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IRJET- Reliability Analysis of Prestressed Concrete Box Girder Bridge Deck
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IRJET- Reliability Analysis of Prestressed Concrete Box Girder Bridge Deck
1.
International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 02 | Feb 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 1781 RELIABILITY ANALYSIS OF PRESTRESSED CONCRETE BOX GIRDER BRIDGE DECK Nataraja harvi1, A R Pradeep2, C. Rangaraju3 1PG Student, Department of Civil Engineering, SSIT, Tumakuru, Karanataka, India 2Assistant Professor, Department of Civil Engineering, SSIT, Tumakuru, Karanataka, India 3Professor, Department of Civil Engineering, SSIT, Tumakuru, Karanataka, India ---------------------------------------------------------------------***---------------------------------------------------------------------- Abstract - In knower days the construction of pre-stressed concrete bridges will be maximum compare to the other type of bridges in universal. Because construction of pre-stressed concrete bridge will be quicker, more economical sections, better quality control, suitable for repetitive construction, etc. considered model will be analysesbythecodeIRC(Indianroad congress).finding the failure of structure applying different load combination like moving load (IRC CLASS AA), vehicle 1 combination (IRC CLASS A) and vehicle 2 combination (IRC CLASS 70R).the probability of failure will be find out by reliability analysis method. Reliability values are within assumed percentage of failure of structure hence considered bridge will be safe. Key Words: Pre-stressed concrete bridge, AFOSM, Reliability index,… 1. INTRODUCTION Pre-stressed concrete bridges of beam form can bedesigned using the working stress method and also by limit state method. In the working stress method, service loads are used in the whole design and the strength of material is not utilized to the fullest extent. In this method of design, stresses acting on structural members are calculated based on elastic method. In fact, the whole structure during thelife span may only experience loading stresses far below the ultimate state. Under such scenario, the most economical design can hardly obtain by using working stress. In Limit state method, for each material and load, a partial safety factor is assigned individually depending on the material properties and loads. Therefore, each element of load and material properties is accurately assessed resulting in a more refined and accurate analysis of the structure. In this connection, the material strength can be utilized to its maximum value during its lifespanandloadscanbeassessed with reasonable probability of occurrence 1.1 Reliability analyses Reliability engineering relates nearly to safety engineering and to system safety, in that they use common techniques for their analysis and may involve the inputfrom each other. Costs of failure affected by system downtime, cost of spares, repair equipment, personnel, and cost of warranty claims are focused by reliability engineering. Safety engineering mainly deals with preserving life and nature than on cost, and hence deals only with particularly dangerous system failure modes. High reliability (safety factor) levels also result from good engineering and from attention to detail, and almost never from only reactive failure management. 1.2 Material properties Material properties Values M40 Unit volume 40kN/m3 Young’s modulus 3.25×e7 kN/m2 Poisons ratio 0.2 Shear modulus 1.31×e10 N/m2 Co-efficient of thermal expansion 5.5×e-6/°C Co- efficient of concrete 5.5×e-6 /°C Compressive strength of concrete 40×e3 kN/m3 2. METHODOLOGY Fig 2.1 Bridge model
2.
International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 02 | Feb 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 1782 Fig 2.2 Cross section view of deck Fig 2.3 Tendons view Table 2.1 Parameters considered for the Box Girder Bridge Total length of the bridge 120m Width of the bridge 9.4m Numberofspans 3 Span distance 40m, 40m, 40m. Number of lanes 2 Number of tendons 3 Area of the tendon 5.04×E-04 Number of columns 3 Restraints Fixed Pier size 1m Circular Bent cap size 1mx1.2m Lane width 4.7m Type of vehicle IRC class AA,IRC class A,IRC class 70R Vehicle speed Lane 1 40kmph, Lane 1 60kmph, Lane 1 80kmph IRC CLASS A Lane 2 40kmph, Lane 2 60kmph, Lane 2 80kmph IRC 70R Lane 1 40kmph, Lane 1 60kmph, Lane 1 80kmph Lane 2 40kmph, Lane 2 60kmph, Lane 2 80kmph Formula for Reliability (R): R = C+0.6(11-(L/D)-(0.026+0.05(L/D-11)*Wt) Where, R =Reliability in limit state of deflection C = Parameter depends on span length. Values of C are given in table below: Table 2.2 Values of C L 4m 5m 6m 7m 8m 9m 10m C 3.7 4 4.2 4.3 4.5 4.5 4.5
3.
International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 02 | Feb 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 1783 Table 2.3 Values of vehicle 1(IRC CLASS A) Shear force values SPAN (m) C SF (kN) max Wt RI (max) % FAILURE 0.00 2.95 20.52 0.80 21.80 5.86 5.00 4.00 22.78 0.90 22.78 10.39 10.00 4.50 93.54 0.78 66.88 28.51 15.00 5.30 234.84 0.64 152.06 35.25 20.00 5.96 393.63 0.53 247.71 37.07 25.00 6.62 526.93 0.49 328.10 37.73 30.00 7.28 702.49 0.62 433.20 38.33 35.00 7.94 472.99 0.85 296.34 37.35 40.00 8.60 9.77 0.43 21.04 53.56 2.3.1 Entire bridge moving load values Maximum values R=C+0.6(11+ (LOAD)-(0.026+0.005(LOAD-11)*Wt) RI = 2.95+.6(11+20.52)-(.026+.005*(23.3-11)*0.8 RI= 21.80 RI = 4+.6(11+20.41)-(.026+.005*(6.4-11)*0.9) RI =22.78 RI = 4.5+.6(11+93.54)-(.026+.005*(16.73-11)*0.78) RI =66.88 RI =5.3+.6(11+234.84)-(.026+.005*(36.91-11)*0.64) RI =152.06 RI = 5.96+.6(11+393.63)-(.026+.005*(50.62-11)*0.53) RI =247.71 RI = 6.62+.6(11+526.93)-(.026+.005*(47.74-11)*0.49) RI =328.10 RI = 7.28+.6(11+702.5)-(.026+.005*(18.35-11)*0.62) RI =433.20 RI = 7.94+.6(11+472.99)-(.026+.005*(17.36-11)*0.85) RI =296.34 RI = 8.6+.6(11+9.77)-(.026+.005*(24.35-11)*0.43) RI =21.04 Percentage of failure % of failure = ((higher value – lower value)/higher value)*100 % of failure = ((21.80-20.52)/ 21.80) *100 =5.86 % of failure = ((22.78-22.78)/ 22.78)*100 =10.39 % of failure = ((93.54-66.88)/ 93.54)*100 =28.51 % of failure = ((234.84-152.06)/ 234.84)*100 =35.25 % of failure = ((393.63-247.71)/ 393.63)*100 = 37.07 % of failure = ((526.93-328.10)/ 526.93)*100 =37.73 % of failure = ((702.49-433.20)/ 702.49)*100 =37.35 % of failure = ((472.99-296.34)/ 472.99)*100 =30.29 % of failure = ((21.04-9.77)/ 21.04)*100 = 53.56 Average % of failure = 31.56 CHART 2.1 Shear force (max) v/s Reliability index (max) The structure is considered in the study the probability of failure obtained is 31.56%. According to the theory of reliability, the probability of Failure within the limit Hence the structure is considered in study is safe Table 2.4 Values of vehicle 1(IRC CLASS A) Bending moment values SPAN (m) C BM(kN- m) min Wt RI (min) % FAILURE 0.00 2.95 10.41 0.80 15.8 33.99 5.00 4.00 86.49 0.90 62.1 28.16 10.00 4.50 195.07 0.78 127.4 34.69 15.00 5.30 299.77 0.64 190.8 36.37
4.
International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 02 | Feb 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 1784 SPAN (m) C BM(kN- m) min Wt RI (min) % FAILURE 20.00 5.96 401.44 0.53 252.4 37.13 25.00 6.62 452.63 0.49 283.7 37.32 30.00 7.28 1295.99 0.62 787.5 39.23 35.00 7.94 2958.01 0.85 1776.8 39.93 40.00 8.60 5909.4 0.43 3548.2 39.95 CHART 2.2 Bending moment (min) v/s Reliability index (min) The structure is considered in the study the probability of failure obtained is 36.31%. According to the theory of reliability, the probability of Failure within the limit. Hence the structure is considered in study is safe Table 2.5 Values of vehicle 2(IRC CLASS 70R) Shear force values SPAN (m) C SF (kN) max Wt RI (max) % FAILURE 0.00 2.95 63.85 0.80 47.62 25.41 5.00 4.00 63.51 0.90 48.44 23.72 10.00 4.50 180.44 0.78 118.68 34.23 15.00 5.30 360.18 0.64 226.86 37.01 20.00 5.96 411.82 0.53 258.57 37.21 25.00 6.62 962.72 0.49 588.51 38.87 30.00 7.28 1343.08 0.62 815.57 39.28 35.00 7.94 1608.17 0.85 972.63 39.52 40.00 8.60 1817.4 0.43 1101.75 39.38 CHART 2.3 Shear force (max) v/s Reliability index (max) The structure is considered in the study the probability of failure obtained is 34.96%. According to the theory of reliability, the probability of Failure within the limit Hence the structure is considered in study is safe Table 2.6 Values of vehicle 2(IRC CLASS 70R) Bending moment values Span (m) C BM(kN- m) min Wt R.I (min) % FAILURE 0.00 2.95 21.52 0.80 22.4 4.06 5.00 4.00 255.8 0.90 163.0 36.2 10.00 4.50 607 0.78 372.9 38.55 15.00 5.30 937.5 0.64 571.4 39.04 20.00 5.96 1249.16 0.53 758.8 39.29 25.00 6.62 1570.32 0.49 951.6 39.49 30.00 7.28 2637.22 0.62 1588.0 39.78 35.00 7.94 5838.76 0.85 3493.0 40.17 40.00 8.60 11055.6 0.43 6624.9 40.07 CHART 2.4 Bending moment (min) v/s Reliability index (min)
5.
International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 02 | Feb 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 1785 The structure is considered in the study the probability of failure obtained is 35.18%. According to the theory of reliability, the probability of Failure within the limit . Hence the structure is considered in study is safe 3. CONCLUSIONS • Reliability index of flanged girder in limit state of deflection is determined by using advanced first order second moment method. • The probability failure of load case will be 33.05%, Failure within the limit hence structure is safe • The probability failure of shear force of vehicle 1 load will be 31.56%, Failure within the limit hence structure is safe • The probability failure of shear force vehicle combination 2 will be 34.96%. Failure within the limit hence structure is safe • The probability failure of Bending moment vehicle combination 1 will be 36.31%, Failure within the limit hence structure is safe • The probability failure of Bending moment vehicle combination 2 will be 35.18%, Failure within the limit hence structure is safe • Hence the probability of failure will be within the limit structure will be reliable . REFERENCES [1]. Ranganathan, R. Structural reliability analysis and design. Jai Co books, Mumbai, 1999. [2]. Nowak, Andrzej S. Reliability of Structure. McGraw-Hill, International Edition, Singapore 2000. [3]. IS 456:2006 “Indian Standard Code of Practice for Plain and Reinforced Concrete- Code of Practice(FourthRevision) July 2000. [4]. “Box beam concrete bridges” – By Ricardo Gaspar and Reboucas stucchi [2014] [5] IRC 6-2000 (section 2) [6] IRC 18-2000 [7] American code of practice - AASHTO BIOGRAPHIES Nataraja haravi is currently pursuing his post-graduation in computer aided Structural Engineering at sri siddhartha Institute of Technology. A R. Pradeep is currently working as an Associate Professor in Civil Engineering Department at sri siddhartha InstituteofTechnology, tumakuru. Dr C Rangaraju is currently working as an Professor in Civil Engineering Department at sri siddhartha InstituteofTechnology, tumakuru.
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