RELATION BETWEEN RELIABILITY AND

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

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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>@

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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 

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([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\HUVUHLQIRUFHPHQWUDWLR DQG‫׋‬DWWKH top. The elements were made in the precast factory.

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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.

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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\LQJVWXGLHVWHQVLOHWHVWIRUUHEDUV  Theoretical bearing capacity of reinforced concrete beam was adopted in the form of the function expressed by equation:

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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.

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20

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24