, T i h abolu mpraur, and λ i h ha onduiviy; in hi Proding FraMCoS-7, May 23-28, 2