Probabilistic uncertainty modeling for thermomechanical analysis of plasterboard submitted to fire load

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Submitted on 4 Apr 2012

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Probabilistic uncertainty modeling for thermomechanical analysis of plasterboard submitted to fire load

S. Sakji, Christian Soize, J.-V. Heck

To cite this version:

S. Sakji, Christian Soize, J.-V. Heck. Probabilistic uncertainty modeling for thermomechanical analysis of plasterboard submitted to fire load. Journal of Structural Engineering-ASCE, 2008, 134 (10), pp.1611-1618. �10.1061/(ASCE)0733-9445(2008)134:10(1611)�. �hal-00685092�

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!"# R# G'/-!/" 8'282 3,( -!N'('/8 @*+='2 ,3 8')1'(*8=(' 0*((!'- ,=8 ,/ 1+*28'( 21'0!)'/24

"(*1& ,3 8&' )'0&*/!0*+ +,*- ?@'(8!0*+ *>!2 !/ QC *2 * 3=/08!,/ ,3 8&' 8(*/2@'(2*+ -!21+*0')'/8

?&,(!D,/8*+ *>!2 !/ ))C4 8&!/ 2,+!- +!/'2 ?(,,) 8')1'(*8=('C6 8&!/ -*2&'- +!/' ?$7STOC6 8&!0E +!/'2?$USTOC6 8&!0E -*2&'- +!/'2?7RSTOC #

!"# Y# %'/2!+' 8'282 ,/ 0*(-.,*(- 3,( 8H, -!N'('/8 @*+='2 ,3 8')1'(*8=('4 "(*1& ,3 *>!*+

28('22 ?!/ WP*C *2 * 3=/08!,/ ,3 28(*!/# 5,+!- +!/'2 ?8'282 *8 (,,) 8')1'(*8=('C6 -*2&'- +!/'2

?8'282 *38'( R)!/ :5I 8&'()*+ +,*-C#

!"# U# 50&')*8!0 ('1('2'/8*8!,/ ,3 0*(-.,*(-M1+*28'(M0*(-.,*(- 1+*8'2#

77

!"# $# %&'()*+ ,!-./!0!12 34 1&' 565 70'(1!8*+ *9!/ !: 7)²//;; */ * 4.:81!3: 34 1&' 1&'()*+

+3*,!:" 1!)' 7&3(!<3:1*+ *9!/ !: 7/;;#

!"# =# %')>'(*1.(' >(3?+'/ !: 1&' 83(' 34 565 >+*1'/# %')>'(*1.(' !: 1&' )!,,+' 34 :.)'(!8*+ +*2'(/ 7@'(1!8*+ *9!/ !:AB; */ * 4.:81!3: 34 1&' 1&'()*+ +3*,!:" 1!)'7&3(!<3:1*+ *9!/

!: /;#

!"# CD# E'8&*:!8*+ *>>+!', +3*, 70'(1!8*+ *9!/ !: F; */ * 4.:81!3: 34 1&' 1(*:/0'(/*+ ,!/>+*8'G )':1 7&3(!<3:1*+ *9!/ !: ));H '9>'(!)':1/ 7,*/&', +!:'/;I :.)'(!8*+ /!).+*1!3: 34 1&' )'*:

)3,'+ *1 (33) 1')>'(*1.(' 71&!8J /3+!, +!:';#

!"# CC# E'8&*:!8*+ *>>+!', +3*, 70'(1!8*+ *9!/ !: F; */ * 4.:81!3: 34 1&' 1(*:/0'(/*+ ,!/>+*8'G )':1 7&3(!<3:1*+ *9!/ !: ));H '9>'(!)':1/ 7,*/&', +!:'/;I :.)'(!8*+ /!).+*1!3: 34 1&' )'*:

)3,'+ *1 CKDA5 71&!8J /3+!, +!:';#

!"# CK# 53:0'("':8' L!1& ('/>'81 13 1&' :.)M'( ns 34 ('*+!<*1!3:/H "(*>& 34 1&' 4.:81!3:

n_s 7→conv(n_s) 43( :.)'(!8*+ /!).+*1!3: *1 (33) 1')>'(*1.('#

!"# CN# 53:0'("':8' L!1& ('/>'81 13 1&' :.)M'( n_s 34 ('*+!<*1!3:/H "(*>& 34 1&' 4.:81!3:

ns 7→conv(ns) 43( :.)'(!8*+ /!).+*1!3: *1 CKDA5#

!"# CO# P'/.+1/ 43( KDA5H )'8&*:!8*+ *>>+!', +3*, 7@'(1!8*+ *9!/ !: F; */ * 4.:81!3: 34 1&' 1(*:/0'(/*+ ,!/>+*8')':1 7&3(!<3:1*+ *9!/ !: ));H '9>'(!)':1/ 7,*/&', 1&!: +!:'/;I :.)'(!8*+

/!).+*1!3:/ L!1& 1&' )'*: )3,'+ 71&!8J /3+!, +!:';I 83:?,':8' ('"!3: L!1& 1&' /138&*/1!8 )3,'+

7"('2 ('"!3:;#

!"# CQ# P'/.+1/ 43( CKDA5H )'8&*:!8*+ *>>+!', +3*, 7@'(1!8*+ *9!/ !: F; */ * 4.:81!3: 34 1&' 1(*:/0'(/*+ ,!/>+*8')':1 7&3(!<3:1*+ *9!/ !: ));H '9>'(!)':1/ 7,*/&', 1&!: +!:'/;I :.)'(!8*+

/!).+*1!3:/ L!1& 1&' )'*: )3,'+ 71&!8J /3+!, +!:';I 83:?,':8' ('"!3: L!1& 1&' /138&*/1!8 )3,'+

7"('2 ('"!3:;#

KN

!"#$% &' ()%$*+, ,-+. /%01) 1-*2-3%. -4' &°' 52%1!*%0 )-,.%$6 7°' *-/!,% 1+$8 +0. 9°'

$+.!+08 2+0%,:

7;

0 200 400 600 800 1000 1200 1400 1600 1800 0

20 40 60 80

Time (s)

Incident flux density (KW/m²)

!"#$% &' ()*!+%), +%)-!,. /%0, 1#2 34%$,!*05 02!- !) 67/8²9 0- 0 :#)*,!;) ;: ,!8% 3/;$!<;),05 02!- !) -%*;)+9' *05*#50,%+ /%0, 1#2 3,/!*= -;5!+ 5!)%9> ?@A 8%0-#$%+ /%0, 1#2 3+0-/%+ 0)+

80$=%+ 5!)%-9> #BB%$ 0)+ 5;C%$ (DE FGH %I#!405%), +%)-!,. 1#2 J;#)+- 3+;,K+0-/%+ 0)+ +0-/%+

5!)%- $%-B%*,!4%5.9L

&M

0 5 10 15 20 0

50 100 150 200 250 300

Transversal displacement (mm)

Load (N)

20°C 120°C

170°C

250°C

!"#$% &' (%)*!)" +%,+ %-.%$!/%)+, 01$ *!2%$%)+ 345#%, 10 +%/.%$4+#$% 1) 676 ,.%8!/%), 84$$!%*

1#+ 4881$*!)" +1 +9% 51)"!+#*!)45 *!$%8+!1)' "$4.9 10 +9% /%894)!845 514* :3%$+!845 4-!, !) ;<

4, 4 0#)8+!1) 10 +9% +$4),3%$,45 *!,.548%/%)+ :91$!=1)+45 4-!, !) //<' +9!8> ,15!* 5!)%, :?@AB6<C +9!) ,15!* 5!)%, :DEAB6<C *1+F*4,9%* 5!)%, :D?AB6<C +9!) *4,9%* 5!)%,:?AB6<G

?H

0 50 100 150 200 250 0

500 1000 1500 2000 2500 3000

Temperature (°C)

Mean Young modulus (MPa)

E_LL E_TT E_LT

!"#$% &' ()%$*+*%,)-.!,-/ %01%$!*%.23 4+$ 2)% 565' "$-1) +4 2)% *%-. 7+#." *+8#/#3 9:%$2!,-/ -0!3 !. ;6-< -3 - 4#.,2!+. +4 2)% -:%$-"% 2%*1%$-2#$% !. 2)% 565 9)+$!=+.2-/ -0!3 !.

>5<' 3+/!8 /!.% *-$?%8 ”^∗”9@LL<A 3+/!8 /!.% *-$?%8”⁺”9@T T<A 3+/!8 /!.% *-$?%8”>” 8-3)%8 /!.%

9@LT<B

CD

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0

10 20 30 40 50 60

Transversal displacement ( 10⁻³ m)

Load (N)

!"#$% &' (%)*!)" +%,+, -.$ *!/%$%)+ 012#%, .- +%34%$1+#$% 51$$!%* .#+ .) 421,+%$ ,4%5!3%),'

"$146 .- +6% 3%561)!512 2.1* 70%$+!512 18!, !) 9: 1, 1 -#)5+!.) .- +6% +$1),0%$,12 *!,4215%3%)+

76.$!;.)+12 18!, !) 33:' +6!) ,.2!* 2!)%, 7$..3 +%34%$1+#$%:< +6!) *1,6%* 2!)% 7=>?@A:< +6!5B 2!)%,7=C?@A:< +6!5B *1,6%* 2!)%,7>&?@A: D

>E