RELATION BETWEEN RELIABILITY AND

0 downloads 0 Views 525KB Size Report
Obliczenia oparto na doświadczalnie ustalonej zmienności losowej parametrów wykonanych w .... w Ntórej podano taNże wartości uzysNanych momen-.

3$:(á7:25=(:6.,1 %$5%$5$*26=&= @ 7KH LQÀXHQFH RI ZRUNPDQVKLS TXDOLW\ RQ WKH UHOLDELOLW\ RI VWUXFWXUHV LV YHU\ GLI¿FXOW WR GH¿QH ,W GHSHQGV DPRQJ RWKHU WKLQJV RQ VXEMHFWLYH IDFWRUV LQFOXGLQJ the human factor (the designer experience, and above DOOWKHUHOLDELOLW\RIWKHFRQWUDFWRU >@ In engineering practice, the assessment of structure or its part safety is based on the analysis RIWKHUHOLDELOLW\LQGH[ȕ7KLVLQGH[LVDQREMHFWLYH determinant of the construction safety and allows the measure of safety to pass from deterministic to probabilistic. Reliability index depends on the 16

:VWĘS 3RZVWDZDQLH ]DJURĪHĔ DZDULL D QDZHW NDWDVWURI EXGRZODQ\FKMHVWF]ĊVWR]ZLą]DQH]MDNRĞFLąLWUZDáRĞFLą ]DVWRVRZDQ\FK PDWHULDáyZ NRQVWUXNF\MQ\FK > @ :Sá\Z MDNRĞFL Z\NRQDQLD QD QLH]DZRGQRĞü NRQVWUXNFML QDOHĪ\ GR RGG]LDá\ZDĔ EDUG]R WUXGQ\FK GR ]GH¿QLRZDQLD 8]DOHĪQLRQ\ MHVW RQ PLĊG]\ LQQ\PL RG F]\QQLNyZ VXELHNW\ZQ\FK REHMPXMąF\FK F]\QQLN OXG]NL W]Q GRĞZLDGF]HQLH SURMHNWDQWD DSU]HGHZV]\VWNLPU]HWHOQRĞüZ\NRQDZF\>@ :SUDNW\FHLQĪ\QLHUVNLHMRFHQDEH]SLHF]HĔVWZDNRQVWUXNFMLEąGĨMHMHOHPHQWXED]XMHQDDQDOL]LHZVNDĨQLND QLH]DZRGQRĞFL ȕ NWyU\ VWDQRZL RELHNW\ZQą PLDUĊ MHM EH]SLHF]HĔVWZD L XPRĪOLZLD SU]HMĞFLH RG SUREDELOLVW\F]QHMGRGHWHUPLQLVW\F]QHMPLDU\EH]SLHF]HĔVWZD

%áņ'@'RLQQ\FKPHWRGPRĪQD]DOLF]\üPHWRGĊSU]HG]LDáRZąOLQHDU\]DFMLRUD]DQDOLW\F]Qą>@ =JRGQLH ] QRUPą 31(1  >@ ]DSHZQLHQLH QLH]DZRGQRĞFL JZDUDQWRZDQH MHVW SRSU]H] SURMHNWRZDQLH ]JRGQH ] QRUPDPL SRSUDZQH Z\NRQDQLH ]DSHZQLHQLH RGSRZLHGQLHM MDNRĞFL PDWHULDáyZ :\UyĪQLDP\WU]\NODV\QLH]DZRGQRĞFL5&5&L5& GH¿QLRZDQHSU]H]PLQLPDOQHZDUWRĞFLZVNDĨQLNyZ QLH]DZRGQRĞFLȕ±WDEHOD >@.ODV\QLH]DZRGQRĞFLVNRUHORZDQHVą]NODVDPL ‡ NRQVHNZHQFML && && && ± ]DOHĪQ\PL RG ]DJURĪHQLD Ī\FLD OXG]NLHJR L NRQVHNZHQFML HNRQRPLF]Q\FK VSRáHF]Q\FK RUD] ĞURGRZLVNRZ\FK ]QLV]F]HQLDNRQVWUXNFML ‡ SR]LRPX QDG]RUX SU]\ SURMHNWRZDQLX '6/ '6/'6/ ‡ LQVSHNFMLZWUDNFLHZ\NRQDQLD,/,/,/ :\WU]\PDáRĞü EHWRQX QD ĞFLVNDQLH L MHM NRQWUROD X]QDZDQDMHVW]DGRPLQXMąF\SDUDPHWUZSá\ZDMąF\QD QRĞQRĞFLNRQVWUXNFMLĪHOEHWRZ\FK3UREOHPDW\ND]ZLą]DQD]MDNRĞFLąEHWRQXZRGQLHVLHQLXGRQLH]DZRGQR17

RELATION BETWEEN RELIABILITY AND REINFORCEMENT MANUFACTURING ERRORS IN REINFORCED CONCRETE BEAMS

SDSHUV>@7KLVLQFOXGHVFRPSOLDQFHFULWHULDIRU DVDPSOHVL]HQ  31(1>@ ,WKDVEHHQ IRXQG WKDW VDPSOH VL]H FULWHULD PD\ LQ VRPH FDVHV result in failure to provide the quality and reliability RIQHZVWUXFWXUHV>@

ĞFLNRQVWUXNFMLMHVWV]HURNRSRUXV]DQDZZLHOXSUDFDFK >@'RW\F]\WRPLĊG]\LQQ\PLNU\WHULXP]JRGQRĞFLGODSUyE\ROLF]HEQRĞFLQ  31(1>@  6WZLHUG]RQR ĪH PRĪH WR Z QLHNWyU\FK SU]\SDGNDFK ZLą]Dü VLĊ ] QLH]DSHZQLHQLHP RGSRZLHGQLHM MDNRĞFL LQLH]DZRGQRĞFLUHDOL]RZDQ\FKRELHNWyZ>@

7DEOH0LQLPXPYDOXHVRIWKHUHOLDELOLW\LQGH[GHSHQGLQJRQWKHUHOLDELOLW\FODVV>@ 7DEHOD0LQLPDOQHZDUWRĞFLZVNDĨQLNyZQLH]DZRGQRĞFLZ]DOHĪQRĞFLRGNODV\QLH]DZRGQRĞFL>@ Reliability Class

Minimum values for reliability index β 12 years reference period

50 yearsreference period

RC3

5.2

4.3

RC2

4.7

3.8

RC1

4.2

3.3

Assessment of reinforcement quality and its impact on the reliability of the construction is much more GLI¿FXOW ,W VKRXOG EH XQGHUOLQHG WKDW LQ WKH FDVH RI reinforced concrete structures the most common mistakes include: incorrect number of rebars, incorrect SRVLWLRQ RI UHEDUV DQG WKHLU GHIRUPDWLRQV 6WXGLHV carried out by ITB show that these errors are the most common cause of defects in concrete structures >@7KHUHDUHPDQ\PHWKRGVWRFRQWUROWKHUHLQIRUFH works quality in concrete products and components >@ZKLFKDUHZLGHO\XVHGLQWKHGLDJQRVLVEXWUDUHO\ XVHGLQWKHTXDOLW\FRQWURO,QWKLVSDSHUWKHLQÀXHQFH of incorrect longitudinal reinforcement bars position in cross-section of element on beam reliability was estimated (based on the measurements carried out for WKHUHDOHOHPHQWV 

OFHQDMDNRĞFLZ\NRQDQLD]EURMHQLDLMHJRZSá\ZXQD QLH]DZRGQRĞüNRQVWUXNFMLMHVW]QDF]QLHWUXGQLHMV]DGR RV]DFRZDQLD1DOHĪ\SRGNUHĞOLüĪHZSU]\SDGNXNRQVWUXNFMLĪHOEHWRZ\FKGRQDMF]ĊVWV]\FKEáĊGyZSRMDZLąF\FKVLĊQDHWDSLHZ\NRQDQLDPRĪQD]DOLF]\üQLHGREyU ]EURMHQLD QLH]JRGQRĞü UR]PLHV]F]HQLD RUD] GHIRUPDFMH SUĊWyZ %DGDQLD ,QVW\WXWX 7HFKQLNL %XGRZODQHM Z\ND]Dá\ĪHEáĊG\WHVąQDMF]ĊVWV]ąSU]\F]\QąXV]NRG]HĔNRQVWUXNFMLĪHOEHWRZ\FK>@,VWQLHMHZLHOHPHWRGNRQWUROL]EURMHQLDZZ\UREDFKLHOHPHQWDFKĪHOEHWRZ\FK>@0DMąRQHV]HURNLH]DVWRVRZDQLHZGLDJQRVW\FH DOH U]DGNR Vą VWRVRZDQH Z NRQWUROL Z\NRQDZVWZD:QLQLHMV]HMSUDF\SRGMĊWRSUyEĊRFHQ\ZSá\ZX RGFK\áHN Z SRáRĪHQLX SUĊWyZ ]EURMHQLD SRGáXĪQHJR ZSU]HNURMXEHOHNĪHOEHWRZ\FKQDLFKQLH]DZRGQRĞü ZRSDUFLXRZ\NRQDQHSRGF]DVEDGDĔSRPLDU\

([SHULPHQWDQG&ROOHFWHG'DWD The results used in analysis were collected during UHVHDUFK FRQGXFWHG LQ WKH /DERUDWRU\ RI &RQFUHWH 6WUXFWXUHV DQG 7HFKQLFDO 2EMHFWV 'LDJQRVLV LQ Kielce University Technology, in the framework of WZR UHVHDUFK SURMHFWV UHVHDUFK DQG GHYHORSPHQW 3URMHFW12>@DQGUHVHDUFKWRSLF7 >@7KHGDWDLQFOXGHGWKHSRVLWLRQLQYHQWRU\RIWKH longitudinal reinforcement bars in cross-section of reinforced concrete beams and strength properties for materials which were used to prepare those elements. For the analysis single-span beams with WKHGLPHQVLRQV[PPLQFURVVVHFWLRQDQG a total length of 3300 mm were selected (planned FRQFUHWH FODVV & VWHHO %6  /RQJLWXGLQDO reinforcement was composed of the following rebars 3 ‫  ׋‬DQG  ‫  ׋‬DW WKH ERWWRP DUUDQJHG LQ WZR OD\HUV UHLQIRUFHPHQWUDWLR DQG‫׋‬DWWKH top. The elements were made in the precast factory.

2SLVSU]HSURZDG]RQ\FKEDGDĽ $QDOL]Ċ Z\NRQDQR QD SRGVWDZLH GDQ\FK ]JURPDG]RQ\FK SRGF]DV Z\NRQ\ZDQLD EDGDĔ  EHOHN ĪHOEHWRZ\FK Z UDPDFK ]UHDOL]RZDQ\FK Z .DWHGU]H :\WU]\PDáRĞFL 0DWHULDáyZ .RQVWUXNFML %HWRQRZ\FK L0RVWRZ\FK3ROLWHFKQLNLĝZLĊWRNU]\VNLHMGZyFKSURMHNWyZEDGDZF]\FKSURMHNWXEDGDZF]RUR]ZRMRZHJR 15>@RUD]WHPDWXEDGDZF]HJR7>@ 'DQHWHREHMPRZDá\LQZHQWDU\]DFMĊSRáRĪHQLDSUĊWyZ ]EURMHQLDSRGáXĪQHJRZSU]HNURMXEHOHNĪHOEHWRZ\FK RUD]Z\QLNLSRPLDUyZFHFKZ\WU]\PDáRĞFLRZ\FK]DVWRVRZDQ\FKGRLFKZ\NRQDQLDPDWHULDáyZ 'R DQDOL]\ Z\EUDQR HOHPHQW\ MHGQRSU]ĊVáRZH RZ\PLDUDFKSU]HNURMX[PPLGáXJRĞFLFDáNRZLWHM  PP SODQRZDQD NODVD EHWRQX & VWDO %6  =EURMHQLH SRGáXĪQH EHOHN ]áRĪRQR ] SUĊWyZ 3 ‫׋‬L‫׋‬GRáHPXáRĪRQ\FKZGZyFKZDUVWZDFK VWRSLHĔ ]EURMHQLD JáyZQHJR   RUD]  ‫  ׋‬JyUą (OHPHQW\Z\NRQDQRZ]DNáDG]LHSUHIDEU\NDFML

18

%áņ'@ZHUHSUHVHQWHGLQ >@ Based on the results of the inventory, the main reinforcement center of gravity in relation to the bottom edge was calculated for each element – value a. The obtained values and the results of the statistical analysis are shown in Table 3.

Z\QLNyZ ] ZDUWRĞFLDPL GRSXV]F]DOQ\PL ]JRGQLH ]31(1>@SU]HGVWDZLRQRZSUDFDFK>@ :RSDUFLXRZ\QLNLLQZHQWDU\]DFMLSRáRĪHQLD]EURMHQLDZ\]QDF]RQRZDUWRĞFLaF]\OLRGOHJáRĞFLĞURGND FLĊĪNRĞFLSUĊWyZUR]FLąJDQHJR]EURMHQLDGRNUDZĊG]L GROQHM EHOHN 2WU]\PDQH ZDUWRĞFL ZUD] ] Z\QLNDPL DQDOL]\ VWDW\VW\F]QHM UR]NáDGX ZDUWRĞFL a SU]HGVWDwiono w tabeli 3.

7DEOH$QDO\VLVUHVXOWVIRUWKHGLVWULEXWLRQRID 7DEHOD:\QLNLDQDOL]\UR]NáDGXZDUWRĞFLDGODUR]SDWU\ZDQ\FKEHOHN Beam symbol A2M-1 A2M-2 D2M-1 D2M-2 C2M-1 C2M-2 S2M-1 S2M-2 S2M-3 S2M-4

a [mm] 47.31 56.64 49.22 53.55 44.32 47.17 37.18 39.18 51.13 49.65

The results of the analysis of the distribution of value a – average value = 47.54 mm S – standard deviation = 6.03 mm amin – minimum value = 37.18 mm amax – maximum value = 56.64 mm V – coefficient of variation = 12.67%

3. Analysis and Results To assess the impact of deviations in the position of the main reinforcement bars in cross-section of beams on their reliability, the following data were used: ‡ data concerning the longitudinal reinforcement bars position in cross-section of elements determined based on inventory, ‡ data about the design position of the bars shown on the working drawings, ‡ data about the distribution of the yield strength of reinforcing steel determined on the basis of the DFFRPSDQ\LQJVWXGLHV WHQVLOHWHVWIRUUHEDUV  Theoretical bearing capacity of reinforced concrete beam was adopted in the form of the function expressed by equation:

3U]HSURZDG]RQDDQDOL]DRUD]X]\VNDQHZ\QLNL 'RSU]HSURZDG]HQLDRFHQ\ZSá\ZXRGFK\áHNZSRáRĪHQLXSUĊWyZ]EURMHQLDJáyZQHJRZSU]HNURMXEHOHN ĪHOEHWRZ\FKQDLFKQLH]DZRGQRĞüZ\NRU]\VWDQR ‡ GDQHGRW\F]ąFHSRáRĪHQLDSUĊWyZ]EURMHQLDSRGáXĪQHJR Z SU]HNURMX HOHPHQWyZ RNUHĞORQH QD SRGVWDZLHZ\NRQDQHMLQZHQWDU\]DFML ‡ GDQH GRW\F]ąFH SURMHNWRZDQHJR SRáRĪHQLD SUĊWyZ SRGDQHQDU\VXQNDFKZ\NRQDZF]\FK ‡ GDQHGRW\F]ąFHUR]NáDGXJUDQLF\SODVW\F]QRĞFLVWDOL ]EURMHQLRZHM RNUHĞORQH QD SRGVWDZLH EDGDĔ WRZDU]\V]ąF\FK SUyED UR]FLąJDQLD SUĊWyZ XĪ\W\FK GR ]EURMHQLD  1RĞQRĞü WHRUHW\F]Qą EHONL ĪHOEHWRZHM SU]\MĊWR ZSRVWDFLIXQNFMLZ\UDĪRQHMZ]RUHP

05G”$6 I\] 

05G”$6 I\] 

where: $6– is the area of reinforcement in the tension ]RQH I\ – is the yield strength of reinforcing steel, ]– is the arm of internal forces. The values of basic variables used in the analysis DUHVXPPDUL]HGLQ7DEOH7KHVWDQGDUGGHYLDWLRQIRU the area of the rebar was adopted to be 0 cm2. This VLPSOL¿FDWLRQ ZDV FRQVLGHUHG VXI¿FLHQW GXH WR WKH small real deviation of this value.

JG]LH$6±SROHSRZLHU]FKQL]EURMHQLDZVWUH¿HUR]FLąJDQHMI\±JUDQLFDSODVW\F]QRĞFLVWDOL]EURMHQLRZHM ]±UDPLĊVLáZHZQĊWU]Q\FK :DUWRĞFL ]PLHQQ\FK SRGVWDZRZ\FK Z\NRU]\VWDQ\FK Z DQDOL]LH ]HVWDZLRQR Z WDEHOL  2GFK\OHQLH VWDQGDUGRZHGODSRODSRZLHU]FKQLSUĊWyZ]EURMHQLRZ\FKSU]\MĊWRUyZQHFP28SURV]F]HQLHWRX]QDQR ]DZ\VWDUF]DMąFH]HZ]JOĊGXQDQLHZLHONLU]HF]\ZLVW\UR]U]XWWHMZDUWRĞFL

20

%áņ'@ .LQDVK 5 0HWRG\ RFHQ\ QLH]DZRGQRĞFL NRQVWUXNFML EXGRZODQ\FK SU]\ QLHSHáQ\FK SDUDPHWUDFK *yQLFWZR L*HRLQĪ\QLHULD  SS >@ $MGXNLHZLF] $ :\]ZDQLH GOD SURMHNWDQWyZ ± SURMHNWRZDQLH NRQVWUXNFML EHWRQRZ\FK QD RNUHV XĪ\WNRZDQLD. ,QĪ\QLHU%XGRZQLFWZD  SS >@ 6WDURVROVNL:1LH]DZRGQRĞüRELHNWXEXGRZODQHJR ZĞZLHWOHSDNLHWXQRUP31,62 . 3U]HJOąG%XGRZODQ\  SS >@ &DVSHHOH56\NRUD07DHUZH/,QÀXHQFHRITXDOLW\FRQWURORIFRQFUHWHRQVWUXFWXUDOUHOLDELOLW\DVVHVVPHQW XVLQJD%D\HVLDQDSSURDFK0DWHULDODQG6WUXFWXUHV  SS >@ 6NU]\SF]DN,%XGD2ĪyJ/,QÀXHQFHRI&RPSOLDQFH&ULWHULDRQWKH9DOXHRI5HOLDELOLW\,QGH[$UFKLYHVRI&LYLO (QJLQHHULQJ  YRO/;,,SS >@ 31(1&RQFUHWH6SHFL¿FDWLRQSHUIRUPDQFHSURGXFWLRQDQGFRQIRUPLW\. >@ 3DZáRZVNL : 3U]HZáRFNL 6 3URFHGXU\ SRPLDURZH GOD SRWU]HE GLDJQRVW\NL RELHNWyZ EXGRZODQ\FK =HV]\W\ 1DXNRZH3ROLWHFKQLNLàyG]NLHMQU%XGRZQLFWZR]SS >@ 5DSRUW]3URMHNWX5R]ZRMRZHJR15 >@ 5DSRUWQDXNRZ\]UHDOL]DFML7HPDWX%DGDZF]HJR7 >@ 31(1([HFXWLRQRIFRQFUHWHVWUXFWXUHV >@ *RV]F]\ĔVND%7ZRU]HZVNL3:Sá\ZEáĊGyZZ\NRQDQLDEHOHNĪHOEHWRZ\FKQDLFKRGNV]WDáFHQLDL]DU\VRZDQLH RUD]JUXERĞüRWXOLQ\3U]HJOąG%XGRZODQ\  SS >@ 7ZRU]HZVNL 3 (UURUV GXULQJ 0DQXIDFWXULQJ RI 5HLQIRUFHG &RQFUHWH %HDPV DW WKH ([DPSOH RI &RQFUHWH &RYHU 'HYLDWLRQV. 7UDQVFRP3URFHHGLQJVVHFWLRQ&LYLO(QJLQHHULQJSS

24