Analysis and Design of Prestressed Concrete Girder

Transcription

1 International Journal o Emerging Science and Engineering (IJESE) ISSN: , Volume2 Issue9, July 2014 Analysis and esign o Prestressed Concrete Girder Vishal U isal, N G Gore, P J Salunke Astract In this present study, cost analysis and design o prestressed concrete girder and reinorced concrete girder is presented The aim and ojective can e summarized as to analyze and design the concrete girder under a IRC class 70 R loading To ormulate the entire prolem or a couple o span under the loading mentioned aove to otain shear orce and ending moment at regular intervals along the eam To use the sotware STAA PRO or the analysis and design o prestressed concrete girders Beore using the sotware or analysis it will e validated y comparing its results with the corresponding classical theory result To carry out the parametric analysis or prestressed concrete I girder and reinorced concrete girder To calculate the quantities o concrete and steel required as per the analysis and design carried out or the girders and to carry out the comparative study or the same Figure 1() shows the same unloaded eams with prestressing orces applied y stressing high strength tendons By placing the prestressing low in the simplespan eam and high in the cantilever eam, compression is induced in the tension zones; creating upward camer Index Terms Reinorced concrete girder, eck sla, I girder, Prestressed concrete I INTROUCTION Prestressed concrete is asically concrete in which internal stresses o suitale magnitude and distriution are introduced so that the stresses resulting rom external loads are counteracted to a desired degree In reinorced concrete memers, the prestress is commonly introduced y tensioning the steel reinorcement The development o early cracks in reinorced concrete due to incompatiility in the strains o steel and concrete was perhaps the starting point in the development o a new material like prestressed concrete The application o permanent compressive stress to a material like concrete, which is strong in compression ut weak in tension, increases the apparent tensile strength o that material, ecause the susequent application o tensile stress must irst nulliy the compressive prestress In 1904, Freyssinet attempted to introduce permanently acting orces in concrete to resist the elastic orces developed under the name o prestressing II PRINCIPLE OF PRESTRESSING The unction o prestressing is to place the concrete structure under compression in those regions where load causes tensile stress Tension caused y the load will irst have to cancel the compression induced y the prestressing eore it can crack the concrete Figure 1 (a) shows a plainly reinorced concrete simplespan eam and ixed cantilever eam cracked under applied load anuscript Received on July2014 r Vishal U isal, (E student), epartment o Civil Engineering, G s College o Engineering & Technology, Kamothe, Navi umai, India Pro N G Gore, (Guide), epartment o Civil Engineering, G s College o Engineering & Technology, Kamothe, Navi umai, India Pro P J Salunke, (Guide), epartment o Civil Engineering, G s College o Engineering & Technology, Kamothe, Navi umai, India Fig 1 Comparison o Reinorced and Prestressed Concrete Beams Figure 1 (c) shows the two prestressed eams ater loads have een applied The loads cause oth the simplespan eam and cantilever eam to delect down, creating tensile stresses in the ottom o the simplespan eam and top o the cantilever eam The Bridge esigner alances the eects o load and prestressing in such a way that tension rom the loading is compensated y compression induced y the prestressing Tension is eliminated under the comination o the two and tension cracks are prevented Also, construction materials (concrete and steel) are used more eiciently; optimizing materials, construction eort and cost III PROBLE FORULATION esign a posttensioned prestressed concrete Ieam sla ridgedeck 1 Permissile stresses: For deck sla: As per IRC: or various grade o concrete and steel Evaluate c, st, m, Q and j For prestressed concrete girder: As per IRC: or various grade o concrete Evaluate ck, ci, ct = 045 ci, cw = 033 ck 2 esign o interior sla panel: a Bending moments ead weight o sla: 1*1* thickness o sla*density o concrete (1) ead weight o wearing coat: thickness o wearing coat* density o wearing coat (2) Total dead load: eq (1+2) 43 Pulished By: & Sciences Pulication Pvt Ltd

2 Live load calculation: or IRC class AA tracked vehicle One wheel is placed at the centre o panel Analysis and esign o Prestressed Concrete Girder Fig 2 Position o IRC Class AA Wheel Load or aximum Bending oment L= length o panel B= Width o panel u= 085+2*thickness o wearing coat v= 360+2*thickness o wearing coat Bending moment along short span ( S ): W (m m 2 ) Bending moment along short span ( L ): W (015m 1 + m 2 ) Where: m 1 and m 2 is computed y using Piegeauds curves & W= 350 KN esign ending moment= 125 * 08 * Bending moment Shear orces: ispersion in the direction o span= [ (thickness o wearing coat + thickness o deck sla)] For maximum shear, load is kept such that the whole dispersion is in the span The load is kept at (dispersion in the direction o span/2) rom the edge o eam (x) Eective width o the sla= kx[1(x/l)]+ w Load per metre width= 350/ Eective width o the sla Shear orce per metre width= [Load per metre width* (Clear width o panel x)]/ Clear width o panel c ead load Bending moments and Shear orce: Total load on panel (W) = (length o panel * width o panel * total dead load) S = W (m m 2 ) L = W (m m 1 ) d esign moment: Including the continuity actor y multiplying 08 to Bending moments e esign o sla section and reinorcement Eective depth, d= Area o steel: Ast= Q st jd Check or shear: (As per IRC: ) V τ v = d 3 esign o longitudinal girder: a Reaction actor Using Couron theory: Fig 3 Transverse isposition o IRC Class AA Tracked Vehicle Reaction actor o outer girder A is R A = 2W 1 4* a * e * 4 2* 2* Reaction actor or inner girder B is R B = 2 2 ( a )( ) 2W 1 4* * e * 4 2* 2* 2 2 ( a )( ) a= distance etween c/l to girder A = distance etween c/l to girder B ead load on sla per girder: Fig 4 etails o Footpath, Parapet and eck Sla Weight o Parapet railing = 092KN/m(assume) Footpath and ker= depth * width * density eck sla= depth * width * density Total dead load o the deck= [2 * {weight o (parapet railing + ootpath and ker + deck sla)} + (total dead load o interior sla panel * width o sla)] It is assume that the deck load is shared equally y all our girders c ead load on main girder: the overall depth o the girder is assumed to e 1800 mm at the rate o 60 mm o every meter o span Overall depth: 60 * span o girder Selweight o girder= (dead weight o ri + dead weight o ottom lange) Weight o cross girder= (width o cross girder * depth o cross girder * density) d ead load moments and shears in the main girder: 44 Pulished By: & Sciences Pulication Pvt Ltd

3 International Journal o Emerging Science and Engineering (IJESE) ISSN: , Volume2 Issue9, July 2014 Fig 5 ead Load on ain Girder X= total dead load on the girder W= reaction on main girder Reaction rom deck sla on each girder: load on each girder Reaction on main girder= Weight o cross girder * spacing o main girders Total dead load on the girder= (selweight o the main girder + Reaction rom deck sla on each girder ) aximum ending moment: it will act at the centre aximum shear orce: e Live load ending moments in the girder: Fig 6 Inluence Line or Bending oment in Girder Where: x= 36m z= Wa/l L= length o girder a== length o girder/2 W= 1 B at centre o span= 05(y+z)*700 B, including the impact and reaction actors, For outer girder is= (reaction at A * 11) For inner girder= (reaction at B * 11) Properties o main girder section: Fig 7 CrossSection o ain Girder Calculate A, Z t, Z g Check or minimum section modulus: Z = q + (1 η ) r d = ( η ) r ct tw h Prestressing orce: P i n ( Ain Z ) = ( Z + Ae) t w = η + η Z i Permissile tendon zone: ct Z e Z P A tw Z e Z P A 4 Check or stresses: A At transer stage P Pe t = + A Zt Zt P Pe = + A Z Z B At working stage: P Pe L t = η η + + A Zt Zt Zt P Pe L = η + η A Z Z Z 5 Check or ultimate lexural strength: According to IS: , the ultimate lexural strength o the centre o span section is computed as ollow: A p = (A pw + A p ) Ap = 045 ck ( w ) p 2 Ap = d x No o tendon in each cale * No o 4 cale A = A A pw p p Apw p Ratio: wd ck pu = x, 087 p x u y d = U = pu Apw ( d 042 xu ) ck ( w ) ( d 05 ) ( ) req = + u L 6 Check or ultimate shear strength: Ultimate shear orce: V u = (15 V g + 25 V q ) 45 Pulished By: & Sciences Pulication Pvt Ltd

4 Analysis and esign o Prestressed Concrete Girder According to IRC: , the ultimate shear resistance o the support section uncracked in lexure is given y, V = h + +ηp θ 2 cw 067 w t 08 cp t sin w = width o the we h= overall depth o girder t = maximum principal tensile stress at the centroidal axis t = ck cp= compressive stress at the centroidal axis due ηp to prestress = A Slope o cale= (4e/L) e= Eccentricity o cale at the centre o span Eccentricity o cale at the support Ast= provide 10 mm diameter twolegged stirrups o Fe 415 HYS ars 087 y A sv d t Spacing= Sv = V V= V u V cw Supplementary reinorcements: Longitudinal reinorcements o not less than 015 percent o the gross crosssectional area are to e provided to saeguard against shrinkage cracking Illustrative examples: For span o 1630 m and 314 m we have design I girder and Box girder y using 45 grade concrete and Fe 415 steel A For164 m span IV RESULT Prestressed girder Reinorced concrete girder Volume o steel 0523 m 3 1 m 3 Volume o concrete m 3 60 m 3 Fig 8 Total Quantities o Steel and Concrete V CONCLUSION In view o achieving the aim and ojectives o this study a detailed literature survey was eing carried out It gave us an idea regarding dierent methodologies adopted or analysis and design o prestressed concrete slas and girders It was decided to go or the use o the sotware STAA PRO or the analysis and design o sla and girders For validation purpose the analysis results o a prolem o I girder using STAA PRO were compared with the corresponding analytical results It is oserved that the result otained y oth method showing good agreement By using this sotware the analysis and design o prestressed concrete I girder and Reinorced concrete Box girder was carried out A comparative study was carried out etween prestressed concrete I girder and Reinorced concrete Box girder By extracting result we have concluded that Prestessed concrete girder is costlier than reinorced concrete girder But y strength wise and long term duraility prestressed concrete is much strong than reinorced concrete girder REFERENCES [1] XJ Chen, CW Shen and L J Jacos: Prediction o election or Prestressed Concrete Girders ACI materials journal (1987), 83, (02) pp: 8391 [2] Roert F ast : Lateral Staility o Long Prestressed Concrete Beams PCI Journals (1987), 32, (06) pp [3] aewaka T, Ichiki T, Niki, T: evelopment o Ultrahigh Strength Prestressing Strand (1991), 22, (02) [4] Husham Almansour, Zouir Lounis: Structural Perormance o Precast Prestressed Bridge Girders Built with Ultra High Perormance Concrete PCI Journal, (1993), 38, (4), pp 6077 [5] Test and Analytical Approach to PC Grouting Based on Filling Perormance (1994), 36, (3) [6] Peter Lundqvist, Juha Riihimäki: Testing o ive 30yearold prestressed concrete eams PCI Journals (1996), 41, (6) [7] Enhanced uraility, Quality Control and onitoring o Electrically Isolated Tendons (1997), 11, (2) [8] Santa aria: TheoreticalExperimental damage determination in prestressed concrete eams (2000), 5, (07) [9] LiveLoad istriution Factors In Prestressed Concrete Girder Bridges Journal o Bridge Engineering, (2001), 6, (5) [10] T Patrick Earney: End cracking in pretensioned concrete girder: PCI journals, (2001), 42, (4) pg [11] Chung C Fu [1], Fellow, and Yi Tang [2] : Torsional Analysis or Prestressed Concrete ultiple Cell Box, Journal o Engineering echanics, (2001), 127, (1) [12] Byung Hwan Oh, Kwang Soo Kim, and Young Lew: Ultimate Load Behavior o PostTensioned Prestressed Concrete Girder Bridge through InPlace Failure Test (2002), 99, (02) [13] OA Rosenoom and SH Rizkalla: Fatigue Behavior o Prestressed Concrete Bridge Girders Strengthened with Various CFRP Systems (2002), 47, (1), pp 7693 [14] Anchoring o Cales or Single Pylon Extradosed Posttensioned Concrete Bridge [6]: (2002) [15] Gladys Graciela, Cuadros Olave Evaluation o high strength concrete prestressed ridge girder design, (2003), 6, (3) [16] akarand Hastak, Amir irmiran, Richard iller, Ronak Shah, and Reid Castrodale: State o Practice or Positive oment Connections in Prestressed Concrete Girders ade Continuous Journal o Bridge Engineering, 2003, (8), 5 [17] Sahahit, N and Hegde, Chetan GA: Optimum esign o Prestressed Concrete eam Journal o Structural Engineering, (2004), 31, (3) pp [18] ongning Li; 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5 r Vishal U isal, (EStructuresStudent) Civil Engg ept, G s College o Engineering & Technology, Kamothe, Navi umai International Journal o Emerging Science and Engineering (IJESE) ISSN: , Volume2 Issue9, July 2014 Pro N G Gore, (EStructural EngineeringGuide) Civil Engg ept, G s College o Engineering & Technology, Kamothe, Navi umai Pro P J Salunke, (Tech Environmental EngineeringGuide) Civil Engg ept, G s College o Engineering & Technology, Kamothe, Navi umai 47 Pulished By: & Sciences Pulication Pvt Ltd