• Nie Znaleziono Wyników

Constitutive model for wood based on continuum damage mechanics

N/A
N/A
Protected

Academic year: 2021

Share "Constitutive model for wood based on continuum damage mechanics"

Copied!
9
0
0

Pełen tekst

(1)

World Conference on Timber Engineering 

&2167,787,9(02'(/)25:22'%$6('21&217,1880

'$0$*(0(&+$1,&6





&DUPHQ6DQGKDDV



-DQ:LOOHPYDQGH.XLOHQ



+DQV-RDFKLP%ODVV















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





 ,1752'8&7,21





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

 '(),1,7,216

0DWHULDO GLUHFWLRQV DQG DUUD\V PXVW EH FOHDUO\ GHILQHG EHIRUHLQWURGXFLQJWKHPDWHULDOPRGHO%RWKDUHJLYHQLQ (TXDWLRQ  DQG)LJXUH7KHNQRZQLQGLFHVLQWLPEHU HQJLQHHULQJ DUH XVHG HJ LQGH[ Y  ORQJLWXGLQDO VKHDU LQGH[ GLUHFWLRQSHUSHQGLFXODUWRJUDLQ  &DUPHQ6DQGKDDV7LPEHU6WUXFWXUHVDQG:RRG7HFKQRORJ\ 'HOIW8QLYHUVLW\RI7HFKQRORJ\6WHYLQZHJ&1'HOIW WKH1HWKHUODQGV6LQFH2FWREHU,QVWLWXWHIRU7LPEHU 6WUXFWXUHVDQG%XLOGLQJ&RQVWUXFWLRQ.DUOVUXKH,QVWLWXWHRI 7HFKQRORJ\*HUPDQ\(PDLOVDQGKDDV#NLWHGX -DQ:LOOHP*YDQGH.XLOHQ+RO]IRUVFKXQJ0QFKHQ 7HFKQLFDO8QLYHUVLW\0XQLFK:LQ]HUHUVWUDVVH 0QFKHQ*HUPDQ\(PDLOYDQGHNXLOHQ#Z]ZWXPGH +DQV-RDFKLP%ODVV,QVWLWXWHIRU7LPEHU6WUXFWXUHVDQG %XLOGLQJ&RQVWUXFWLRQ.DUOVUXKH,QVWLWXWHRI7HFKQRORJ\5 %DXPHLVWHU3ODW].DUOVUXKH*HUPDQ\(PDLO KDQVEODVV#NLWHGX        7 7 / 5 7 /5 /7 57 V V V V V V V V V V V V ª º ª º «¬ »¼ «¬ »¼ ı        7 5 7 Y5 Y7 UROO V V V V V V ª º « » ¬ ¼     Longitudinal X, L, 1 Tangential Z, T, 3 Radial Y, R, 2 σ11 σ12 σ21 σ13 σ33 σ31 σ 32 σ23 σ22  )LJXUH'HILQLWLRQRIPDWHULDOGLUHFWLRQDQGVWUHVV FRPSRQHQWV

7KH GHYHORSHG PDWHULDO PRGHO LV RUWKRWURSLF +RZHYHU WKHVDPHPDWHULDOSURSHUWLHVZHUHXVHGIRUWKHUDGLDODQG WKHWDQJHQWLDOGLUHFWLRQKDYLQJWKXVDVPHDUHGGLUHFWLRQ SHUSHQGLFXODUWRJUDLQ

 )$,/85(02'(6

&ODVVLFDO WKHRU\ RI SODVWLFLW\ LV JHQHUDOO\ EDVHG RQ VLQJOHVXUIDFHIDLOXUHFULWHULDWKDWDUHQRWDEOHWRLGHQWLI\ IDLOXUHPRGHVDVWKHPDWHULDOVWDUWVIDLOLQJLQDOOPDWHULDO GLUHFWLRQV RQFH WKH IDLOXUH FULWHULRQ LV H[FHHGHG ([DPSOHV DUH WKH ZLGHVSUHDG +LOO >@ RU +RIIPDQ >@ FULWHULD

7KHUHIRUH LQ RUGHU WR UHFRJQLVH IDLOXUH PRGHV WKH VLQJOHVXUIDFHZDVGLYLGHGGLIIHUHQWIDLOXUHFULWHULDZHUH DVVLJQHG WR VWUHVV FRPSRQHQWV WKDW ZHUH YDOLG RQO\ IRU WKH UHVSHFWLYH VWUHVVVWUDLQ TXDGUDQWV )RU

(2)

World Conference on Timber Engineering

LPSOHPHQWDWLRQWKLVPHDQVWKDWDFDVHGLVWLQFWLRQKDVWR EHFDUULHGRXWIRUWKHVLQJOHQRUPDOVWUHVVFRPSRQHQWVDW HYHU\ LQFUHPHQW LQ RUGHU WR DVVLJQ WKH VLQJOH IDLOXUH FULWHULD

x V/ •   &ULWHULRQ , )DLOXUH LQ WHQVLRQ SDUDOOHOWR JUDLQ LV D EULWWOH IDLOXUH PRGH RI ZRRG ZKLFK LV FDXVHG E\ WHQVLOH VWUHVVHVV/ SDUDOOHOWRJUDLQ ,W LV DVVXPHG WKDW RWKHU VWUHVV FRPSRQHQWV GR QRW LQIOXHQFH WKH WHQVLRQ VWUHQJWK SDUDOOHOWRJUDLQ 0D[LPXPVWUHVVFULWHULRQ   /  W W ) I V V d     (2) x V/&ULWHULRQ,,)DLOXUHLQFRPSUHVVLRQSDUDOOHO WRJUDLQ LV D GXFWLOH IDLOXUH PRGH RI ZRRG ZKLFK LV FDXVHG E\ FRPSUHVVLRQ VWUHVVHVV/ SDUDOOHOWRJUDLQ 0D[LPXPVWUHVVFULWHULRQ   /  F F ) I V V  d     (3)

7KH WUDQVYHUVH WHQVLRQ PRGHV DQG VKHDU PRGHV KDYH WR EHFRPELQHGDVIRULQVWDQFHVSOLWWLQJSDUDOOHOWRWKH/5 SODQH FDQ EH FDXVHG E\ WHQVLRQ SHUSHQGLFXODUWRJUDLQ PRGH ,  VKHDU PRGH ,,  RU D FRPELQDWLRQ RI ERWK PL[HGPRGH ,WLVQRWSRVVLEOHWRGHILQHVHSDUDWHIDLOXUH PRGHVIRUHDFKVWUHVVFRPSRQHQWDVGHJUDGDWLRQRIRQH FRPSRQHQW DOVR OHDGV WR GHJUDGDWLRQ RI WKH RWKHU FRPSRQHQWV7KLVPHDQVWKDWGDPDJHGXHWRORQJLWXGLQDO VKHDU DOVR OHDGV WR GDPDJH LQ WHQVLRQ SHUSHQGLFXODUWR JUDLQ HYHQ WKRXJK WKH DFWXDO QRUPDO WHQVLRQ VWUHVV FRPSRQHQW SHUSHQGLFXODUWRJUDLQ PD\ VWLOO EH ORZHU WKDQWKHWUDQVYHUVHWHQVLRQVWUHQJWK

x V57•&ULWHULD,,,,9)DLOXUHLQWHQVLRQSHUSHQ GLFXODUWRJUDLQ ZLWK VSOLWWLQJ LQ /7SODQH UHVS LQ /5SODQH LV DEULWWOH IDLOXUHPRGH RIZRRG ZKLFK LV FDXVHGE\WHQVLOHVWUHVVHVV57LQWKHUDGLDOGLUHFWLRQ ORQJLWXGLQDO VKHDU VWUHVVHVV/5/7 LQ WKH /7SODQH RU UROOLQJVKHDUVWUHVVHVV574XDGUDWLFFULWHULRQ            5 7 /7 /5 57  W 5 7 W Y UROO ) I I I V V V V   d   (4) x V57&ULWHULD99,,,7ZRIDLOXUHPRGHV³SXUH WUDQVYHUVHFRPSUHVVLRQ´DQG³VKHDU´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d    (5)        /7 /5 57 Y5 7 Y UROO ) I I V V V  d    (6) 

 0(7+2'2/2*<

 '$0$*((92/87,21 &'0LVDQRQOLQHDUHODVWLFDSSURDFKZKHUHWKHQRQOLQHDU EHKDYLRXULVREWDLQHGE\PRGLI\LQJWKHVWLIIQHVVPDWUL[ 'RULWVLQYHUVHWKHFRPSOLDQFHPDWUL[&&'0FDQEH

LPSOHPHQWHG LQ DQ LQFUHPHQWDOLWHUDWLYH )( IUDPHZRUN 7KH VWUHVV LQFUHPHQWV DUH FDOFXODWHG IURP VWUDLQ LQFUHPHQWVYLDDYDULDEOHVWLIIQHVVPDWUL[7KHUHIRUHDQG DV RSSRVHG WR FODVVLFDO SODVWLFLW\ WKH XQORDGLQJ LQ GDPDJH PHFKDQLFV LV IROORZLQJ WKH VHFDQW VWLIIQHVV DQG QRW IROORZLQJ WKH HODVWLF VWLIIQHVV VHH )LJXUH  1R SODVWLF GHIRUPDWLRQV FDQ EH PRGHOOHG &'0 LV D ZLGHVSUHDG DSSURDFK IRU ILEUH FRPSRVLWHV PRGHOOLQJ PDQ\GLIIHUHQWPRGHOVKDYHDOUHDG\EHHQGHYHORSHGHJ >@RU>@ ,Q&'0DGDPDJHYDULDEOHG”G”LVGHWHUPLQHG DQG LQVHUWHG LQWR WKH IXQGDPHQWDO +RRNH HTXDWLRQ DV IROORZV  LM G 'LMNO NO V  H     (7)

,I G  QR GDPDJH LV SUHVHQW LI G  WKH PDWHULDO KDV IDLOHG 7KLV SULQFLSOH RI &'0 DV D QRQOLQHDU HODVWLF DSSURDFKLVYLVXDOLVHGLQ)LJXUH





)LJXUH%DVLFLGHDRI&'0OLQHDUGDPDJHIXQFWLRQ

+RZHYHU DQLVRWURSLF GDPDJH LV REVHUYHG IRU ZRRG ZKLFK PHDQV WKDW VHYHUDO GDPDJH YDULDEOHV PXVW EH GHILQHG WR UHSUHVHQW WKH ' EHKDYLRXU RI ZRRG ([FHHGLQJ WKH DERYH GHVFULEHG IDLOXUH FULWHULD , WR 9,,, DFWLYDWHGFRQMXJDWHGGDPDJHYDULDEOHVGZKHUHWKHVKHDU GDPDJH YDULDEOHV FDQ GHYHORS XQGHU WUDQVYHUVH WHQVLRQ DQGFRPSUHVVLRQDQGKDYHWREHVXSHUSRVHG

x &ULWHULRQ,GW x &ULWHULRQ,,GF

x &ULWHULD,,,DQG,9GW57GY57DQGGUROO x &ULWHULD9WR9,,,GF57GY57DQGGUROO

$V IRU LQVWDQFH WKH ILUVW WZR GDPDJH YDULDEOHV GW DQG

GFDUHGHSHQGLQJRQWKHVDPHVWUHVVFRPSRQHQWV/WKH 0DFDXOD\RSHUDWRUDVGHILQHGLQ(TXDWLRQ  LVXVHGWR GLIIHUHQWLDWHEHWZHHQWHQVLRQDQGFRPSUHVVLRQ(TXDWLRQ     D D D       (8)    / / W F / / G G V G V V V      (9)

(3)

World Conference on Timber Engineering



7ZR GLIIHUHQWVWUHVVVWUDLQEHKDYLRXUV DUH LPSOHPHQWHG HODVWLF SHUIHFWO\ SODVWLF DQG HODVWLF OLQHDU VRIWHQLQJ ([FHHGLQJ WKH FRPSUHVVLRQ VWUHQJWK WULJJHUV GXFWLOH VWUHVVVWUDLQ EHKDYLRXU ZKHUH WKH GDPDJH YDULDEOH IROORZVDQHODVWLFSHUIHFWO\SODVWLFODZ   G N N       (10) 7KHIDLOXUHFULWHULDIRUWHQVLRQDQGVKHDULQVWHDGOHDGWRD OLQHDUVRIWHQLQJVWUHVVVWUDLQUHODWLRQVKLSDVLOOXVWUDWHGLQ )LJXUH  PD[  PD[     I I * ( G I I * ( N N    § · ¨ ¸ © ¹  (11)

ZKHUH IPD[  PD[LPXP VWUHQJWK (  PRGXOXV RI HODVWLFLW\ *I IUDFWXUHHQHUJ\

$V FDQ EH VHHQ LQ (TXDWLRQV   DQG   WKH GHYHORSPHQW RI WKH GDPDJH YDULDEOHV LV QRW GHSHQGLQJ RQWKHVWUDLQVHEXWRQDKLVWRU\SDUDPHWHUNLQVWHDG7KH GDPDJHSDUDPHWHUVGFDQQRWEHDIXQFWLRQRIWKHVWUDLQV H )RU LQVWDQFH RQFH IDLOXUH FULWHULRQ ,,,  )W5 VSOLWWLQJ SDUDOOHO WR /7SODQH  LV DFWLYDWHG GXH WR KLJK ORQJLWXGLQDOVKHDUVWUHVVHVV/7WKHVWLIIQHVVYDOXHVRIDOO RWKHUFRQWULEXWLQJVWUHVVFRPSRQHQWV (5DQG(57 PXVW GHJUDGH DV ZHOO DOWKRXJK WKH UHVS XQLD[LDO VWUHVVHVV5 DQGV57PD\VWLOOEHEHORZWKHXQLD[LDOVWUHQJWKVIWDQG

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

7KH IDLOXUH FULWHULD ) FDQ EH UHIRUPXODWHG LQWURGXFLQJ VWDWHYDULDEOHVNWKDWNHHSWUDFNRIWKHORDGLQJKLVWRU\

  d

Ĭ ) ț ) ț     (12)

7KLV SULQFLSOH LV DQDORJRXV WR WKH IORZ WKHRU\ RI SODVWLFLW\ 7KH ³\LHOG´ VXUIDFHV ) DUH WKH GDPDJH LQLWLDWLRQ IXQFWLRQV RU IDLOXUH FULWHULD $V LQ FODVVLFDO SODVWLFLW\ DQG IROORZLQJ >@ WKH VRFDOOHG .XKQ7XFNHU FRQGLWLRQVPXVWKROG  d Ĭ țtțĬ     (13) )XUWKHUPRUHLWLVUHTXLUHGWKDWWKHGDPDJHYDULDEOHVFDQ RQO\JURZDVJLYHQLQ(TXDWLRQ  ZKLFKIROORZVDOVR IURPWKHVHFRQG.XKQ7XFNHUFRQGLWLRQ  t G       (14)

7KH ILQDO LPSOHPHQWDWLRQ RI WKH KLVWRU\ SDUDPHWHUV DV VWDWHYDULDEOHVLVFDUULHGRXWDVVKRZQLQ(TXDWLRQ  

^ `

^



`

PD[  PD[ W LQFU LQFU W ț )     (15)  &2167,787,9(02'(/ 7KHLQWURGXFHGGDPDJHYDULDEOHVKDYHWREHFRPELQHGLQ D FRQVWLWXWLYH PRGHO (TXDWLRQ   VKRZV WKH FRQVWLWXWLYHUHODWLRQVKLSEHWZHHQVWUDLQVHDQGVWUHVVHVV ZLWK&GDPEHLQJWKHGDPDJHGFRPSOLDQFHPDWUL[ GDP İ & ı    (16) ,Q WKLV GDPDJHG FRPSOLDQFH PDWUL[ ZKLFK LV WKH DQDORJRXV IRUPXODWLRQ WR (TXDWLRQ   VKRZLQJ WKH GDPDJHG VWLIIQHVV PDWUL[ G ā' GDPDJH HIIHFWV DQG LQWHUDFWLRQVKDYHWREHUHSUHVHQWHG)RULQVWDQFHGDPDJH LQ FRPSUHVVLRQ SDUDOOHOWRJUDLQ FRXOG EH DVVXPHG WR OHDGWRDGHFUHDVHRIWKHVWLIIQHVVLQWHQVLRQSDUDOOHOWR JUDLQ GXULQJ D VXEVHTXHQW ORDGLQJ F\FOH )XUWKHUPRUH DVVXPSWLRQV DERXW WKH HIIHFWV RI GDPDJH SDUDOOHOWR JUDLQ RQ WKH VWUHQJWK SHUSHQGLFXODUWRJUDLQ QHHG WR EH WDNHQ

,QWKHGHYHORSHGPDWHULDOPRGHOQRGDPDJHLQWHUDFWLRQV ZHUHPRGHOOHG)RULQVWDQFHLWLVDVVXPHGWKDWGDPDJH LQ WHQVLRQ SHUSHQGLFXODUWRJUDLQ GRHV QRW OHDG WR D GHJUDGDWLRQRI WKH SURSHUWLHV SDUDOOHOWRJUDLQ (TXDWLRQ   VKRZV WKH GDPDJHG FRPSOLDQFH PDWUL[ ZKHUH WKH VLQJOHPDWUL[HQWULHVDUHJLYHQ

,Q ILQLWH HOHPHQW SURJUDPPHV WKH LQYHUVH RI WKH FRPSOLDQFH PDWUL[ & LV QHHGHG LQ RUGHU WR XSGDWH WKH VWUHVVHV +RZHYHU ZKHQ FDOFXODWLQJ WKH LQYHUVH RI WKH GDPDJHG FRPSOLDQFH PDWUL[ DV JLYHQ LQ (TXDWLRQ   QRQGLDJRQDO QRQ]HUR HQWULHV RI WKH IRUP QLM G  FRQWDLQLQJ 3RLVVRQ¶V UDWLRVDQG GDPDJH SDUDPHWHUV ZLOO EH REWDLQHG LQ WKH GDPDJHG VWLIIQHVV PDWUL[ %\ PHDQV RI WKH 3RLVVRQ¶V UDWLRV WKH UHODWLRQVKLS EHWZHHQ WKH QRUPDO VWUHVVHV UHVS VWUDLQV LV GHILQHG 6XEVHTXHQWO\ WKHVH QRQGLDJRQDO HQWULHV PXVW DOVR EH DGMXVWHG WDNLQJ GDPDJHLQWRDFFRXQWQLM QLM G 

,WLVVDIHWRDVVXPHWKDWZLWKLQFUHDVLQJGDPDJHDOVRWKH 3RLVVRQ¶V UDWLRV ZLOO GHJUDGH +RZHYHU H[FHSW IRU >@ QROLWHUDWXUHLVNQRZQWRWKHDXWKRUZKHUHWKHHYROXWLRQ RI WKH 3RLVVRQ¶V UDWLRV GXULQJ D WHVW ZDV PHDVXUHG /LQHDUGHJUDGDWLRQDVVKRZQLQ)LJXUHRUH[SRQHQWLDO GHJUDGDWLRQ FRXOG EH LPSOHPHQWHG +HUH WKH FKRVHQ 3RLVVRQ¶VUDWLRVKDYHWKHYDOXHRIWKHGDPDJHG3RLVVRQ¶V UDWLRV DOUHDG\ DW WKH EHJLQQLQJ RI WKH PRGHOOLQJ VHH )LJXUH  7KH QRUPDO GDPDJH SDUDPHWHUV G DQG G57 DUHFRQVLGHUHGWREHGHFRXSOHG

/LQHDU GHJUDGDWLRQ ZDV LPSOHPHQWHG EXW SURYHG WR EH WRRZHDNLQRUGHUWRDYRLGDZURQJ3RLVVRQHIIHFWZKLFK LVZK\ORZ3RLVVRQ¶VUDWLRVIURPWKHEHJLQQLQJRQZHUH FKRVHQ                                                           G ( ( ( ( G 5( ( ( ( G ( GDP 7 GY5* GY7* GUROO* X X X X X X ª º   «  » « » « » «   » «  » « » « » «   » «  » « » « » «  » « » « » « »  « » « » « » «  » ¬ ¼ & (17)

(4)

World Conference on Timber Engineering   )LJXUH'HJUDGDWLRQRI3RLVVRQ¶VUDWLRV   0(6+5(*8/$5,6$7,21

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

,Q OLWHUDWXUH PDQ\ GLIIHUHQW UHJXODULVDWLRQ PHWKRGV DUH DYDLODEOH >HJ @ +HUH WKH FUDFN EDQG PHWKRG DV GHVFULEHGLQ>@ZDVFKRVHQWRUHJXODULVHWKHPHVK:LWK WKHFUDFNEDQGPHWKRGWKHIUDFWXUHHQHUJ\LVH[SUHVVHG LQWHUPVRIFKDUDFWHULVWLFILQLWHHOHPHQWOHQJWKKZKHUHK LVDJHRPHWULFDOYDOXHLQ>OHQJWK@FRQWDLQLQJLQIRUPDWLRQ RQWKHHOHPHQW¶VDVSHFWUDWLR I I * J K      (18)

,Q HTXDWLRQ   WKH IUDFWXUH HQHUJ\ *I QHHGV WR EH UHSODFHG E\ WKH FKDUDFWHULVWLF IUDFWXUH HQHUJ\ JI LI WKH FUDFN EDQG PRGHO LV DFWLYDWHG 7KH LQWURGXFWLRQ RI D FKDUDFWHULVWLF IUDFWXUH HQHUJ\ JI WKDW LV FRUUHODWHG WR WKH HOHPHQWVL]HSURYLGHVWKHWUDQVIRUPDWLRQRIWKHIUDFWXUH HQHUJ\*ILQWRDµPHVKGHSHQGHQW¶YDOXH)RULQVWDQFHLQ DFRDUVHPHVKKZLOOEHODUJHDQGOHDGVKHQFHWRDVPDOO FKDUDFWHULVWLF IUDFWXUH HQHUJ\ JI LQ FRPSDULVRQ WR WKH ODUJH JI RI D ILQH PHVK ZLWK D VPDOO FKDUDFWHULVWLF HOHPHQWOHQJWKK7KLVDGMXVWPHQWRIWKHIUDFWXUHHQHUJ\ FRQVLGHULQJ WKH PHVK VL]H FRPSHQVDWHV IRU WKH WUHQG RI FRQWLQXXP VRIWHQLQJ PRGHOV WR GLVVLSDWH DV OHVV HQHUJ\ DVSRVVLEOH

+RZHYHUWKHFUDFNEDQGPRGHORQO\ZRUNVLIRQHIDLOXUH PRGHLVGRPLQDWLQJDQGLIDORFDOLVHGVROXWLRQRFFXUV,W LV YDOLG LI GDPDJH GHYHORSV RQO\ LQ D EDQG RI HOHPHQWV DQG QRW LQ DOO HOHPHQWV KRPRJHQHRXVO\ 7KHUHIRUH WKH GHFLVLRQZKHWKHUWRDFWLYDWHWKHFUDFNEDQGPRGHORUQRW PXVWEHFDUHIXOO\WDNHQIRUHDFKPRGHO

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a. b. )LJXUHD0RGHOZLWKRXWUHJXODULVDWLRQ E&UDFNEDQGPHWKRGDFWLYDWHG   9,6&28667$%,/,6$7,21 9LVFRXVVWDELOLVDWLRQDQDORJRXVO\WR>@LVXVHGLQRUGHU WR LPSURYH WKH FRQYHUJHQFH FKDUDFWHULVWLFV RI WKH GHYHORSHGPDWHULDOPRGHO$ILFWLWLRXVYLVFRXVSDUDPHWHU K LV LQWURGXFHG LQ WKH PRGHO 'XH WR WKH DGGLWLRQDO YLVFRXV FRPSRQHQW WKH VWLIIQHVV PDWUL[ LV JHQHUDOO\ SRVLWLYHGHILQLWH7KHUHIRUHYLVFRXVVWDELOLVDWLRQOHDGVWR D PRUH UREXVW VROXWLRQ SURFHVV ZLWK OHVV FRQYHUJHQFH SUREOHPV

$V YLVFRVLW\ LV D WLPHGHSHQGHQW PDWHULDO SDUDPHWHU YLVFRXV VWDELOLVDWLRQ PXVW EH D IXQFWLRQ RI WKH UDWH RI GDPDJH 7KH UDWH RI WKH GDPDJH YDULDEOH RU RI WKH GDPDJH WKUHVKROG  IDLOXUH FULWHULD  PD\ EH XVHG (TXDWLRQ   VKRZV WKH VWDELOLVDWLRQ DV D IXQFWLRQ RI UDWHRIGDPDJHYDULDEOHV

G G9

G K        (19)

,Q (TXDWLRQ   WKH YLVFRXV SDUDPHWHUK GHILQHV WKH UDWH DW ZKLFK WKH WUXH GDPDJH G DQG WKH VWDELOLVHG GDPDJH G9 DV GHILQHG LQ (TXDWLRQ   DSSURDFK HDFK RWKHU (TXDWLRQ   FDQ QRZ EH GLVFUHWLVHG LQ WLPH (TXDWLRQ   VKRZV WKH GLVFUHWLVHG HTXDWLRQ EDVHG RQ WKH EDFNZDUG (XOHU DOJRULWKP WR LQVHUW DQ DUWLILFLDO YLVFRVLW\KWKDWLVDFWLQJRQWKHGDPDJHYDULDEOHV   PD[   W W W W 9 9 9 GW G G G G GW GW K K K      ­ ½ ® ¾ ¯ ¿  (20)

$V YLVFRXV VWDELOLVDWLRQ LV DSSOLHG WR LPSURYH FRQYHUJHQFH WKH HQHUJ\ RXWSXW PXVW EH FRQWUROOHG LQ RUGHUWRMXGJHWKHPRGHOSHUIRUPDQFHDQGUHOLDELOLW\LH WR FRQWURO WKDW ILFWLWLRXV YLVFRVLW\ LV QRW LQIOXHQFLQJ PRGHOOLQJ UHVXOWV 7R WKLV VFRSH WKH WRWDO GLVVLSDWHG HQHUJ\DQGWKHGLVVLSDWHGHQHUJ\DVVRFLDWHGZLWKYLVFRXV UHJXODULVDWLRQ DUH FDOFXODWHG DV LQWHUQDO VWDWH YDULDEOHV %RWKYDULDEOHVGRQRWKDYHDQ\LQIOXHQFHRQWKHVROXWLRQ 7KH\DUHPHUHO\XVHGIRUHQHUJ\RXWSXWFRQWURODQGSRVW SURFHVVLQJ



 0$7(5,$/3523(57,(6

$ PDMRU LVVXH RI DOO PDWHULDO PRGHOV LV WKH QHHG RI PHFKDQLFDO LQSXW SDUDPHWHUV VXFK DV VWLIIQHVV DQG VWUHQJWK YDOXHV ZKLFK XVXDOO\ GHULYH IURP WHVWV 7KH GHYHORSHG ZRRG PRGHO QHHGV VHYHQWHHQ SURSHUWLHV DV OLVWHGLQ7DEOHIRUWKUHHGLIIHUHQWZRRGVSHFLHV

(5)

World Conference on Timber Engineering



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

$OVRWKHIUDFWXUHHQHUJLHVVXIIHUIURPDODUJHVFDWWHUDQG WKH IDFW WKDW WKH\ DUH XVXDOO\ PHDVXUHG RQ VPDOO FOHDU ZRRGVSHFLPHQVZKHUHDVIRUDKHWHURJHQHRXVPDWHULDOLW FDQ EH VDIHO\ DVVXPHG WKDW IUDFWXUH HQHUJLHV DUH QRW FRQVWDQW 0RUHRYHU WKH QHHGHG PDWHULDO YDOXHV DUH UDWKHU HDVLO\ SURFXUDEOH IRU VRIWZRRGV EXW QRW IRU KDUGZRRGV

,Q >@ D WKRURXJK OLWHUDWXUH VWXG\ KDV EHHQ FDUULHG RXW ZKHUHWKHLVVXHVDURXQGUHOLDEOHPDWHULDOSDUDPHWHUVDUH GLVFXVVHG DQG WKH FKRVHQ YDOXHV IURP 7DEOH  DUH PRWLYDWHG 7DEOH0DWHULDOSURSHUWLHVIRUVSUXFHEHHFKDQGD]REp  9DULDWLRQ$%HHFKQHHGHGIRUODWHUPRGHOOLQJ  3DUDPHWHU 8QLWV 6SUXFH 3LFHD DELHV %HHFK )DJXV V\OYDWLFD $]REp /RSKLUD DODWD 9DULDWLRQ $ %HHFK (     ( (     * *     *     IW     IF     IW     IF     IY     IUROO     *I     *I     *IY     *IUROO     K -     03D 1PP    6800$5<

7KH GHYHORSHG PDWHULDO PRGHO ZDV SURJUDPPHG LQ D XVHU VXEURXWLQH UMAT DQG LQVHUWHG LQWR WKH FRPPHUFLDO )(VRIWZDUH$%$486Š

)LJXUHVKRZVWKHIORZGLDJUDPRIWKHGHYHORSHG&'0 PDWHULDOVXEURXWLQH7KHVXEURXWLQHLVJLYHQLQ>@ 7KH LQWURGXFHG PDWHULDO PRGHO EDVHG RQ SLHFHZLVH GHILQHG IDLOXUH FULWHULD DQG VHYHUDO GDPDJH SDUDPHWHUV IROORZLQJ HODVWLF SHUIHFWO\ SODVWLF RU OLQHDU VRIWHQLQJ ODZVUHSUHVHQWVDVLPSOLILHGDSSURDFKIRUZRRG

Read actual total deformations at end of increment t

kltot= klt-1+ klt

Calculate predictive elastic stress at end of increment t

ijef= Dijklākltot

Check failure initiation F(fmax, material, ijef) •

Calculate damage parameters dij with: 0≤dij<1 and ∂dij/∂t≥0

YES NO

dij= 0

Update stresses

ijt= inv(Cijkldam)ākltot



)LJXUH)ORZGLDJUDPRI&'0

'HQVLILFDWLRQ ILEUH NLQNLQJ RU RWKHU HIIHFWV GXH WR WKH DQDWRPLFDOVWUXFWXUHFDQQRWEHPRGHOOHG+RZHYHUDIWHU D WKRURXJK OLWHUDWXUH VWXG\ RI ERWK DYDLODEOH PRGHOOLQJ DSSURDFKHV DQG PHFKDQLFDO PDWHULDO EHKDYLRXU >@ WKH LQQRYDWLYH SRWHQWLDO RI &'0 LQ FRPELQDWLRQ ZLWK FOHDU DQGVLPSOHFRQVWLWXWLYHODZVLVFRQYLQFLQJ

6LPSOH FRQVWLWXWLYH ODZV ZLWK H[SOLFLW PHFKDQLFDO SURSHUWLHV IDFLOLWDWH XQGHUVWDQGLQJ DQG LQVSHFWLRQRI WKH PRGHOV1RVPHDUHGLQSXWYDOXHVQHHGWRLQWURGXFHGDQG WKHLU HIIHFW FDQ EH GLUHFWO\ WUDQVODWHG WR WKH PRGHO UHVXOWV

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



 02'(//,1*

 9$/,'$7,21

:KHQ GHYHORSLQJ FRQVWLWXWLYH ODZV UHVXOWV RI VLQJOH HOHPHQWPRGHOVRURQPRGHOVZLWKIHZHOHPHQWVQHHGWR EH YDOLGDWHG )RU WKLV SXUSRVH GLIIHUHQW PRGHO YDOLGDWLRQV ZHUH FDUULHG RXW DPRQJ ZKLFK FRPSUHVVLRQ RQDFXEHZLWKGLIIHUHQWDQJOHVWRWKHJUDLQ

)LJXUHVKRZVPRGHOOLQJUHVXOWVRQVSUXFHZRRGXVLQJ WKH GHYHORSHG UMAT WRJHWKHU ZLWK WKH )( PRGHO KHUH ZLWKOLQHDUEULFNHOHPHQWVZLWKIXOOLQWHJUDWLRQ 7KH FUDFNEDQGPRGHOZDVGHDFWLYDWHGDVQRORFDOFUDFNEDQG LV H[SHFWHG DQG WKHUHIRUH WKH FUDFN EDQG PRGHO LV QRW

(6)

World Conference on Timber Engineering

YDOLG $V FDQ EH REVHUYHG LQ )LJXUH  FRPSUHVVLRQ SDUDOOHO DQG SHUSHQGLFXODUWRJUDLQ VKRZHG HODVWLF SHUIHFWO\ SODVWLF EHKDYLRXU DV LPSOHPHQWHG ZKHUHDV IRU ƒ DQG ƒ EULWWOH EHKDYLRXU GXH WR WKH LQIOXHQFH RI EULWWOHVKHDUGDPDJHODZVFRXOGEHREVHUYHG7KLVFDQEH FRQILUPHGZLWKWHVWUHVXOWVVHH>@>@

)LJXUH  VKRZV WKH RYHUODS RI WKH +DQNLQVRQ HTXDWLRQ >@ZLWK)(UHVXOWV VDPHPRGHODVVKRZQLQ)LJXUH EXW FRQVLVWLQJ RI RQH HOHPHQW  7KH ORDG FDUU\LQJ FDSDFLW\ FDQ EH VDWLVI\LQJO\ SUHGLFWHG ZLWK D PD[LPXP GLIIHUHQFHEHWZHHQ)(PRGHODQG+DQNLQVRQHTXDWLRQRI 

)LJXUHDQG)LJXUHXQGHUOLQHWKHSUHGLFWLRQFDSDELOLW\ RI WKH &'0 PRGHO 1RW RQO\ ORDG FDUU\LQJ FDSDFLWLHV FDQ EH SUHGLFWHG EXW DOVR WKH JHQHUDO VWUHVVVWUDLQ EHKDYLRXU ZLWK FRPELQHG GXFWLOH DQG EULWWOH IDLOXUHV (VSHFLDOO\ WKH SUHGLFWLRQ RI WKH GLIIHUHQW ORDGVOLS EHKDYLRXUEHWZHHQWKHPRGHOVORDGHGDWDQDQJOHWRWKH JUDLQRIƒEULWWOHDQGƒPRUHGXFWLOHLVJRRG )XUWKHUYDOLGDWLRQVZHUHFDUULHGRXWZLWKGLIIHUHQWPHVK VL]H DQG PDWHULDO RULHQWDWLRQV GLIIHUHQW ORDGLQJ IURP UHYHUVHG F\FOLF ORDGLQJ WR FRPELQHG ORDGLQJ RI QRUPDO VWUHVVHVDQGVKHDU$OOYDOLGDWLRQVDUHVKRZQLQ>@DQG FRQILUPHGWKHFRUUHFWLPSOHPHQWDWLRQDQGFDOFXODWLRQRI WKHVXEURXWLQH               'LVSODFHPHQW>PP@ /RDG>N1@ GHJUHHV GHJUHHV GHJUHHV GHJUHHV  )LJXUH5HVXOWV)(PRGHOIRUFRPSUHVVLRQZLWK GLIIHUHQWDQJOHVWRWKHJUDLQVSUXFH 0 5 10 15 20 25 30 35 40 0 10 20 30 40 50 60 70 80 90 Angle D to the grain

C o m pr essi o n st re n gt h [M P a ]  )LJXUH6XSHUSRVLWLRQRI)(UHVXOWVZLWK +DQNLQVRQHTXDWLRQVSUXFH  0$7(5,$/02'(/6 ,QRUGHUWRYHULI\WKHFDSDELOLW\RIWKHPRGHOVWRSUHGLFW WKH PHFKDQLFDO EHKDYLRXU RI ZRRG DYDLODEOH PDWHULDO WHVWVIURPOLWHUDWXUHZHUHPRGHOOHG0DWHULDOWHVWVGRQRW

\HW FRQWDLQ DQ\ RWKHU PDWHULDO ODZV RU FRQWDFW IRUPXODWLRQV DQG DUH WKH ILUVW ORJLFDO PRGHOOLQJ VWHS EHIRUHGHYHORSLQJHPEHGPHQWPRGHOV

7KH FKRVHQ WHVWV ZHUH XQGHUWDNHQ E\ >@ 7HQVLRQ WHVWV SDUDOOHOWRJUDLQ DV VKRZQ LQ )LJXUH  ZLWK DV\PPHWULF GRJ ERQH VSHFLPHQV ZLWK D WDSHUHG DUHD RI [PP DUHSUHVHQWHGKHUH)RURWKHUPDWHULDOWHVWVSOHDVHUHIHU WR >@ $OO WHVWV ZHUH FDUULHG RXW RQ VPDOO FOHDU VSUXFH VSHFLPHQV+RZHYHUWKHPDWHULDOSDUDPHWHUVIRUVSUXFH XVHG LQ WKH )( PRGHOV ZHUH GHULYHG IRU VWUXFWXUDOVL]H ZRRG DQG DUH JLYHQ LQ 7DEOH  /LQHDU EULFNV ZLWK IXOO LQWHJUDWLRQ ZHUH XVHG DQG WKH FUDFN EDQG PRGHO ZDV DFWLYDWHG

)LJXUH  VKRZV WKH PRGHOOLQJ UHVXOWV LQ WHUPV RI ORDG VOLS ZKHUH VRPH LQFUHPHQWV DUH LQGLFDWHG 7KH VDPH LQFUHPHQWV DUH VKRZQ LQ )LJXUH  LQ WHUPV RI GDPDJH YDULDEOHGWIRUGDPDJHGXHWRWHQVLRQSDUDOOHOWRJUDLQ 7KH FUDFN GHYHORSPHQW LQ WKH WDSHUHG DUHD ZKLFK LV DV\PPHWULF GXH WR WKH VSHFLPHQ JHRPHWU\  LV FOHDUO\ LGHQWLILHG )XUWKHUPRUH VWDEOH FUDFN JURZWK FDQ EH PRGHOOHG

7KH FRPSDULVRQ ZLWK WKUHH W\SLFDO ORZHU ERXQG WHVW UHVXOWV>@VKRZHGJRRGTXDOLWDWLYHDJUHHPHQW+RZHYHU WKHORDGFDUU\LQJFDSDFLW\ZDVJHQHUDOO\XQGHUHVWLPDWHG ZKLFKLVH[SOLFDEOHDVWKHFKRVHQPDWHULDOSURSHUWLHVIRU PRGHOOLQJ ZHUH EDVHG RQ VWUXFWXUDOVL]H ZRRG ZKHUHDV WKHWHVWVZHUHRQFOHDUZRRG  ; < = ZRRG 80$7 ZRRG OLQHDUïHODVWLF 6WHHO 8\ PP 8[ 8]  8[ 8\ 8]  VWLFNïVOLSIULFWLRQ EHWZHHQGRZHO DQGZRRG P   )LJXUH7HQVLRQSDUDOOHOWRJUDLQJHRPHWU\IURP>@              'LVSODFHPHQW>PP@ /RDG>N1@ PRGHO WHVWV  )LJXUH/RDGVOLSJUDSKRIWHQVLRQPRGHO  ; < = 6WHHOSODWHV :RRG 80$7 6WLFNïVOLS Q  8[ 8]  8[ 8\ 8]  DOORWKHU%&8[  8[ ïPP Hankinson FE 1 element

(7)

World Conference on Timber Engineering   $YJ 6'9 H Hï Hï Hï Hï Hï Hï Hï Hï Hï Hï Hï H ïHï ; < =  ODVW )LJXUH7HQVLRQSDUDOOHOWRJUDLQGDPDJHYDULDEOHGWDWLQGLFDWHGLQFUHPHQWV   (0%('0(1702'(/6

(PEHGPHQW PRGHOV ZHUH GHYHORSHG ZKRVH RXWFRPHV FRXOG EH YHULILHG ZLWK WHVWV WDNHQ IURP OLWHUDWXUH >@ 7KUHHGLIIHUHQWZRRGVSHFLHVZHUHFKRVHQVSUXFHEHHFK DQGD]REp7KHPDWHULDOSURSHUWLHVDUHJLYHQLQ7DEOH 7KH)(PRGHOLVVKRZQLQ)LJXUHRQO\DTXDUWHURI DQ HPEHGPHQW VSHFLPHQ ZLWK D PP GRZHO ZDV PRGHOOHG $OVR KHUH QR ORFDOLVHG GDPDJH LV H[SHFWHG DQG WKH FUDFN EDQG PRGHO ZDV GHDFWLYDWHG $JDLQ ' VROLGV ZLWK OLQHDU LQWHUSRODWLRQ EHWZHHQ WKH HLJKW LQWHJUDWLRQ SRLQWV ZHUH FKRVHQ )ULFWLRQ EHWZHHQ GRZHO DQGZRRGZDVVLPXODWHGZLWKWKHVWLFNVOLSPRGHODQGD IULFWLRQFRHIILFLHQWRIP 

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ïVOLS 8[ PP GLVSODFHPHQWIRUORDGïVOLS  )LJXUH4XDUWHURIHPEHGPHQWPRGHOZLWKERXQGDU\ FRQGLWLRQVPDWHULDOVDQGGHIDXOWPHVK  DEF )LJXUH(PEHGPHQWRIVSUXFHZLWKPPGRZHO DGDPDJHYDULDEOHGFLQFRPSUHVVLRQ SDUDOOHOWRJUDLQEWHVWUHVXOW FGDPDJHYDULDEOHGWLQWHQVLRQ SHUSHQGLFXODUWRJUDLQ 7LPH      6WUHVVHOHPHQWD>03D@        663,7,0%(5ï(,3 663,7,0%(5ï(,3 7LPH      6WUHVVHOHPHQWD>03D@       663,7,0%(5ï(,3 663,7,0%(5ï(,3  a. b. )LJXUH6WUHVVFRPSRQHQWVVDQGV DHOHPHQWDEHOHPHQWE )LJXUH  )LJXUHVKRZVORDGVOLSJUDSKVRID]REp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ime Time Stres s [MP a] e le m en t a Stres s [MP a] e le m en t b

(8)

World Conference on Timber Engineering                 'LVSODFHPHQW>PP@ (PEHGPHQWVWUHQJWK>03D@ PRGHO WHVWV  )LJXUH)(UHVXOWYHUVXVWHVWUHVXOWVRIHPEHGPHQW WHVWVRQD]REpZLWKPPGRZHOV 7LPH       6WUDLQ>ï@ ï ï ï    ((((3,=8*67$%ï(,3 ((((3,=8*67$%ï(,3 ((((3,=8*67$%ï(,3 ((((3,=8*67$%ï(,3 ((((3,=8*67$%ï(,3 ((((3,=8*67$%ï(,3  )LJXUH7\SLFDOVWUDLQFRPSRQHQWVRILQGLFDWHG HOHPHQWDPRGHOVKRZQLQ)LJXUH $FFRUGLQJO\WKHUHDUHWKUHHPDLQRSWLRQVWRLPSURYHWKH PRGHO SHUIRUPDQFH DQG WR DYRLG ORFDO HDUO\ EULWWOH IDLOXUHVGXHWRVSXULRXVHQHUJ\PRGHV

x ,QWURGXFWLRQ RI D WKUHVKROG YDOXH IRU WKH GDPDJH YDULDEOHV LQ RUGHU WR DYRLG FRPSOHWH GDPDJH DQG WR NHHSDUHVLGXDOVWLIIQHVV7KLVKRZHYHULVQRWWKRXJKW WR EH D JRRG VROXWLRQ DV DQ XQFRQWUROODEOH ILFWLWLRXV SDUDPHWHUZRXOGEHLQWURGXFHG

x &KDQJHUHVSLQFUHDVHPHFKDQLFDOSURSHUWLHVLQRUGHU WRDYRLGHDUO\FRPSOHWHGDPDJHRIHOHPHQWV

x 5HIRUPXODWHDQGVPHDUGDPDJHRYHUPRUHWKDQRQH HOHPHQW GLVDVVRFLDWH GDPDJH IURP WKH VLQJOH LQWHJUDWLRQSRLQWV

3RLQWWKUHHLVSDUWRIIXWXUHUHVHDUFKDVWKHQWKHPDWHULDO VXEURXWLQH ZLOO EH RSWLPLVHG DQG VROXWLRQV ZLOO EH GHYHORSHGWRFRQWUROH[FHVVLYHHOHPHQWGLVWRUWLRQ 7KH VHFRQG RSWLRQ KRZHYHU ZDV FDUULHG RXW LQ RUGHU WR XQGHUVWDQGWKHLQIOXHQFHRIWKHPDWHULDOSDUDPHWHUV$OVR FRQVLGHULQJWKHUDWKHUGLIILFXOWGHWHUPLQDWLRQRIPDWHULDO SURSHUWLHVLWLVWKRXJKWWREHDGPLVVLEOHWRPRGLI\WKHVH SDUDPHWHUV7DEOHJLYHVPRGLILHGPDWHULDOSDUDPHWHUV IRU EHHFK ZRRG QRPLQDWHG ³YDULDWLRQ $´ ZKHUH WKH SURSHUWLHV GHILQLQJ WKH ' EULWWOH EHKDYLRXU DUH LQFUHDVHG)LJXUHVKRZVWKHPRGHOOLQJUHVXOWVIRUDQ HPEHGPHQWWHVWVSHFLPHQZLWKWKHGHIDXOWSURSHUWLHVIRU EHHFKDQGYDULDWLRQ$VXSHUSRVHGZLWKWHVWUHVXOWV7KH ORDGVOLS EHKDYLRXU DSSO\LQJ WKH GHIDXOW SURSHUWLHV VKRZV DJDLQ WRR EULWWOH EHKDYLRXU GXH WR QXPHULFDO VRIWHQLQJ 7KH PRGHO XVLQJ PRGLILHG SURSHUWLHV ³YDULDWLRQ$´UHDFKHVKLJKHUGHIRUPDWLRQVEHIRUHIDLOXUH 7KH KLJKHU YDOXHV IRU VWUHQJWK DQG IUDFWXUH HQHUJLHV DV

GHILQHGIRU³YDULDWLRQ$´OHDGWRQXPHULFDOVRIWHQLQJDW KLJKHUGHIRUPDWLRQVZKLFKLVPRUHUHDOLVWLF

$V WKH UHVXOWLQJ FXUYH IRU ³YDULDWLRQ $´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³YDULDWLRQ$´LVFOHDUO\REVHUYDEOHLQWKH GHWDLO 7KH JOREDO VWLIIQHVV LV WKXV GHFUHDVLQJ DOWKRXJK WKHPRGHOVWLOOVKRZVDYHU\FOHDUORDGLQFUHDVH7KLVLVD UHDOLVWLFSUHGLFWLRQ               'LVSODFHPHQW>PP@ (PEHGPHQWVWUHQJWK>03D@ PRGHO YDULDWLRQ$ YDULDWLRQ$ZLWKIF 03D YDULDWLRQ$ZLWKIF 03D WHVWV     )LJXUH)(UHVXOWYHUVXVWHVWUHVXOWVRIHPEHGPHQW WHVWVRQEHHFKZLWKPPGRZHOVPDWHULDO SDUDPHWHUVPRGLILHG±YDULDWLRQ$ZLWKGHWDLO 

 &21&/86,216

$ SURPLVLQJ KROLVWLF FRQVWLWXWLYH ' PRGHO IRU WKH PDWHULDO ZRRG FRXOG EH GHYHORSHG WKDW FDQ LGHQWLI\ IDLOXUH PRGHV DQG FRPELQH VLPXOWDQHRXV GXFWLOH DQG EULWWOH IDLOXUHV ZLWKLQ RQH PRGHO 7KH PHFKDQLFDO PDWHULDO SDUDPHWHUV QHHGHG IRU WKH FRQVWLWXWLYH UHODWLRQVKLSDUHFOHDUO\GHILQHG7KHPDWHULDOPRGHOUXQV LQDFRPSOH[)(HQYLURQPHQWLQFRPELQDWLRQZLWKRWKHU PDWHULDOPRGHOVDQGFRQWDFWIRUPXODWLRQV

7KH GHYHORSHG PDWHULDO PRGHO LV D VLPSOLILHG PDWHULDO PRGHOWKDWFDQQRWSHUIHFWO\UHSURGXFHPDWHULDOWHVWVHJ NLQN EDQGV RU GHQVLILFDWLRQ FDQQRW EH UHSUHVHQWHG ,W FRXOGEHVKRZQKRZHYHUWKDWVXFKDVLPSOLILHGPRGHOLV VXIILFLHQWO\SUHFLVHIRUPRUHFRPSOH[ PRGHOVWKDQSXUH PDWHULDOPRGHOVLHHPEHGPHQWPRGHOV

)LUVW PRGHOOLQJ UHVXOWV ZHUH VDWLVI\LQJ LQ WHUPV RI VWLIIQHVVDQGORDGFDUU\LQJFDSDFLW\1XPHULFDOVRIWHQLQJ FDXVHG E\ VSXULRXV HQHUJ\ PRGHV RI FRPSOHWHO\ FROODSVHGHOHPHQWVKRZHYHUOHGWRHDUO\EULWWOHIDLOXUHRI PRGHOV WKDW GLG QRW UHSUHVHQW SK\VLFDO IDLOXUH )XUWKHUPRUH RQFH XQORDGLQJ KDV VWDUWHG LQ WKH PRVW VWUHVVHG HOHPHQWV WKH ORDG LV QRW WUDQVIHUUHG WR QHLJKERXULQJHOHPHQWV 7KHVH QXPHULFDO SUREOHPV QHHG WREHVROYHGLQRUGHUWRRSWLPLVHWKHVXEURXWLQH

$VIRUDQ\RWKHUPRGHOOLQJDSSURDFKDPDMRULVVXHOLHV LQ WKH GHWHUPLQDWLRQ RI WKH QHHGHG PHFKDQLFDO SURSHUWLHV $V WKH PRGHO SHUIRUPDQFH DQG SUHGLFWLRQ

; <

=

(9)

World Conference on Timber Engineering FDSDFLW\ LV KLJKO\ GHSHQGHQW RQ WKHVH SURSHUWLHV PHWKRGVWRGHULYHUHOLDEOHYDOXHVPXVWEHGHYHORSHG 

5()(5(1&(6

>@ +LOO5$WKHRU\RIWKH\LHOGLQJDQGSODVWLFIORZRI DQLVRWURSLF PHWDOV 3URFHHGLQJV 5R\DO 6RFLHW\

/RQGRQ 6HULHV$

>@ +RIIPDQ 2 7KH EULWWOH VWUHQJWK RI RUWKRWURSLF PDWHULDOV -RXUQDO RI &RPSRVLWH 0DWHULDOV   

>@ 0DLPt 3 0RGHOL]DFLyQ FRQVWLWXWLYD \ FRPSXWD FLRQDO GHO GDxR \ OD IUDFWXUD GH PDWHULDOHV FRPSXHVWRV 3K' WKHVLV 8QLYHUVLWDW GH *LURQD 

>@ 0DW]HQPLOOHU $ /XEOLQHU - DQG 7D\ORU 5/ $ &RQVWLWXWLYH 0RGHO IRU $QLVRWURSLF 'DPDJH LQ )LEHU&RPSRVLWHV0HFKDQLFVRI0DWHULDOV  >@ )UDQNH6=XU%HVFKUHLEXQJGHV7UDJYHUKDOWHQVYRQ +RO]XQWHU9HUZHQGXQJHLQHVSKRWRJUDPPHWULVFKHQ 0HVVV\VWHPV 3K' WKHVLV %DXKDXV8QLYHUVLWlW :HLPDU

>@ 6OX\V /- :DYH 3URSDJDWLRQ /RFDOLVDWLRQ DQG 'LVSHUVLRQ LQ 6RIWHQLQJ 6ROLGV 3K' WKHVLV 7HFKQLVFKH8QLYHUVLWHLW'HOIW

>@ %DåDQW =3 DQG 2K %+ &UDFN EDQG WKHRU\ IRU IUDFWXUHRIFRQFUHWH0DWpULDX[HW&RQVWUXFWLRQV 

>@ 6DQGKDDV&0HFKDQLFDOEHKDYLRXURIWLPEHUMRLQWV ZLWKVORWWHGLQVWHHOSODWHV3K'WKHVLV8QLYHUVLW\RI 7HFKQRORJ\'HOIWLQSUHSDUDWLRQ

>@ 0RVHV '0 DQG 3ULRQ +*/ 6WUHVV DQG IDLOXUH DQDO\VLV RI ZRRG FRPSRVLWHV D QHZ PRGHO

&RPSRVLWHV3DUW%(QJLQHHULQJ

>@ 6DQGKDDV & ' 0DWHULDO 0RGHO IRU :RRG %DVHG RQ&RQWLQXXP'DPDJH0HFKDQLFV6WHYLQUDSSRUW

 6WHYLQ ,, /DERUDWRU\ 8QLYHUVLW\ RI

7HFKQRORJ\'HOIW

>@ +DQNLQVRQ 5/ ,QYHVWLJDWLRQ RI FUXVKLQJ VWUHQJWK RI VSUXFH DW YDU\LQJ DQJOHV RI JUDLQ 8 6 $LU

6HUYLFH,QIRUPDWLRQ&LUFXODU9RO1R

>@ 6DQGKDDV & YDQ GH .XLOHQ -: %ODVV +- DQG 5DYHQVKRUVW * (PEHGPHQW WHVWV SDUDOOHOWRJUDLQ DQG GXFWLOLW\ LQ WURSLFDO KDUGZRRG VSHFLHV

3URFHHGLQJV:&7(5LYDGHO*DUGD,WDO\ )LQLWH(OHPHQW6RIWZDUHSDFNDJH

$%$486Š 9HUVLRQ  'DVVDXOW 6\VWqPHV 6LPXOLD &RUS3URYLGHQFH5,86$

Cytaty

Powiązane dokumenty

W afektywnej historii sztuki interesuje mnie to, w jaki sposób afekty po- wstają (jako biologiczne fenomeny) w swojej ramie historycznej, jak są przez artystów problematyzowane

dat voor korrelige materialen &#34;acoustic emission&#34; activiteit en. plastische rek door eenzelfde mechanisme

Jednak poglądy, firmowane przez IPCC, nie zamy- kają dyskusji: w artykule [13] R.Harris prezentuje trzy wizje glo- balnych zmian klimatycznych, powołując się na opinie R.Alleya

Dla wszystkich badanych modeli przekroczenie nośności granicznej powodo- wało zniszczenie zespolenia na skutek ścięcia lub wyciągnięcia gwoździ mocują- cych łączniki,

[r]

[r]

Małżonek, od którego zasądzono należ­ ność, nie może się bowiem bronić zarzutem, że nie jest dłużnikiem, jeżeli w toku egzekucji prowadzonej przeciwko

Problem jednak polega na tym, że bardzo trudno jest być konsekw entnym transcendentalistą, trudno jest utrzymać się na transcendentalnym poziomie bez robienia „wycieczek”