CHAPTER 5 CONCRETE DESIGN

Transcription

1 BRIDGE DESIGN PRCTICE OCTOBER 2011 CHPTER 5 CONCRETE DESIGN TBEL OF CONTENTS 5.1 INTRODUCTION STRUCTURL MTERILS Conrete Reinoring Steel Pretreing Steel DESIGN LIMIT STTES FLEXURE DESIGN Strength Limit State Deign Requirement Nominal Flexural Reitane Reinorement Limit Servie Limit State Fatigue Limit State SHER DESIGN Bai Conept o Modiied Compreion Field Theory Shear Strength Flexure - Shear Interation Tranvere Reinorement Limit COMPRESSION DESIGN Fatored xial Compreion Reitane Pure Compreion Combined Flexure and Compreion Reinorement Limit NOTTION REFERENCES Chapter 5 Conrete Deign 5-i

2 BRIDGE DESIGN PRCTICE OCTOBER 2011 CHPTER 5 CONCRETE DESIGN 5.1 INTRODUCTION Conrete i the mot ommonly ued material in Caliornia highway truture, epeially ater the wide aeptane o pretreing tehnology in the 195 Nowaday, onrete bridge, pretreed or non-pretreed, aount or about 90% o all bridge in the Caliornia highway ytem. Suh dominany i attributable to the many advantage that onrete oer: bility to be at in almot any hape Low ot Durability Fire reitane Energy eiieny On-ite abriation etheti propertie Conrete deign ha evolved rom llowable Stre Deign (SD), alo Working Stre Deign (WSD), to Ultimate Strength Deign (USD) or Load Fator Deign (LFD), to today Limit State Deign (LSD) or Load and Reitane Fator Deign (LRFD). Conrete deign take on a whole new look and eel in the SHTO LRFD Bridge Deign Speiiation (SHTO 2007). New onept that had been ruminating amongt onrete expert or deade reahed a level o maturity appropriate or implementation. While not peret, the new method are more rational than thoe in the SHTO Standard Speiiation, (SHTO 2002) and entail an amount o eort appropriate given today tehnology ompared to that available when the LFD wa developed. Change inlude: Uniied deign proviion or reinored and pretreed onrete Modiied ompreion ield theory or hear and torion lternative Strut and Tie modeling tehnique or hear and lexure End zone analyi or tendon anhorage New proviion or egmental ontrution Revied tehnique or etimating pretre loe Chapter 5 will ummarize the general apet o onrete omponent deign uing the SHTO LRFD Speiiation with Caliornia mendment, while Chapter 7 will give a detailed deription o the deign proedure or pot-tenioned box girder bridge, and Chapter 8 will over the deign o preat pretreed girder bridge. Conrete dek are overed in Chapter 1 Chapter 5 Conrete Deign 5-1

3 BRIDGE DESIGN PRCTICE OCTOBER STRUCTURL MTERILS Conrete The mot important property o onrete i the ompreive trength. Conrete with 28-day ompreive trength = 3.6 ki i ommonly ued in onventionally reinored onrete truture while onrete with higher trength i ued in pretreed onrete truture. The Caliornia mendment (Caltran 2008) peiy minimum deign trength o 3.6 ki or pretreed onrete, although SHTO- LRFD (SHTO 2007) rtile require minimum deign trength o 4.0 ki. When a higher trength i peiied or a projet, deigner hould onider variou ator inluding ot and loal availability Reinoring Steel Steel reinoring bar are manuatured a plain or deormed bar. In Caliornia, the main reinoring bar are alway deormed. Plain bar are uually ued or piral and tie. Reinoring bar mut be low-alloy teel deormed bar onorming to requirement in STM 706/ 706M with a 60 ki yield trength, exept that deormed or plain billet-teel bar onorming to the requirement on STM 615/ 615M, Grade 40 or 60, may be ued a reinorement in ome minor truture a peiied in Caltran Standard Speiiation (Caltran 2006a) Pretreing Steel Two type o high-tenile trength teel ued or pretreing teel are: 1. Strand: STM 416 Grade 250 and 270, low relaxation. 2. Bar: STM 722 Type II ll Caltran deign are baed on low relaxation trand uing either 5 in. or 6 in. diameter trand. 5.3 DESIGN LIMIT STTES Conrete bridge omponent are deigned to atiy the requirement o ervie, trength, and extreme-event limit tate or load ombination peiied in SHTO LRFD Table with Caltran reviion. The ollowing are the our limit tate into whih the load ombination are grouped: Chapter 5 Conrete Deign 5-2

4 BRIDGE DESIGN PRCTICE OCTOBER 2011 I. Servie Limit State Conrete tree, deormation, and raking, ditribution o reinorement, deletion and amber are invetigated at ervie limit tate. Servie I: Crak ontrol and limiting ompreion in pretreed onrete Servie III: Crak ontrol/tenion in pretreed onrete Servie IV: Pot-tenioned preat olumn etion II. Strength Limit State xial, lexural, hear trength and tability o onrete omponent are invetigated at trength limit tate. Reitane ator are baed on SHTO LRFD (SHTO 2007). Strength I: Bai load (HL-93) Strength II: Owner peiied load (Permit) Strength III: Wind on truture Strength IV: Struture with high DL/LL (>7) Strength V: Wind on truture and live load III. Extreme Event Limit State Conrete bridge omponent and onnetion mut reit extreme event load due to earthquake and appropriate olliion ore, but not imultaneouly. IV. Fatigue Limit State Fatigue o the reinorement need not be heked or ully pretreed onrete member atiying requirement o ervie limit tate. Fatigue need not be invetigated or onrete dek lab on multi-girder bridge. For atigue requirement, reer to SHTO LRFD (SHTO 2007). 5.4 FLEXURE DESIGN Strength Limit State Deign Requirement In lexure deign, the bai trength deign requirement an be expreed a ollow: M M M u n r where M u i the atored moment at the etion (kip-in.); M n i the nominal lexural reitane (kip-in.); and M r i the atored lexural reitane o a etion in bending (kip-in.). Chapter 5 Conrete Deign 5-3

5 BRIDGE DESIGN PRCTICE OCTOBER 2011 In aeing the nominal reitane or lexure, the SHTO LRFD proviion (SHTO 2007) uniy the trength deign o onventionally reinored and pretreed onrete etion baed on their behavior at ultimate limit tate. In the old LFD Speiiation, a lexure member wa deigned o that the etion would ail in a tenion-ontrolled mode. Thu, there wa a maximum reinorement ratio. Wherea, in the new LRFD peiiation, there i no expliit upper bound or reinorement. There i a ditintion o ompreion and tenion-ontrolled etion baed on the train in the extreme tenion teel. To penalize or the undeirable behavior o ompreion-ontrolled etion, a lower value o reitane redution ator i aigned to ompreion-ontrolled etion ompared to tenionontrolled etion. The new proedure deine a tranition behavior region in whih the reitane ator, to be ued or trength omputation, varie linearly with the train in the extreme teel iber. The deign o etion alling in thi behavior region may involve an iterative proedure. Here are a ew term ued to deribe the lexural behavior o the reinored etion: Balaned train ondition: Strain in extreme tenion teel reahe it yielding train a the onrete in ompreion reahe it aumed ultimate train o 003. Compreion-ontrolled train limit: Net Tenile Strain (NTS) (exluding eet o pretreing, reep, et.) in the extreme tenion teel at the balaned ondition. It may be aumed equal to 002 or Grade 60 reinorement and all pretreed reinorement. Compreion-ontrolled etion: NTS ompreion-ontrolled train limit jut a the onrete in ompreion reahe it aumed train limit o 003. When a etion all into thi ituation, it behave more like a olumn than a beam. Thu, the omponent hall be properly reinored with tie and piral a required by SHTO LRFD with appropriate reitane ator (Caltran 2008). Tenion-ontrolled etion: NTS reahe it aumed train limit o jut a the onrete in ompreion Reitane ator are a ollow: or preat pretreed member or at-in-plae pretreed member or non-pretreed member Tranition region: Compreion ontrolled train limit < NTS < 005. For the tranition region, the reitane ator i alulated by uing linear interpolation. Caltran mendment require that reinored onrete etion in lexure be deigned Chapter 5 Conrete Deign 5-4

6 BRIDGE DESIGN PRCTICE OCTOBER 2011 o that NTS 004. Thi requirement i to enure that the etion will not ail in ompreion-ontrolled mode. Figure Illutrate thoe three region and equation or reitane ator o lexural reitane (Caltran 2008). Figure Reitane Fator Variation or Grade 60 Reinorement and Pretreing Steel Nominal Flexural Reitane The proviion or onventionally reinored and pretreed onrete are now one-and-the-ame. The bai aumption ued or lexural reitane (SHTO LRFD ) are a ollow: Plane etion remain plane ater bending, i.e., train i linearly proportional to the ditane rom the neutral axi, exept the deep member. For unonined onrete, maximum uable train at the extreme onrete ompreion iber i not greater than 003. For onined onrete, the maximum uable train exeeding 003 may be ued i veriied. Stre in the reinorement i baed on it tre-train urve. Tenile trength o onrete i negleted. Conrete ompreive tre-train ditribution i aumed to be retangular, paraboli, or any hape that reult in predited trength in ubtantial agreement with the tet reult. n equivalent retangular ompreion tre ' blok o 85 over a zone bounded by the edge o the ro-etion and a traight line loated parallel to the neutral axi at the ditane a = β 1 rom Chapter 5 Conrete Deign 5-5

7 BRIDGE DESIGN PRCTICE OCTOBER 2011 the extreme ompreion iber may be ued in lieu o a more exat onrete tre ditribution, where i the ditane meaured perpendiular to the neutral axi and ' where i in ki For a T-beam etion, there are two ae (Figure 5.4-2) depending on where the neutral axi all into: Cae 1: langed etion when the neutral axi all into the web Cae 2: retangular etion when the neutral axi all into the lange Figure Stre and Strain Ditribution o T-Beam Setion in Flexure (hown with mild reinorement only) For langed etion, the M n an be alulated by the ollowing equation auming the ompreion lange depth i le than a = β 1 : M n p p d p a 2 d a 2 ' d ' a 2 85 ( b b ) h w a 2 h 2 (SHTO ) where a i the depth o equivalent retangular tre blok (in.); i the ditane rom the extreme ompreion iber to the neutral axi (in.); b i the width o the ompreion ae o the member (in.); b w i the web width (in.); h i the thikne o lange (in.); d i the ditane rom ompreion ae to entroid o tenion reinorement (in.); d i the ditane rom ompreion ae to entroid o mild tenile reinorement (in.) and d p i the ditane to the entroid o pretreing teel (in.); i the area o mild tenile reinorement (in. 2 ) and p i the area o Chapter 5 Conrete Deign 5-6

8 BRIDGE DESIGN PRCTICE OCTOBER 2011 pretreing teel (in. 2 ); i the area o mild ompreive reinorement (in. 2 ); i the tre in mild tenile teel (ki); i the tre in the mild teel ompreion reinorement (ki) and p i the tre in pretreing teel (ki). For retangular etion, let b w = b. The lat term o the above equation will be dropped. For irular and other nontandard ro-etion, train-ompatibility mut be ued. WinCon (Caltran 2005) i a uitable tool, and ha been modiied or LRFD. To evaluate the pretreing tree, the ollowing equation an be ued: For bonded reinorement and tendon p pu 1 k (SHTO ) d In whih: pu p py k (SHTO ) For langed etion: p pu 85 For retangular etion: 1 b w 85 k p d ( b pu p b w )h (SHTO ) p pu 85 1 b k p d pu p (SHTO ) For unbonded tendon d p p pe 900 py (SHTO ) l e Chapter 5 Conrete Deign 5-7

9 BRIDGE DESIGN PRCTICE OCTOBER 2011 In whih: l e 2li 2 N (SHTO ) For langed etion: p p b w ( b b w )h (SHTO ) For retangular etion: p p 85 1 b (SHTO ) where py and pu are the yield and ultimate tenile trength o pretreing teel repetively; pe i the eetive tre in pretreing teel ater lo (ki); l e i the eetive tendon length (in.); l i i the length between anhorage (in.); and N i the number o upport hinge roed by the tendon between anhorage Reinorement Limit mentioned beore, there i no expliit limit on maximum reinorement. Setion are allowed to be over reinored but hall be ompenated or redued dutility in the orm o a redued reitane redution ator. The minimum reinorement hall be provided o that, M r, at leat equal to leer o M r and 1.3 M u Servie Limit State Servie limit tate are ued to atiy tre limit, deletion, and raking requirement. To alulate the tre and deletion, the deigner an aume onrete behave elatially. The modulu o elatiity an be evaluated aording to the ode peiied ormula uh a SHTO LRFD The reinorement and pretreing teel are uually tranormed into onrete. For normal weight onrete with w = 145 k, the modulu o elatiity, may be taken a: E 1, 820 (SHTO C ) Chapter 5 Conrete Deign 5-7

10 BRIDGE DESIGN PRCTICE OCTOBER 2011 For pretreed onrete member, pretreing ore and onrete trength are determined by meeting tre limit in the ervie limit tate, and then heked in the trength limit tate or ultimate apaity. ll other member are deigned in aordane with the requirement o trength limit tate irt, the raking requirement i atiied by proper reinorement ditribution. To deign the pretreed member, the ollowing tre limit lited in Table hould be atiied. Table Stre Limit or Conrete Condition Stre Loation llowable Stre Temporary Stre beore lo Tenile In area other than Preompreed Tenile Zone and without bonded tendon or reinorement Final Stre ater lo at ervie load Permanent load only (ki) In area with bonded tendon or reinorement uiient to reit the tenile ore in the onrete omputed auming an unraked etion, where reinorement i proportioned uing a tre o 5 y, not to exeed 30 ki Compreion ll loation 6 Tenile In the Preompreed Tenile Zone, auming unraked etion: Component with bonded tendon or reinorement, and are loated in Caltran Environment rea I and II Component with bonded tendon or reinorement, and are loated in Caltran Environment rea III Component with unbonded tendon 0 Compreion ll loation due to : Permanent load and eetive pretre load Live load plu one-hal permanent load and eetive pretre load ll load ombination Tenile Preompreed Tenile Zone with bonded pretreing tendon or reinorement 24 (ki) 19 (ki) 0948 (ki) Chapter 5 Conrete Deign 5-8

11 BRIDGE DESIGN PRCTICE OCTOBER Fatigue Limit State per SHTO (SHTO 2007), the tre range in reinoring bar due to the atigue load ombination hould be heked and hould atiy: (SHTO ) min where: = Stre range (ki) min = Minimum live load tre (ki) reulting rom the atigue load ombined with the more evere tre rom either the permanent load or the permanent load, hrinkage, and reep-indued external load; poitive i tenion, negative i ompreion For the atigue hek: The atigue load ombination i given in C mendment Table load ator o 875 i peiied on the live load (Fatigue truk) or inite atigue lie and a load ator o 1.75 or the ininite atigue lie. atigue load i one deign truk with a ontant 30-t. paing between the 32.0-kip axle a peiied in SHTO (SHTO 2007). pply the IM ator to the atigue load. There i no permanent load onidered in thi hek. Chek both top and bottom reinorement to enure that the tre range in the reinorement under the atigue load tay within the range peiied in the above equation. 5.5 SHER DESIGN Bai Conept o Modiied Compreion Field Theory Perhap the mot igniiant hange or onrete deign in SHTO LRFD Speiiation i the hear deign methodology. It provide two method: Setional Method, and Strut and Tie Method. Both method are aeptable to Caltran. The Setional Method, whih i baed on the Modiied Compreion Field Theory (MCFT), provide a uniied approah or hear deign or both pretreed and reinored onrete omponent. For a detailed derivation o thi method, pleae reer to the book by Collin and Mithell (1991). The two approahe are ummarized a ollow: Setional Method - Plane etion remain plane Bai Beam Theory Chapter 5 Conrete Deign 5-10

12 BRIDGE DESIGN PRCTICE OCTOBER Baed on Modiied Compreion Field Theory (MCFT) - Ued or mot girder deign, exept diturbed-end region - Ued or any unditurbed region Strut and Tie Method - Plane etion doe not remain plane - Ued in diturbed region and deep beam - Example o uage: Deign o Bent Cap (lear pan to depth ratio le than 4); pile ap; anhorage zone (general or loal); area around opening In thi hapter, only the Setional Method will be outlined. The Strut and Tie Method will be diued in other hapter. Compreion Field Theory (CFT) i highlighted a ollow: ngle or ompreive trut (or rak angle) i variable Plane etion remain plane (or train ompatibility) Strength o onrete in tenion i ignored Element level train inorporate the eet o axial ore, hear and lexure Equation are baed on element level tree and train The hear apaity i related to the ompreion in diagonally raked onrete through equilibrium Thi theory i urther modiied by inluding the trength o onrete in tenion, and it i reerred to a the Modiied Compreion Field Theory (MCFT) Shear Strength ording to SHTO LRFD , the nominal hear reitane, V n, hall be determined a: V n = V + V + V p (SHTO ) But total reitane by onrete and teel: V + V hould be no greater than 25 b v d v. In the end region o the beam-type element when it i not built integrally with the upport, V + V hould not exeed 18 b v d v. I it exeed thi value, thi region hould be deigned uing the Strut and Tie Method and peial onideration hould be given to detailing. V b d (SHTO ) v v Chapter 5 Conrete Deign 5-11

13 BRIDGE DESIGN PRCTICE OCTOBER 2011 v y d v (ot ot ) in V (SHTO ) where V p i the omponent in the diretion o applied hear o the eetive pretreing ore (kip); b v i the eetive web width (in.); and d v i the eetive hear depth (in.). In thee equation, i the angle o rak and i a ator. Unlike in the old LFD ode where the angle o rak wa aumed a a ontant 45º, the MCFT method aume it i a variable, whih i a more aurate depition o atual behavior. For member with minimum tranvere reinorement, and value alulated rom the MCFT are given a untion o x, hear tre v u, and in SHTO LRFD Table x i taken a the alulated longitudinal train at mid-depth o the member when the etion i ubjeted to M u, N u, and V u. x M d v u 5N u 2( E 5V u E V p p p ot ) p po (SHTO ) For member without tranvere reinorement, and value alulated rom the MCFT are given a untion o x, and the rak paing xe in SHTO LRFD Table x i taken a the larget alulated longitudinal train whih our within the web o the member when the etion i ubjeted to M u, N u, and V u. x M d v u 5N u ( E 5V u E p V p p ot ) p po (SHTO ) I the value o x rom either equation above i negative, the train i taken a: x M d v u 5N 2( E u 5V E u V p E ot p p ) p po (SHTO ) The rak paing parameter xe, i determined a: xe x 80 in. (SHTO ) a 63 g Chapter 5 Conrete Deign 5-12

14 BRIDGE DESIGN PRCTICE OCTOBER 2011 where a g i maximum aggregate ize (in.); and x i the leer o either d v, or the maximum ditane between layer o longitudinal rak ontrol reinorement (in.). one an ee, x, and are all inter-dependent. So, deign i an iterative proe: 1. Calulate hear tre demand v u at a etion and determine the hear ratio (v u / ) 2. Calulate x at the etion baed on normal ore (inluding p/), hear and bending and an aumed value o 3. Longitudinal train x i the average train at mid-depth o the ro etion 4. Knowing v u / & x, obtain the value o and rom the table 5. Realulate x baed on revied value o ; repeat iteration until onvergene in i ahieved. where v u, the hear tre on the onrete, hould be determined a: Vu V p v u (SHTO ) b d v v To impliy thi iterative approah, Proeor Bentz, Vehio, and Collin have propoed a impliied method (Bentz, E. C. et al, 2006) Flexure - Shear Interation In the MCFT model, the onrete i eentially modeled a a erie o ompreion trut in reiting hear ore. The horizontal omponent o thee diagonal ore have to be reited by horizontal tie - longitudinal reinorement. Thereore, ater the deign o lexure and hear i ompleted, the longitudinal reinorement i heked or uh interation. Provide additional reinorement i required. The ollowing equation hould be ued or heking the adequay o longitudinal reinorement: M u Nu Vu p p y 0. 5 V p 5V d V V u v v ot (SHTO ) Vu p p y 0. 5V V p ot (SHTO ) v Chapter 5 Conrete Deign 5-13

15 BRIDGE DESIGN PRCTICE OCTOBER 2011 Requirement or the interation hek depend on the upport / load traner mehanim (diret upport or indiret upport) Maximum lexural teel baed on moment demand need not be exeeded in / near diret upport Interation hek i required or imple pan made ontinuou or live load or where longitudinal teel i not ontinuou Equation ( ) i required to be atiied at the inide edge o the bearing area o imple upport Diret Support / Diret Loading Figure how ome o the example o diret upport and diret loading: Figure Example o Diret Support and Diret Loading Speial Note: I lexural reinorement i not urtailed (eg: in bent ap), then there i no need to hek or interation. I lexural reinorement i urtailed (eg: in a upertruture), hek or interation: - Chek at 1/10 point and/or at urtailment loation. - I reinorement per equation i inadequate, extend primary lexural reinorement. - rea o tenile reinorement need not exeed that required or maximum moment demand ating alone. Indiret Support / Integral Girder Figure how ome o the example o indiret upport and integral girder. The girder raming into the bent ap are indiretly upported while the bent ap itel i diretly upported by the olumn. Chapter 5 Conrete Deign 5-14

16 BRIDGE DESIGN PRCTICE OCTOBER 2011 Figure Example o Indiret Support and Integral Girder Speial Note: In bent ap, hek interation at 10 point, and at the girder loation / loation o major onentrated load Chek or interation at ae o integral upport I interation i not atiied, then adopt one o the ollowing: - Inreae lexural reinorement - Inreae hear reinorement - Combination o the above Tranvere Reinorement Limit Minimum Tranvere Reinorement Exept or egmental pot-tenioned onrete box girder bridge, the area o teel hould atiy: bv v (SHTO ) y Maximum Spaing o Tranvere Reinorement The paing o the tranvere reinorement hould not exeed the maximum paing, max, determined a: I ν u < 125 then: max = 8d v 24.0 in. (SHTO ) I ν u 125 then: max = 4d v 12.0 in. (SHTO ) Chapter 5 Conrete Deign 5-15

17 BRIDGE DESIGN PRCTICE OCTOBER COMPRESSION DESIGN tated previouly, when a member i ubjeted to a ombined moment and ompreion ore it reulting train an be in a ompreion-ontrolled tate. Compreion deign proedure applie. The ollowing eet are onidered in addition to bending: degree o end ixity; member length; variable moment o inertia; deletion; and duration o load. Thi hapter will only over the two bai ae: pure ompreion, and ombined lexure and ompreion ignoring lenderne. SHTO LRFD provide an approximate method or evaluating lenderne eet Fatored xial Compreion Reitane Pure Compreion The atored axial reitane o onrete ompreive member, ymmetrial about both prinipal axe, i taken a: P (SHTO ) r P n In whih: P n, the nominal ompreion reitane, an be evaluated or the ollowing two ae: For member with piral reinorement: P n = 85[85 ( g t p )+ y t p ( pe E p ε u )] (SHTO ) For member with tie reinorement: P n = 80[85 ( g t p )+ y t p ( pe E p ε u )] (SHTO ) where g i the gro area o the etion (in. 2 ); t i the total area o longitudinal mild reinorement (in. 2 ); p i the area o pretreing teel (in. 2 ); E p i the modulu o elatiity o pretreing teel (ki); and u i the ailure train o onrete in ompreion. In order to ahieve the above reitane, the ollowing minimum piral hall be upplied: g (SHTO ) yh where yh i the peiied yield trength o tranvere reinorement (ki). Chapter 5 Conrete Deign 5-16

18 BRIDGE DESIGN PRCTICE OCTOBER 2011 To ahieve more dutility or eimi reitane, Caltran ha it own et o requirement or piral and tie. For urther inormation, pleae reer to the urrent verion o the Seimi Deign Criteria (Caltran 2010) Combined Flexure and Compreion When a member i ubjeted to a ompreion ore, end moment are oten indued by eentri load. The end moment rarely at olely along the prinipal axi. So at any given etion or analyzing or deign, the member i normally ubjeted to biaxial bending a well a ompreion. Furthermore, to analyze or deign a ompreion member in a bridge ubtruture, many load ae need to be onidered. Under peial irumtane, the Speiiation allow deigner to ue an approximate method to evaluate biaxial bending ombined with axial load (SHTO LRFD ). Generally, deigner rely on omputer program baed on equilibrium and train ompatibility, uh a WinYield (Caltran 2006b), to generate a moment-axial interation diagram. For ae like nonirular member with biaxial lexure, an interation urae i required to deribe the behavior. Figure how a typial moment-axial load interation urae or a onrete etion (Park and Pauley 1975). Figure Moment-xial Interation Surae o a Nonirular Setion In day-to-day pratie, uh a urae ha little value to deigner. Rather, the deign program normally give out a erie o line, baially lie o the urae, at ixed interval, uh a 15º. Figure i an example plot rom WinYield (Caltran 2006b). Chapter 5 Conrete Deign 5-17

19 BRIDGE DESIGN PRCTICE OCTOBER 2011 Figure Interation Diagram Generated by WinYield From thee line, it an be een that below the balaned ondition the moment apaity inreae with the inreae o axial load. So, when deigning a olumn, it i not enough to imply take a et o maximum axial load with maximum bending moment. The ollowing ombination need to be evaluated: 1. M ux max, orreponding M uy and P u 2. M uy max, orreponding M ux and P u 3. et o M ux and M uy that give larget M u ombined, and orreponding P u 4. P u max and orreponding M ux and M uy Speial Note: Column will be more thoroughly overed in Chapter 13. For load ae 1 through 3, the load ator γ p orreponding to the minimum hall be ued. P n and M n hall be multiplied by a ingle ator depending on whether it i ompreion ontrolled or tenion ontrolled, a illutrated previouly and a hown in SHTO LRFD Figure C Slenderne eet hall be evaluated with appropriate nonlinear analyi program or the ue o approximate method uh a SHTO LRFD In Caliornia, the olumn deign i normally ontrolled by eimi requirement. That topi i not overed in thi hapter. Chapter 5 Conrete Deign 5-18

20 BRIDGE DESIGN PRCTICE OCTOBER Reinorement Limit The maximum area o pretreed and non-pretreed longitudinal reinorement or non-ompoite ompreion member i a ollow: g p g pu y 08 (SHTO ) nd p g pe 30 (SHTO ) The minimum area o pretreed and non-pretreed longitudinal reinorement or non-ompoite ompreion member i a ollow: g y p g pu 135 (SHTO ) Due to eimi onern, Caltran put urther limit on longitudinal teel in olumn. For uh limit, pleae reer to the latet verion o the Caltran Seimi Deign Criteria (Caltran 2010). Chapter 5 Conrete Deign 5-19

21 BRIDGE DESIGN PRCTICE OCTOBER 2011 NOTTION = area o ore o pirally reinored ompreion member meaured to the outide diameter o the piral (in. 2 ) g = gro area o etion (in. 2 ) p = area o pretreing teel (in. 2 ) = area o non-pretreed tenion teel (in. 2 ) = area o ompreion reinorement (in. 2 ) h = ro-etional area o olumn tie reinorement (in. 2 ) t = total area o longitudinal mild teel reinorement (in. 2 ) v = area o tranvere reinorement within ditane (in. 2 ) a b b v b w D d d b = depth o equivalent retangular tre blok (in.) = width o ompreion ae o the member (in.) = eetive web width taken a the minimum web width (in.) = web width (in.) = ditane rom the extreme ompreion iber to the neutral axi (in.) = external diameter o the irular member (in.) = ditane rom ompreion ae to entroid o tenion reinorement (in.) = nominal diameter o a reinoring bar (in.) d e = eetive depth rom extreme ompreion iber to the entroid o tenile ore in the tenile reinorement (in.) d p d d v E E p E pe pe = ditane rom extreme ompreion iber to entroid o pretreing trand (in.) = ditane rom extreme ompreion iber to entroid o non-pretreed tenile reinorement (in.) = eetive hear depth (in.) = modulu o elatiity o onrete (ki) = modulu o elatiity o pretreing tendon (ki) = modulu o elatiity o reinoring bar (ki) = peiied ompreive trength o onrete (ki) = ompreive tre in onrete due to eetive pretre ore only (ater allowane or all pretre loe) at extreme iber o etion where tenile tre i aued by externally applied load (ki) = eetive tre in pretreing teel ater loe (ki) Chapter 5 Conrete Deign 5-20

22 BRIDGE DESIGN PRCTICE OCTOBER 2011 p pu py r y yh h l e l i M b M r M n M dn M r M u M ux M uy N u N P n P o P r P u V V n V p = average tre in pretreing teel at the time or whih the nominal reitane o member i required (ki) = peiied tenile trength o pretreing teel (ki) = yield trength o pretreing teel (ki) = modulu o rupture o onrete (ki) = tre in mild tenile reinorement at nominal lexural reitane (ki) = tre in mild ompreion reinorement at nominal lexural reitane (ki) = peiied minimum yield trength o reinoring bar (ki) = peiied yield trength o tranvere reinorement (ki) = thikne o lange (in.) = eetive tendon length (in.) = length o tendon between anhorage (in.) = nominal lexural reitane at balaned ondition (kip-in.) = raking moment (kip-in.) = nominal lexural reitane (kip-in.) = total unatored dead load moment ating on the monolithi or non-ompoite etion (kip-t.) = atored lexural reitane o a etion in bending (kip-in.) = atored moment at the etion (kip-in.) = atored moment at the etion in repet to prinipal x axi (kip-in.) = atored moment at the etion in repet to prinipal y axi (kip-in.) = atored axial ore (kip) = number o upport hinge roed by the tendon between anhorage or diretely bonded point = nominal axial reitane o a etion (kip) = nominal axial reitane o a etion at 0 eentriity (kip) = atored axial reitane o a etion (kip) = atored axial load o a etion (kip) = paing o reinoring bar (in.) = nominal hear reitane provided by tenile tree in the onrete (kip) = nominal hear reitane o the etion onidered (kip) = omponent in the diretion o the applied hear o the eetive pretreing ore; poitive i reiting the applied hear (kip) Chapter 5 Conrete Deign 5-21

23 BRIDGE DESIGN PRCTICE OCTOBER 2011 V r V V u v u S S n γ = atored hear reitane (kip) = hear reitane provided by the hear reinorement (kip) = atored hear ore (kip) = average atored hear tre on the onrete (ki) = etion modulu or the extreme iber o the ompoite etion where tenile tre i aued by externally applied load (in. 3 ) = etion modulu or the extreme iber o the monolithi or non-ompoite etion where tenile tre i aued by externally applied load (in. 3 ) = angle o inlination o tranvere reinorement to longitudinal axi (º) = ator relating eet o longitudinal train on the hear apaity o onrete, a indiated by the ability o diagonally raked onrete to tranmit tenion 1 = ratio o the depth o the equivalent uniormly treed ompreion zone aumed in the trength limit tate to the depth o the atual ompreion zone u x v = load ator = ailure train o onrete in ompreion (in./in.) = Longitudinal train in the web reinorement on the lexural tenion ide o the member (in./in.) = angle o inlination o diagonal ompreive tre (º) = reitane ator = reitane ator or ompreion = reitane ator or moment = reitane ator or hear = ratio o piral reinorement to total volume o olumn ore Chapter 5 Conrete Deign 5-22

24 BRIDGE DESIGN PRCTICE OCTOBER 2011 REFERENCES 1. SHTO (2007). SHTO LRFD Bridge Deign Speiiation, 4 th Edition with 2008 Interim, merian oiation o State Highway and Tranportation Oiial, Wahington, D.C. 2. SHTO (2002). Standard Bridge Deign Speiiation, 17 th Edition, merian oiation o State Highway and Tranportation Oiial, Wahington, D.C. 3. Bentz, E. C. et al (2006). Simpliied Modiied Compreion Field Theory or Calulating Shear Strength o Reinored Conrete Element, CI Strutural Journal/July-ugut Caltran (2010). Caltran Seimi Deign Criteria, Verion 1.6, Caliornia Department o Tranportation, Saramento, C. 5. Caltran (2008). Caliornia mendment to SHTO LRFD Bridge Deign Speiiation, 4 th Edition, Caliornia Department o Tranportation, Saramento, C. 6. Caltran (2006a). Standard Speiiation, Caliornia Department o Tranportation, Saramento, C. 7. Caltran (2006b). WinYield, Caliornia Department o Tranportation, Saramento, C. 8. Caltran (2005). WinCon, Caliornia Department o Tranportation, Saramento, C. 9. Collin, M. P. and Mithell, D. (1991). Pretreed Conrete Struture, Prentie Hall, Englewood Cli, NJ. 1 Park, R. and Paulay, T. (1975). Reinored Conrete Struture, John Willey & Son, New York, NY. Chapter 5 Conrete Deign 5-23