Thermal expanson of wood and tmber-concrete composte members under ISO-fre exposure ANDREA FRANGI and MARIO FONTANA Insttute of Structural Engneerng, ETH Zurch, Swtzerland Summary Ths paper dscusses the nfluence and effects of thermal expanson on the structural behavour of tmber slabs and tmber-concrete composte slabs exposed to ISO-fre. The frst part of the paper presents a smplfed model to calculate the effects of the thermal expanson, n the second part the calculaton model s compared to fre test results. Keywords Thermal expanson, wood members under ISO-fre exposure, tmber-concrete composte slabs, calculaton model for fre Introducton A research project was carred out at the ETH on the fre behavour of tmber slabs made of hollow elements and tmber-concrete composte slabs, whch consst of tmber members n the tensle zone, a thn concrete layer n the compresson zone and the shear connecton between tmber and concrete. In a seres of small-scale tests the fre behavour of the connectors and the separatng elements was expermentally analysed. A seres of fre tests on slabs looked at the global structural behavour of the tmber slabs and tmberconcrete composte slabs. All fre tests were based on ISO-fre exposure and performed at the Swss Federal Laboratores for Materals Testng and Research n Dübendorf. Detaled expermental results of all fre tests are descrbed n [5] and [6]. The desgn models developed for the calculaton of the fre resstance of tmber slabs and tmberconcrete composte slabs s presented n [7]. The fre tests permtted the study of the nfluence and effects of thermal expanson on the structural behavour of tmber slabs and tmber-concrete composte slabs. Frst a smplfed model to calculate the effects of the thermal expanson s presented, ts results are then compared to the fre tests. Calculaton model The nfluence and effects of thermal expanson on the structural behavour of tmber slabs and tmber-concrete composte slabs exposed to ISO-fre was studed usng a lnear elastc calculaton model. The calculaton model was appled to the tested slabs usng the followng basc assumptons: - lnear elastc materal behavour - Bernoull s hypothess s vald also n the fre stuaton - smply supported member (statcally determnate system) subjected to thermal and mechancal actons Copyrght Internatonal Assocaton for Fre Safety Scence
- ISO-fre exposure as thermal acton producng the same temperature feld on each secton along the member - unformly dstrbuted loads and/or concentrated loads as mechancal actons producng only bendng moments M (no axal forces N) The geometres of the tested hollow core tmber slabs and of the tmber-concrete slab wth a wood secton made of tmber planks are shown n Fg. 4. The tmber slabs and the tmber-concrete composte slab were exposed to ISO-fre on one sde. Calculaton model The cross-secton of the structure s dvded nto n hypothetcal longtudnal unconnected layers (see Fg. 1a) wth dfferent stffness and strength propertes as a functon of temperature Θ (t). The temperature of each layer depends on the consdered fre tme and the secton geometry. Fgure 1 Calculaton model: (a) cross-secton composed of dfferent layers, (b) temperature gradent of the cross-secton, (c) thermal strans ε th,, (d) resultng strans ε res, Because of the good nsulatng behavour of charred and uncharred wood, typcal temperature profles through wood members exposed to fre exhbt a steep temperature gradent as presented n Fg. 1b. The steep temperature gradent wll nduce thermal strans ε th,, whch are not lnearly dstrbuted (see Fg. 1c). The thermal strans ε th, are calculated takng nto account the coeffcent of thermal expanson α T as: ε t) = α Θ (t) (1) th, ( T To fulfl the hypothess of Bernoull-Naver of a plane secton, nternal strans ε E, producng resdual thermal stresses σ E, must be ntroduced. The total strans ε res, resultng from the thermal strans ε th, and the nternal strans ε E, may be calculated takng nto account the stran of the upper layer ε 0 and the curvature χ of the cross-secton as (see Fg. 1d): ε t) = ε (t) + ε (t) = ε (t) + χ(t) z (t) () res, ( th, E, 0
Therefore the nternal strans ε E, and the resdual thermal stresses σ E, may be calculated n functon of ε 0 and χ as: ε t) = ε (t) ε (t) = ε (t) + χ(t) z (t) ε (t) (3) E,( res, th, 0 th, σ t) = E ( Θ ) ε (t) = E ( Θ ) [ ε (t) + χ(t) z (t) ε (t)] (4) E,( E, 0 th, For a smply supported member whch s not subjected to external loads, the thermal acton does not produce external bendng moments M and external axal forces N. Therefore the stran of the upper layer ε 0 and the curvature χ of the cross-secton can be found from statc equlbrum requrng that the nternal bendng moment force M Θ and nternal axal force N Θ due to the resdual thermal stresses σ E, must be zero: n NΘ (t) = Σ σ (t) A = 0 (5) = 1 n E, MΘ (t) = Σ σ (t) A z (t) = 0 (6) = 1 E, The solutons of equatons 5 and 6 are: ( Σε EA ) ( ΣEA z ) ( ΣEA z ) ( Σε EA z ) th, th, ε 0(t) = (7) ( ΣEA ) ( ΣEA z ) ( ΣEA z) ( ΣEA ) ( Σε EA z ) ( Σε EA ) ( ΣEA z ) th, th, χ (t) = (8) ( ΣEA ) ( ΣEA z ) ( ΣEA z) The deflecton w due to the curvature χ of the cross-secton s calculated accordng to the prncple of vrtual work (see Fg. ) as: l 1 l χ(t) l w(t) = M(x) χ(t) dx = χ(t) l = (9) 0 4 8 Fgure Model for the deflecton for a smply supported beam exposed to fre only
On the other hand, for a smply supported member whch s subjected to external loads producng a bendng moment M(x), the stran of the upper layer ε 0 and the curvature χ of the cross-secton can be found from the condtons of equlbrum by: n NΘ (t) = Σ σ (t) A = 0 (10) = 1 n E, MΘ (t) = Σ σ (t) A z (t) = M(x) (11) = 1 E, The solutons of the equatons 10 and 11 are: ( Σε EA ) ( ΣEA z ) ( ΣEA z ) [( Σε EA z ) + M(x)] th, th, ε 0(x, t) = ( ΣEA ) ( ΣEA z ) ( ΣEA z) (1) ( ΣEA ) [( Σε EA z ) + M(x)] ( Σε EA ) ( ΣEA z ) th, th, χ (x, t) = (13) ( ΣEA ) ( ΣEA z ) ( ΣEA z ) The deflecton w due to the curvature χ of the cross-secton s calculated as: w(x, t) l = M(x) 0 M EI (x, t) l dx = M(x) χ(x, t) dx 0 (14) Materal propertes For the calculaton of the nfluence and effects of thermal expanson on the structural behavour of tmber slabs and tmber-concrete composte slabs exposed to ISO-fre, t s necessary to know the temperature development n the cross-secton n functon of tme as well as the thermal and mechancal materal propertes such as coeffcent of thermal expanson and modulus of elastcty of the dfferent components of the structure (tmber and concrete) n functon of temperature. The thermal expanson of tmber may be calculated accordng to Chrstoph [1] as: ε 6 th, = l = αt Θ = 4.0 10 l / Θ (15) The thermal expanson of concrete may be calculated accordng to ENV-1994-1- [3] as: ε 4 6 11 th, = l = 1.8 10 + 9.0 10 Θ +.3 10 l / Θ (16) 3 The steep temperature gradent of wood members exposed to ISO-fre can be descrbed as a functon of fre tme and charrng rate. From all temperatures measured durng the ETH fre tests the followng expresson was developed for the calculaton of the temperature profle n a wood member subjected to ISO-fre on one sde [7]:
α(t) β t Θ (x) = 0 + 180 (17) x α ( t) = 0.05 t + 1.75 (18) Θ: temperature n C n functon of the depth x β: charrng rate n mm/mn t: fre tme n mnutes x: depth measured from the surface of the cross-secton n mm The charrng rate β s the man parameter to descrbe the process of thermal degradaton (pyrolyss) of wood subjected to fre producng combustble gases, accompaned by a loss n weght and cross-secton. The ETH fre tests performed wth wood members exposed to ISO-fre of 30 up to 110 mnutes demonstrated that a constant charrng rate β of about 0.7mm/mn may be assumed. Fre reduces the cross-secton as well as the stffness and strength propertes n functon of temperature. For the concrete slab, the temperature-dependent reduced stffness and strength propertes accordng to ENV-1994-1- [3] are consdered n ths study. Fgure 3 Thermal expanson and modulus of elastcty E of tmber and concrete consdered n ths study n functon of the temperature For the temperature-dependent materal propertes of wood a large and often contradctory varaton of values s gven by dfferent sources [11]. Glos [8] conducted tests on structural tmber members of szes used n practce n bendng, compresson and tenson. The test specmens were heated to a constant temperature and then loaded to falure. The reduced modulus of elastcty obtaned for bendng s shown n Fg. 3 wth E(0.85). Köng [10] conducted extensve expermental research on the fre behavour of lght tmber frame assembles. Especally the performance of tmber frame members n bendng at standard fre exposure was studed [9]. The fre tests were conducted such that the fre-
exposed sde was ether n compresson or tenson. Thereby t was possble to separate the effect of temperature on the modulus of elastcty E n tenson and compresson. The reduced modul of elastcty obtaned are shown n Fg. 3 wth E(0.5) for tenson and E(0.35) for compresson. They devate consderably from those gven by Glos wth E(0.85). There are several reasons for ths. One s that t s dffcult to mantan a controlled level of mosture content durng the tests. Another reason s the effect of loadng rate: already consderable at normal temperature, t s much greater at elevated temperatures and senstve to mosture. Fgure 3 shows the thermal and mechancal propertes of tmber and concrete n functon of temperature, used for the followng parametrc study. Comparson wth fre tests The calculated effects of thermal expanson are compared to results of bendng tests performed wth a tmber-concrete composte slab and two tmber slabs made of hollow core elements shown n Fg. 4. All slabs were exposed to ISO-fre from below. Fgure 4 Cross-sectons of the slabs exposed to ISO-fre The tmber-concrete composte slab conssted of sawn spruce tmber planks 100 and 10 mm hgh and a 80 to 100 mm thck concrete layer (see Fg. 4). The composte slab had no connectors between the tmber planks and the concrete layer. The shear connecton between concrete and tmber was realsed by mcro-mechancal nterlock between concrete and the raw sawn surface of the tmber planks wth an alternatng heght of 100 and 10 mm. The slab was loaded wth hydraulc jacks postoned at about a thrd of the span. The load level F fre durng the fre test was set n such a way that the maxmum bendng moment corresponded to that n a slab of 6.5 m span, wth a permanent load of 1.5 kn/m and a reduced accompanyng varable load of 0.3*3.0 kn/m allowng for a reducton of the varable load due to the low probablty of concdence of the maxmum varable load and fre accordng to the Swss acton code SIA 160 [1]. The tmber concrete composte
slab, whch showed no slp between concrete and tmber durng the test, was exposed to 90 mnutes of ISO-fre. The two tmber slabs were made of 00 mm hgh hollow elements of spruce wth a mean densty of 450 kg/m 3. Two dfferent types of slab wth three dfferent types of jont between the tmber elements were desgned for a fre resstance of 60 and 90 mnutes (see Fg. 4). The load level durng the fre tests was set n such a way that the maxmum bendng moment corresponded to that n a slab of about 7.10 m span, wth a permanent load of 1.5 kn/m and a reduced accompanyng lve load of 0.5*3.0 kn/m accordng to ENV-1991-1 []. The tmber slabs were exposed to 70 mnutes and 105 mnutes of ISOfre. No relevant smoke or flame penetraton was observed through the three dfferent types of jont between the tmber elements. In the fre tests the temperatures n selected locatons, the vertcal deflectons and the horzontal deformatons were measured. Detaled expermental results of the fre tests are descrbed n [5] and [6]. Influence of thermal expanson on the deflecton Fgure 5 compares the deflecton measured durng the fre tests wth the deflecton calculated n functon of the three dfferent cases for the temperature-dependent reducton of the modulus of elastcty E of tmber as shown n Fg. 3. The assumed stffness propertes of the slabs at room temperature were calculated from the deflectons measured before the fre tests. Fgure 5 left llustrates the deflecton w th due to the nfluence of the thermal expanson α T accordng to equaton 15 and the deflecton w due to the external mechancal loads. Fgure 5 rght gves the total deflecton w tot. From Fg. 5 the followng conclusons can be drawn: - the sharp ncrease n the deflectons measured at the begnnng of the fre tests shows the nfluence of the thermal expanson of tmber. - the calculated deflectons w due to the external mechancal loads depend strongly on the dfferent materal laws for the temperature-dependent reducton of the modulus of elastcty E of tmber. Further t can be seen that the calculated deflectons w are always smaller than the deflecton measured durng the fre tests. Therefore a calculaton model, whch does not consder the effects of thermal expanson, underestmates the deflectons measured durng the fre tests. - the calculated deflectons w th due to the nfluence of thermal expanson depend only slghtly on the dfferent cases for the temperature-dependent reducton of the modulus of elastcty E of tmber. However the nfluence of thermal expanson leads to a consderable ncrease of the deflecton durng the fre tests. - the calculated deflectons w tot whch consder the effects of thermal expanson are n good agreement wth the deflecton measured durng the fre tests.
Fgure 5 Comparson of calculated and measured deflectons for dfferent materal laws accordng to Fg. 3 left and a charrng rate of 0.7 mm/mn.
Fgure 6 Influence of the assumed charrng rate and thermal coeffcent on the calculaton model Fgure 6 llustrates the nfluence of the charrng rate β and thermal coeffcent α T assumed for the calculaton model. The deflecton was calculated wth a charrng rate β of 0.70 mm/mn or 0.75 mm/mn and a thermal coeffcent α T of 4*10-6 K -1 or 5*10-6 K -1. Fgure 6 shows that: - the assumed charrng rate of tmber has a consderable nfluence on the calculated deflectons w due to the external mechancal loads. On the other hand, the nfluence of the charrng rate on the calculated deflectons w th due to thermal expanson s small. - the calculated deflectons w th due to the nfluence of thermal expanson depend strongly on the assumed thermal coeffcent α T of tmber. However, as the calculated deflecton w due to the external mechancal loads s consderably hgher than the calculated deflecton w th due to the nfluence of thermal expanson, the nfluence of the assumed thermal coeffcent α T of tmber on the calculated total deflecton w tot s qute small.
Influence of resdual thermal stresses Fgure 7 shows the resdual thermal stresses due to the nfluence of thermal expanson calculated after 30, 60 and 90 mnutes for the tmber-concrete composte slab shown n Fg. 4. The resdual thermal stresses were calculated n functon of temperature-dependent reductons of the modulus of elastcty E of tmber E(0.5) and E(0.85) as shown n Fg. 3. Fgure 7 Resdual thermal stresses due to the nfluence of the thermal expanson calculated after 30, 60 and 90 mnutes for the tmber-concrete composte slab From Fg. 7 followng conclusons can be drawn: - the effect of thermal expanson leads to resdual thermal compressve stresses n the upper and lower part of the cross-secton and resdual thermal tensle stresses n the mddle part of the cross-secton. - the resdual thermal compressve stresses slghtly decrease wth ncreasng fre tme, whle the resdual thermal tensle stresses slghtly ncrease. - because of the thermal degradaton of wood, the postons of the greatest compressve and tensle resdual thermal stresses move towards the unexposed sde of the crosssecton wth ncreasng fre tme. - the calculated resdual thermal stresses are qute small. Further t can be seen that the resdual thermal stresses σ E calculated wth E(0.85) are slghtly greater than σ E calculated wth E(0.5).
Fgure 8 Resultng stresses calculated wth and wthout the nfluence of the thermal expanson for the cross-secton wth the maxmum bendng moment due to the external mechancal loads Fgure 8 shows the resultng stresses calculated wth and wthout the nfluence of thermal expanson for the cross-secton subjected to the maxmum bendng moment due to the external mechancal loads. The resultng stresses were calculated after 60 and 90 mnutes n functon of the temperature-dependent reducton of the modulus of elastcty E of tmber E(0.5) and E(0.85) as shown n Fg. 3. Fgure 8 shows that the dfferences between the resultng stresses calculated wth and wthout the nfluence of thermal expanson are qute small. For ths reason, the fre resstance t R of a tmber-concrete slab calculated consderng the nfluence of thermal expanson dffers by only few mnutes from t R calculated wthout the nfluence of thermal expanson [7].
Conclusons A research project was carred out at the ETH on the fre behavour of tmber slabs and tmber-concrete composte slabs. The fre tests permtted studyng the effects of thermal expanson on the structural behavour of the slabs. The frst part of the paper presented a smplfed lnear elastc model to calculate the effects of thermal expanson on deflectons and stresses, n the second part ths calculaton model was compared to fre test results. From the study the followng conclusons can be drawn: - the effect of thermal expanson leads to an ncrease of the deflecton. Therefore calculaton models, whch do not consder ths nfluence, underestmate the deflecton measured durng fre tests. - the effect of thermal expanson leads to resdual thermal stresses. However, the calculaton model showed that the resdual thermal stresses are small n comparson to the stresses due to external mechancal loads and may therefore be neglected n the calculaton of the fre resstance tme of beams and slabs. References 1. Chrstoph N., Brettel G., Untersuchungen zur Wärmedehnung von Holz n Abhänggket von Rohdchte und Temperatur, Holz als Roh- und Werkstoff 35, 1977.. ENV 1991-1 (Eurocode 1), Bass of desgn and actons on structures Part 1: Bass of desgn, CEN, Brussels, 1994. 3. ENV 1994-1- (Eurocode 4), Desgn of composte steel and concrete structures Part 1-: General rules Structural fre desgn, CEN, Brussels, 1995. 4. ENV 1995-1- (Eurocode 5), Desgn of tmber structures Part 1-: General rules Structural fre desgn, CEN, Brussels, 1994. 5. Frang A., Fontana M., Zum Brandverhalten von Holzdecken aus Hohlkastenelementen, Insttute of Structural Engneerng (IBK). ETH Zurch, IBK Report No. 44, Brkhäuser Basle, 1999. 6. Frang A., Fontana M., Versuche zum Tragverhalten von Holz-Beton-Verbunddecken be Raumtemperatur und Normbrandbedngungen, Insttute of Structural Engneerng, ETH Zurch, IBK Report No. 49, Brkhäuser Basle, 000. 7. Frang A., Fontana M., Brandverhalten von Holz-Beton-Verbunddecken, Insttute of Structural Engneerng, ETH Zurch, IBK Report No. 69, Brkhäuser Basle, 001. 8. Glos P., Henrc D., Festgket von Bauholz be hohen Temperaturen, Fnal report 87505, Insttut für Holzforschung der Unverstät München, 1990. 9. Köng J., Fre resstance of tmber josts and load bearng wall frames, Swedsh Insttute for Wood Technology Research, Rapport I 941071, Stockholm, 1995. 10. Köng J., Wallej L., Tmber frame assembles exposed to standard and parametrc fres. Part : a desgn model for standard fre exposure, Swedsh Insttute for Wood Technology Research (Trätek), Rapport I 0001001, Stockholm, 000. 11. Köng J., Källsner B., Thermal and mechancal propertes of tmber and some other materals used n lght tmber frame constructon, CIB-W18, Paper 33-16-3, Meetng 33, Delft, 000. 1. SIA 160 (Code), Enwrkung auf Tragwerke, Schwez. Ingeneur- und Archtektenveren, Zürch, 1989.