Seismic Vulnerability of RC Bridge Piers Designed as per Current IRC Codes including Interim IRC: Provisions

Transcription

1 Seimic Vulnerability of RC Bridge Pier Deigned a per Current IRC Code including Interim IRC: Proviion Rupen Gowami 1 and C. V. R. Murty 2 Synopi The paper preent a review of eimic trength deign proviion for reinforced concrete (RC) bridge pier given in Indian code. In the earlier IRC code, the eimic deign force for bridge wa low and the flexibility of the tructure wa not accounted for in the deign force etimate. Thee deficiencie have been overcome in the Interim IRC: proviion. However, the current Indian code treat RC pier a gravity load carrying compreion member, and no proviion are available for their hear deign. Analytically obtained monotonic lateral load-diplacement relation of RC bridge pier bending in ingle curvature indicate that the Indian code-deigned pier are vulnerable to trong haking. Alo, the longitudinal reinforcement in thee bridge pier i alo likely to buckle, and the nominal tranvere reinforcement requirement of Indian code are hown to be inadequate. 1. Introduction Bridge are lifeline facilitie that mut remain functional even after major earthquake haking; their damage and collape may not only caue lo of life and property, but alo hamper pot-earthquake relief and retoration activitie. In ome major earthquake in the pat, a large number of bridge uffered damage and collaped due to failure of foundation (tructural and geotechnical), ubtructure, upertructure, and upertructure-ubtructure and ubtructure-foundation connection. Bridge foundation i not eaily acceible for inpection and retrofitting after an earthquake, and any inelatic action or failure of the upertructure render the bridge dyfunctional for a long period. Connection failure i generally brittle in nature and hence avoided. Therefore, the ubtructure i the only component where inelaticity can be allowed to diipate the input eimic energy and that too in flexural action. In addition, a flexurally damaged pier can be more eaily retrofitted. In an earlier tudy 1 on trength deign of ingle-column type RC bridge pier, uch pier deigned a per the earlier IRC code 2, 3, 4 (namely, IRC:6-2000, IRC: , and IRC: ) were invetigated. The deign hear capacitie of hort pier (of apect ratio of about 2 to 3) were found to be lower than the correponding hear demand under flexural overtrength condition. Further, olid circular pier with ingle hoop a tranvere reinforcement howed the leat hear capacity and were found mot 1 Graduate Student, Department of Civil Engineering, IIT Kanpur, Kanpur ; rupen@iitk.ac.in 2 Profeor, Department of Civil Engineering, IIT Kanpur, Kanpur ; cvrm@iitk.ac.in

2 vulnerable, while hollow rectangular pier had relatively higher hear capacity owing to better ditributed tranvere reinforcement. Alo, buckling of longitudinal reinforcement wa found to be common in pier reulting in rapid trength lo. Further, increaing the amount of tranvere reinforcement, including providing additional radial link in hollow circular pier, wa found to enhance the diplacement ductility and produce improved pot-yield repone. Thi paper conduct a imilar invetigation on the eimic trength deign proviion of the current IRC code, namely the Interim IRC: , IRC: and IRC: Performance of Bridge in Pat Earthquake Poor eimic performance of bridge i recalled from a early a the 1923 Kanto earthquake (M 8.3) in Japan. Maonry pier upporting bridge pan crumbled during the trong haking. Baed on damage to highway bridge utained during thi earthquake, eimic force were formally recognized in the deign of highway bridge in Japan ince 1926, and the equivalent tatic Seimic Coefficient Method wa introduced for the analyi of bridge ytem ubjected to earthquake lateral load 8. The 1971 San Fernando earthquake (M 6.6) erved a a major turning point in the development of eimic deign criteria for bridge in the United State of America. Prior to 1971, pecification for the eimic deign of bridge were primarily baed on the philoophy of the then exiting lateral force requirement for building. During thi earthquake, pier primarily failed in hear, both outide and within the platic hinge region, due to inufficient hear trength and lack of adequate confinement from tranvere reinforcement, and thereby howed inadequate flexural ductility. Inadequate tranvere reinforcement alo ed to cruhing of concrete in the core of the cro-ection on reaching the unconfined concrete train and to buckling of longitudinal teel, reulting in rapid trength degradation. In addition, tranvere reinforcement opened up at lap plicing location accelerating the failure proce. Pullout failure of column reinforcement occurred due to inadequate development length into the footing and traight-bar anchorage detailing. Further, pan collape expoed the inadequate eat width proviion to accommodate the large relative movement at top of pier. Failure of horizontal retrainer bolt acro the movement joint alo led to collape of pan. The leon learnt from thi earthquake and the ubequent major earthquake, coupled with extenive reearch and deign experience, prompted the development of new and refined deign pecification for bridge in USA. A a reult, today USA ha 2

3 two tate-of-the-art document for eimic deign of bridge, namely the AASHTO LRFD Bridge Deign Specification [AASHTO, 1998] 9 by the American Aociation of State Highway and Tranportation Official and the Seimic Deign Criteria [CALTRANS, 2004] 10 by the California Department of Tranportation. The 1989 Loma Prieta earthquake (M 7.1) in California caued widepread damage to the region highway and bridge. The major contributor to the collape of over a length of a viaduct i generally undertood to be due to inufficient anchorage of cap beam reinforcement into the column, coupled with improperly deigned joint hear reinforcement. In addition, inadequate lap-plice length of longitudinal bar caued bond failure in column, and underetimation of eimic diplacement reulted in inadequate clearance between tructural component cauing pounding of tructure. In the 1995 Hyogo-Ken Nanbu (Kobe) earthquake (M 7.8) in Japan, highway tructure were everely affected, particularly the ingle-column-type RC pier 11. Mot concrete pier failed due to inufficient hear trength caued by inufficient tranvere reinforcement, inadequate confinement, and large unupported length of longitudinal bar. Premature curtailment of longitudinal reinforcement caued a number of column to develop flexure-hear failure at mid-height. Supertructure were motly imply upported over teel pin bearing, and with hort eat length; dilodging of girder off the bearing wa common. Stiff tenion-link retrainer failed and uneated a number of pan. At ome location, lateral preading of weak oil aggravated the relative diplacement of pier, again reulting in uneating of pan. Bridge with multiplecolumn frame type ubtructure generally performed better than ingle column type one. The Specification for Highway Bridge and Commentary, Part V: Seimic Deign publihed in 1990 by Japan Road Aociation wa revied in 1996 in view of thee extenive damage, and i available a a deign tandard, the Deign Specification of Highway Bridge, Part V-Seimic Deign [PWRI 9810, 1998] 12. Over the pat two decade, India ha experienced many moderate earthquake that caued damage to highway and railway bridge 13. Thee earthquake include the 1984 Cachar earthquake (M 5.6), the 1988 Bihar earthquake (M 6.6), the 1991 Uttarkahi earthquake (M 6.6), the 1993 Killari earthquake (M 6.4), the 1997 Jabalpur earthquake (M 6.0), the 1999 Chamoli earthquake (M 6.5) and the recent 2001 Bhuj earthquake (M 7.7) 14. Alo, during , India had experienced four great earthquake 3

4 (M > 8), namely the 1897 Aam earthquake (M 8.7), the 1905 Kangra earthquake (M 8.6), the 1934 Bihar-Nepal earthquake (M 8.4) and the 1950 Aam-Tibet earthquake. Today, over 60% of the country lie in the higher three eimic zone III, IV and V (Figure 1). Thu, India ha potential for trong eimic haking, and the large number of exiting bridge and thoe being contructed a a part of the ongoing National Highway Development Project, a per the exiting deign pecification, will be put to tet. 3. Indian Code Proviion IS:1893 (Part 1) provide the eimic loading criteria for tructure in India. However, load and tree (including thoe due to eimic effect) for the deign and contruction of road bridge in India are governed by the Indian Road Congre pecification IRC: The eimic deign criteria in thi ha been upereded by the interim proviion in IRC: Additional deign proviion pecifically for concrete tructure are pecified in Indian Road Congre pecification IRC: (earlier in IRC: ) and for bridge foundation and ubtructure in IRC: (earlier in IRC: ). In IRC: , the horizontal deign earthquake load on bridge i calculated baed on a eimic coefficient. The equivalent tatic horizontal eimic load on the bridge i pecified (vide Claue in IRC:6-2000) a F eq = αβλw, (1) where α i horizontal eimic coefficient (Table 1), β i oil-foundation ytem factor (Table 2), λ i importance factor (1.5 for important bridge, and 1.0 for regular bridge), and W i the eimic weight of the bridge. The eimic weight, acting at the vertical center of ma of the tructure, include the dead load plu fraction of the uperimpoed load depending on the impoed load intenity; effect of buoyancy or uplift are ignored when eimic effect are conidered. From above, the deign eimic force come out to be only 8% of it eimic weight for a normal bridge on hard oil with individual footing in eimic zone V. Thi wa alo the level of deign force for normal building under imilar condition. But, building have more redundancy than bridge. Thu, it eem that Indian bridge would be under-deigned a per IRC: The AASHTO and PWRI pecification et thi deign force level for bridge at 20-30% of their eimic weight in their mot evere eimic zone. In addition, in the IRC: deign procedure, the flexibility and dynamic behaviour of the bridge were not 4

5 conidered in calculation of deign eimic force for bridge. Further, IRC: (vide Claue 222.5) recommend horizontal eimic force etimation by dynamic analyi only for bridge of pan more than 150 m. The eimic deign philoophy in the Indian code primarily cover elatic trength deign. Thu, the deign force i ame for all element of the bridge and doe not conider the difference in ductility of the element. A per IRC:21 3, 6, RC member are deigned by Working Stre Method with a 50% increae in permiible tree for eimic load combination (a per IRC:6 2, 5 ). The code precribe a modular ratio of 10 to be ued in deign irrepective of the concrete. Thi caue maller calculated tree in concrete of higher grade. The analyi for force and tree are baed on gro cro-ectional propertie of component, although under eimic haking, ection rigidity reduce with increae in cracking reulting in higher deformability. Such increaed deformability, epecially of the ubtructure, can alo lead to uneating of the upertructure and/or impounding of adjacent tructural component a ha been oberved in a number of pat earthquake. Hence, when the reultant tenion at any ection due to the combined action of direct compreion and bending i greater than a pecified permiible tenile tre, IRC:21 recommend cracked ection analyi by working tre deign with no tenion capacity to be done. In Claue of IRC: , the general proviion for hear deign of RC beam are tated. The code attribute the deign hear wholly to the tranvere reinforcement. Only, the average hear tre calculated i checked againt a maximum permiible hear tre that i a function of the grade of concrete and ubject to a maximum value of 2.5 MPa. In the 2000 verion of IRC:21 6, unlike in the 1987 verion, contribution of both concrete and hear reinforcement are acknowledged. Thi i a forward tep following the worldwide reearch on hear trength of reinforced concrete (for example, refer 16 ). However, in IRC:21 3, 6, the deign proviion for column and compreion member (vide Claue 306) do not include hear deign even under lateral loading condition uch a during earthquake. However, detailing proviion are included for tranvere reinforcement (vide Claue 306.3). The minimum diameter of tranvere reinforcement (i.e., lateral tie, circular ring or helical reinforcement) i required to be the larger of one-quarter of the maximum diameter of longitudinal reinforcement, and 8 mm. The maximum centre-to-centre pacing of uch tranvere reinforcement along 5

6 the member length i required to be the leer of (a) leat lateral dimenion of the compreion member, (b) 12 time the diameter of the mallet longitudinal reinforcement bar in the compreion member, and (c) 300 mm. Further, there are no proviion on the need for confinement of concrete in vertical member. Alo, poible buckling of longitudinal reinforcement i not conidered. The incomplete treatment of hear deign and of tranvere reinforcement quetion on the performance of uch Indian bridge pier under the expected trong eimic haking. IRC:78 4, 7 pecifie an additional requirement for tranvere reinforcement in wall of hollow RC pier. The minimum area of uch reinforcement (vide Claue ) i given a 0.3% of the ectional area of the wall. Such reinforcement i to be ditributed on both face of the wall: 60% on the outer face and the remaining 40% on the inner face. Again, here alo, there are no proviion on additional intermediate tie or link to hold together the tranvere hoop on the outer and inner face of the hollow RC pier. In IRC: , the minimum and maximum area of longitudinal reinforcement for hort column are pecified to be 0.8% and 8%, repectively, of the gro croectional area of the member. IRC:21 require that every corner and alternate longitudinal bar have lateral upport provided by the corner of a tie having an included angle of not more than 135, and that no longitudinal bar be farther than 150 mm clear on each ide along the tie of a laterally upported bar. When the bar are located on the periphery of a circle, a complete circular tie i to be ued. No other pecial eimic deign apect are addreed. Thu, the Indian code advocate only flexural trength deign; ductility deign i not addreed at all; it i not enured that the hear capacity of the pier ection exceed the hear demand when platic moment hinge are generated during trong haking. 3.1 Interim IRC: Proviion After the devatating 2001 Bhuj earthquake, one of the important change wa the reviion of the eimic zone map of the country. The country i now claified into four eimic zone (Figure 1). In thi, the old Zone I i merged with Zone II with ignificant change in the peninular region; ome part in Zone I and II are now in Zone III. Further, the Indian Road Congre came up with interim meaure 5 to be read with the revied zone map (Claue 222.2). A per Claue of thi interim proviion, now all bridge in Zone IV and V are required to be deigned for eimic effect, 6

7 unlike in IRC: wherein only in Zone V, all bridge were required to be deigned for eimic effect. Claue of the interim proviion make it mandatory to conider the imultaneou action of vertical and horizontal eimic force for all tructure in Zone IV and V. Claue of thi interim proviion recognize that for bridge having pan more than 150 m, the eimic force are to be determined baed on ite-pecific eimic deign criteria. One of the mot important and welcome change enforced through the 2002 interim proviion i with regard to the procedure for eimic force etimation. Now, the deign horizontal eimic force given a F eq of a bridge i dependent on it flexibility, and i Feq = AhW, (2) where the deign horizontal eimic coefficient A h Z 2 = R I Sa g 7 A h i given by. (3) In Eq.(3), Z i the zone factor (Table 3), I i the importance factor (ame a in IRC:6-2000), R i repone reduction factor taken to be 2.5, and S a g i the average repone acceleration coefficient for 5% damping depending upon the fundamental natural period T of the bridge (Table 4). The S a g value depend on the type of oil (namely rocky or hard oil, medium oil and oft oil) and the natural period T of the tructure. Appendix A of the interim proviion give a rational method of calculating the fundamental natural period of pier/abutment of bridge. But, the interim proviion recommend a ingle value of 2.5 for the repone reduction factor R. Thi factor i to be ued for all component of the bridge tructure. However, the bearing do not have redundancy in them and are expected to behave elatically under trong eimic haking. Therefore, deigning the bearing for a much lower eimic force than that it hould carry from upertructure to pier i not deirable. In advanced eimic code, the R factor for deign of connection i generally recommended to be 1.0 or le 17, 18. Thi interim proviion need to be revied immediately from the point of view of afety of bridge bearing. With the enforcement of the interim proviion, the precribed eimic hazard of tructure in the country ha changed ignificantly. A an example, conider a ingle

8 pan RC National Highway bridge (importance factor I = 1.5) on Type II (medium) oil with well foundation (β =1.2 a per IRC:6-2000). For ingle pier bridge vibration unit (BVU), for mot of the normal contruction practice in India, pier tend to be lender in the direction of traffic or the longitudinal direction (L), and tiffer in the direction (T) tranvere to that of the traffic (Figure 2). Thu, in general, the natural period of pier i different in the longitudinal and tranvere direction. Foe example, the ingle pier BVU under conideration ha natural period of 1.5 ec in the longitudinal direction and 0.3 ec in the tranvere direction. Thu, a per the interim proviion, the S a g value for the longitudinal and tranvere direction are 0.91 and 2.5, repectively. The deign eimic coefficient for the bridge in different eimic zone in the country calculated a per the IRC: and the Interim IRC: proviion are a given in Table 5. In general, the deign lateral force on pier in their tranvere direction a per the Interim proviion i about twice thoe a per IRC: Now, conider bridge in the two metropolitan citie, namely Delhi and Madra. Delhi i in Zone IV in both the old and the new zone map of India, while Madra, originally in Zone II, i now placed in Zone III. Thu, the deign eimic coefficient for the ingle pier BVU in Delhi change from to (L) and (T), i.e., the eimic force increae by 100% in the tranvere direction for uch a pier. For bridge in Madra, the deign eimic coefficient for the ingle pier BVU change from to (L) and (T). Here, the eimic force increae by about 22% and 233% in the longitudinal and tranvere direction, repectively. Hence, bridge in Madra become deficient a per the Interim proviion. In addition, there are pecial mandatory and recommended meaure in the 2002 Interim proviion for better eimic performance of bridge. Thee include ductile detailing, dilodgement prevention unit, and iolation unit. However, thee are beyond the cope of thi paper and hence not dicued. 4. Capacity Deign for Bridge Pier The capacity deign philoophy warrant that deirable ductile mode of damage (e.g., ductile under-reinforced flexural damage) precede undeirable brittle one (e.g., brittle hear failure and bond failure). Under trong haking, inelaticity in bridge i admiible only in the pier. Further, for trong eimic haking, ince it may not be economically viable to deign a tructure for elatic repone, thi inelaticity i deliberately introduced in pier but with adequate ductility. Thi inelatic action under 8

9 diplacement loading caued by the earthquake in RC pier i aociated with large overtrength. Under thee overtrength condition, if the hear demand on the pier exceed it deign hear capacity, undeirable brittle failure for the whole tructure may reult. Thu, if capacity deign of bridge pier i conducted, the pier are deigned for hear correponding to the overtrength flexural capacity of the pier. In the capacity deign of pier, the important item that come into play are deign tranvere reinforcement, concrete confinement by tranvere reinforcement, hear trength of confined concrete, and tability (buckling) of longitudinal reinforcement. In countrie like Japan, New Zealand and USA, the deign of the bridge pier for eimic condition i a paramount tep in the entire proce of bridge deign practice. The American highway pecification (AASHTO), California Tranportation Department pecification (CALTRANS), and New Zealand Standard pecification (NZS) recommend capacity deign for hear deign of bridge pier 9, 10, 19. The Japanee pecification (PWRI) 12 explicitly identify pier atifying Eq.(4) (with φ = 1 ) a one of flexural failure type, i.e., they will not fail in brittle hear. In the capacity deign approach, the following procedure i adopted in the above mentioned international code, in general. Firt, through an elatic analyi under the pecified load, the bending moment and axial load at all critical ection are determined, and the member deigned for the combined effect of axial load and bending moment. Second, the potential platic hinge location and the preferred collape mechanim are identified. The overtrength flexural capacitie of the platic hinge are determined baed on the actual reinforcement provided and the propertie of actual material ued. Thi i often done by a moment-curvature analyi conidering the cracked 10 cro-ectional propertie of the member. Third, the tructure i reanalyed auming all potential platic hinge to have developed their overtrength flexural capacitie. The aociated axial load, hear force and bending moment in all tructural component other than thoe with the platic hinge are determined; thee member are deigned for thee force. The member with platic hinge (pier) are deigned for the hear uch that where n n V o V o correponding to the tate when flexural hinge are formed, φ V, (4) V = V + V. (5) c 9

10 In Eq.(4) and (5), V n i the nominal hear capacity (calculated uing the nominal pecified material trength), V o i the flexural overtrength-baed eimic hear demand (calculated uing actual material propertie 10 or by multiplying the nominal hear capacity by an overtrength multiplier Ω 9 ), φ i a reitance factor (le than unity), and V c and V are hear trength offered by concrete and reinforcing teel repectively. It i clear that thi capacity deign approach for hear deign of ubtructure may not be poible for ubtructure of the wall-type; it i not poible to generate the flexural hinge even under the extreme eimic haking. Detailed tudie are required to addre the eimic deign of wall-type ubtructure. The flexural overtrength of the tructure, which in turn reult in higher flexural overtrength-baed hear demand, hould be baed on realitic propertie. The flexural overtrength i caued due to many factor. One of them i due to the material ued in contruction having trength higher than the nominal trength employed in deign. For intance, the actual tenile yield trength of teel i higher than it characteritic yield trength ued in deign f y, and the actual compreive trength of concrete i higher than the characteritic compreive trength f ck. Hence, the mot likely material propertie/trength have to be ued a uch while etimating the flexural overtrength-baed demand on concrete component reiting eimic effect 10, i.e., without uing any factor of afety or partial afety factor on actual value. On the other hand, eimic hear capacity i to be conervatively determined baed on the nominal material trength only 10, i.e., by employing trength maller than the actual value. In reiting hear, concrete carrie ignificant part of the total hear force, particularly in large concrete cro-ection and thoe carrying vertical compreive load, uch a thoe of bridge pier. In general, the hear force capacity V c offered by a concrete ection depend on the hear trength of both concrete and longitudinal teel; hear trength improve with concrete grade and amount of tenion teel (though through dowel action). The hear trength of concrete itelf depend on the level of confinement provided by tranvere reinforcement, and on the impoed curvature; it increae with increae in volumetric ratio of tranvere teel and with decreae in curvature 20. Alo, the average concrete hear trength in platic hinge region decreae with increae in number of loading cycle and with increae in effective depth of the 10

11 ection. Thee are conidered in the PWRI pecification in calculating the hear capacity of RC ection 12. In RC tructure, the actual contitutive tre-train relation of concrete and teel ignificantly affect the eimic repone of the tructure. Tranvere reinforcement caue a confining preure on concrete reulting in an enhancement of it trength and train capacitie 21, 22, 23 ; thi, in turn, caue an increae in the load carrying capacity of member. In capacity deign, ince the maximum flexural overtrength-baed hear demand decide the ductile repone of the tructure, the actual contitutive relation of cover and core concrete mut be ued conidering the confinement action of tranvere reinforcement in the analyi 10, 12. Under confinement, the maximum train in concrete may be a high a 15 to 20 time the maximum train of normally ued in deign, and the peak compreive trength may be 4 time the 28-day characteritic compreive trength f ck (Figure 3 24 ). Tranvere reinforcement in RC pier erve a three-fold purpoe, namely for (a) providing hear trength, (b) confining the core concrete and thereby enhancing it trength and deformation characteritic, and (c) controlling the tability of the longitudinal reinforcement bar. The firt two function have been dicued earlier. Regarding the third one, literature report that inelatic buckling of longitudinal reinforcement in compreion can be prevented by limiting the maximum pacing of tranvere reinforcement bar to within ix time the nominal diameter of longitudinal reinforcement 25, 26, 21. Thi limit i generally recommended within the potential platic hinge region (Table 6). However, the limit i relaxed outide the potential platic hinge region, only if deign calculation are made in line with deign lateral force obtained a per Eq.(4). Alo, different code precribe minimum amount of tranvere reinforcement in platic hinge zone. For example, for circular pier, the American highway pecification (AASHTO 9 ) recommend that volumetric ratio of piral reinforcement be at leat the greater of ρ A ' g f c = and (6) Ac f yt ρ ' fc = (7) f yt Likewie, the AASHTO recommendation for non-circular hoop or tie reinforcement i 11

12 that the total effective area in each principal direction within pacing in pier i to be at leat the greater of A ' ' g f c A h = 0. 30D 1 and (8) Ac f yt ' ' fc A = h 0. 12D. (9) f yt The NZS 19 pecification recommend that in potential platic hinge region of circular pier, the volumetric ratio of piral reinforcement be at leat the greater of ρ = ( 1.3 ρ m) 2.4 l A A g c f f ' c yt P ' φf c A g and (10) ρ A f l yl 1 = ; (11) 110 D ' f yt db and for non-circular hoop or tie reinforcement, the area within pacing be greater than A h = ' ' ( 1 m) D Ag f ρ N ' l 3.3 A c f c yt φf ' c A g 12 A h in each principal direction D. (12) A detailed dicuion on the international practice of eimic deign of bridge and RC bridge pier i available elewhere 27, 28, Puhover Analyi The review of the Indian code proviion for RC pier deign in light of the international eimic deign practice, and importance of employing the capacity deign concept in bridge deign neceitate checking the eimic afety of pier deigned a per the exiting Indian tandard. The lateral trength and deformation characteritic of uch pier can be determined by conducting, monotonic diplacement-controlled experiment on prototype or model pecimen. However, in India, the infratructure required to perform experimental tudie i till limited and expenive. Thu, an analytical tool providing ufficient data regarding the pier repone i required not only for checking the performance of the deigned pier, but alo for development of improved deign tandard; puhover analyi i one uch tool. Thu, a diplacement-baed puhover cheme i developed that would provide ufficient inight into the full repone, i.e., till failure, of the mot commonly ued pier, the ingle column pier bending in ingle curvature.

13 5.1 Geometric Model Mot analytical tudie on RC bridge pier, including thoe with large croection, till idealie the member by it centroidal axi and define the inelatic action of the whole cro-ection in a lumped ene. Thi doe not accurately model the pread of inelaticity both along the member length and acro the cro-ection. Hence, a ditributed platicity model i required, which i decribed below Model Decription In the preent analytical model, the pier i dicretied into a number of egment along the length, and each egment into a number of fibre acro the cro-ection (Figure 4). A an RC ection i compoed of both concrete (of two type, namely the confined and unconfined) and longitudinal reinforcing teel, the ection i further dicretied into eparate concrete and teel fibre (Figure 5). Such a general approach of dicretiing RC ection into a number of dicrete fibre wa long adopted to accommodate general geometric irregularitie and geometric and material nonlinearitie, and to capture the complex tre ditribution acro the cro-ection under any loading condition 30, 31. Alo, procedure for obtaining tangent tiffne matrix of a egment dicretied into uch dicrete fibre wa preented earlier 32, 31. For analyi involving material and geometric nonlinearity, incremental equilibrium equation between incremental tre reultant and incremental deformation, i.e., the incremental or tangent load-deformation relation, are derived for all the fibre. Thee incremental equation are combined to form the incremental equilibrium equation of a egment. Finally, the incremental equilibrium equation of the entire pier i obtained by aembling thoe of it egment. Large diplacement and mall train are conidered in the analyi. Each fibre i treated a a two-nodded axial member with no flexural property. Thu, for a egment of length L, made of material of Young modulu E and hear modulu G, inclined at an angle α to the global axe (Figure 6), the egment tangent tiffne matrix relating the nodal force increment to the nodal diplacement increment in global coordinate i given by where ab h [ K ] t [ K] t + [ K] t =, (13) [ Λ] [ Λ] [ Λ] [ Λ] ab [ K ] t =, and (14) 13

14 h [ K] t = GA 1 β + 2 b L β Sym. ab L 2 a L b 2 a 2 L 4 2 b L ab L b 2 2 b L ab L 2 a L a 2 ab L 2 a L b 2 a 2 L 4, (15) b 2 a 2 L 4 in which [ Λ] 2 2 a ab ay b ab 0 E = t A 2 P 2 ab b by + ab a 0 ; (16) L 2 L ay by y a = co α and b = in α. (17) In Eq.(9), y, A and L are the ditance of each fibre (concrete or teel) center from the gro cro-ection centroidal axi of the ection, it cro-ectional area and it length (equal to the egment length), repectively. P i the axial load (poitive for tenile load) and E t i the tangent modulu of elaticity of the material at the prevailing train level. In Eq.(6), the total tiffne of a egment, modeled a a general frame member, comprie two et of action, namely the combined axial and bending action ab [ K ] t, and the hear action h [ K ] t. The uffix t repreent the tangent modulu at a given train level. Here, the hear repone wa aumed to be uncoupled from the axial load and bending effect, and hence, the linear uperpoition wa conducted even under non-linear and inelatic condition. In bridge pier of large cro-ection, hear deformation contribute ignificantly to the overall deformation repone of the pier. Hence, it i important to include the ame. The tiffne matrix derived i applicable for a general frame member that may be a lender one with predominant flexural behaviour, or a tocky one with ignificant hearing behaviour. The factor β, which i the relative ratio of flexural lateral tranlational tiffne and hear tiffne of the egment 33, i.e., 12EI L β =. (18) GA L 3 help achieve thi. 14

15 The complete incremental equilibrium equation of a egment in global coordinate (Figure 6) i given by [ K] t { d} { f& } {} d& 1 d& {} f& f& & =, (19) T d& = d& d& d& 5 d& 6, and (20a) T f& = f& f& f& 5 f& 6 ; (13b) where { d & } and { f & } are the incremental egment end-diplacement and end-force vector. The incremental equilibrium matrix equation of the whole pier i formed by aembling thoe of all it egment. Symbolically, if [ K ] t i the complete global tangent tiffne matrix of the pier, [ K ] t i the global tangent tiffne matrix of the egment from Eq.(6), then N { t } [ K] = [ K] t = 1 where i the aembly operator and, (21) N i the number of egment in the member. 5.2 Material Model The load-deformation relationhip of each fibre i derived uing material contitutive law. In RC tructure, the two different material, namely reinforcing teel and concrete, require two different material contitutive law model. Moreover, core concrete fibre are confined and the cover concrete unconfined. Alo, the longitudinal and tranvere teel can be of different grade and amount. Tranvere teel affect the confinement of the core concrete and influence the axial tre-train relation of the core concrete. On the other hand, longitudinal teel play a direct role in the axial, bending and hear reitance of the ection. In India, the mot widely ued reinforcing teel, both for longitudinal and tranvere teel, i of HYSD teel conforming to IS: A model repreenting the virgin tre-train curve for HYSD bar, developed through regreion analyi of experimental data from uniaxial tenile tet i ued 35. Brief decription of ome of the contitutive law model of concrete available in literature are dicued elewhere 35. Of the different contitutive model available, the analytical model that i applicable to hollow ection alo i ued in thi tudy 35 ; thi model i an extenion to an earlier model 36. Hollow ection addre a new ituation, wherein the outer and inner hoop are tied by link leading to two ditinctly different 15

16 confining action, namely hoop action and the direct action of link. The falling branch a defined by the original ingle equation 37, 36 i too flat and i een to be above the experimental uniaxial tre-train data. Hence, the equation i modified 33 in the train range beyond the train ε 1 correponding to the peak tre a f c = r o f ' cc xr o 1 + x r o ; > ε1 ε c (22) where ( 1+1 / r r ) o = r, (23) Ec fcc ' r =, E ec =, E c = 3320 f E E c, and (24) c = c ε 1 ec ' ε 1 ε x. (25) In Eq.(15) to (18), the unit of both the compreive tre f and the modulu E i MPa. During puhover analyi of the pier, initially all the fibre are in compreion under the action of gravity load. A the pier tip i diplaced horizontally, the curvature at any ection i gradually increaed; the compreive train in ome fibre increae, while in other, it decreae and eventually become tenile (unloading in compreion and ubequent loading in tenion). At a certain curvature, palling of cover concrete occur, which reult in reditribution of tree within the ection. There i poibility of unloading and reloading of both concrete and teel fibre. However, for the purpoe of a monotonic puhover analyi, exhautive hyteretic model for material tretrain curve may not be required; imple loading, unloading and reloading rule are therefore ued. The following are the alient feature of the hyteretic tre-train model of teel ued in thi tudy: a) All unloading and initial reloading lope, upto yield, are equal to the initial elatic modulu E ; there i no tiffne degradation. b) There i no trength deterioration. c) A the material unload from the virgin curve, the whole tre-train curve tranlate along the train axi with the total tranlation being dependent on the platic train hitory; a kinematic hardening approach i utilized, wherein the tre-train path tranlate with accumulation of platic train, but without any change of ize or hape (a a conequence of (a) and (b)). Likewie, a imple hyteretic tre-train model of concrete i ued in thi tudy. 16

17 The alient feature of thi model are: a) Linear unloading and reloading occur with tangent modulu equal to the initial modulu. b) The reidual train capacity i calculated from the accumulated platic train. c) The tenile trength of concrete i neglected. The load-carrying capacity of compreion reinforcement in RC compreion member i ignificantly affected by the unupported length of the longitudinal bar between the tranvere tie that are expected to provide lateral upport and thereby prevent buckling of longitudinal bar. In the preent tudy, longitudinal bar are conidered to have buckled if the axial compreive tre in them exceed the critical tre In Eq.(19), σ cr, b, given by [ σ σ ] σ. (26) cr,b = Min cr,b ; cr,b σ cr 1, b i the critical elatic buckling tre of the longitudinal bar under clamped-clamped condition between the tranvere tie, given by Further, 1 cr,b 2 π E σ =. (27) ( / d ) 2 4 b 2 σ cr, b i the inelatic critical buckling tre, given by σ 2 cr,b f = f f u y y + ( f u 5 f y ) d b 5 for for for < 5 db 5 < < d b > 10 db 10. (28) 6. Diplacement Baed Puhover Analyi Procedure An analytical procedure i developed to ae the inelatic drift capacity of cantilever (circular and quare, olid and hollow) RC pier bending in ingle curvature. The pier i ubjected to a monotonically increaing diplacement (in increment) at it tip in one tranvere direction until it final collape. The force required to utain the pecified diplacement i calculated conidering the trength of the material, the deformation of the pier and the progreion of internal cracking. From thi, the overtrength hear demand, drift capacity and diplacement-ductility of the RC cantilever pier bending in ingle curvature, are extracted. Thu, the full lateral load- 17

18 deformation repone i traced. 6.1 Algorithm To begin with, the gravity load i applied at the top of the pier and the train and tree in all fibre of all egment are obtained; the tree developed in the cro-ection are enured to be in equilibrium with the external gravity load. Then, a mall diplacement increment i impoed at the tip of the cantilever pier. Correponding to thi tip diplacement, an initial deformed profile i aumed. Uually, the deformed hape of an elatic cantilever with only bending deformation conidered under the action of a concentrated load at the tip, i a good firt approximation. Thu, the initial lateral tranvere diplacement x ( z) and rotation θ ( z) at a ditance z from the bottom upport, for a firt diplacement increment of the cantilever of height (length) h (Figure 7) are given by x z 2 ( z) = ( 3h z) o 2 3 h 18 o at the tip, and (29a) 3z θ( z) = ( 2h z) o. (22b) 3 2h The change in length of the cantilever i conidered while etimating the internal reitance of the pier. For thi aumed diplacement profile along the height h of the pier, the internal reitance vector along the degree of freedom { p } i calculated (a dicued later). The external load vector { f } conit of vertical concentrated load at the top of the pier from the gravity load of the upertructure and vertical dead load at all intermediate node from the dead load of the pier egment. Puhover analyi involve iterative computation due to the nonlinearitie in the contitutive relation of the material and due to geometric effect. Modified Newton-Raphon Method i ued for the iteration. Thu, at the global iteration level, at a general diplacement tep r and iteration level k, the force unbalance { u} { u} k r f p till iteration (k-1) i computed. From thi, the incremental deformation vector along the unknown diplacement direction r { x& i obtained from r 1 r r [ Kuu ] { x& u} k = { fu} { pu} k r 1 where [ K ] uu } k u, (30) i the iterating matrix correponding to the unknown degree of freedom extracted from the partitioned tangent tiffne matrix [ K ] t of the pier, obtained from Eq.(14), baed on the cracked ection propertie at the end of the lat

19 diplacement tep (r-1). The net incremental deformation vector r {} x& net k in the diplacement tep r and up to iteration k i then obtained a r net r net r {} x & k {} x& k + {} x& k = 1, (31) where r {} x& k i the incremental deformation vector along all, known and unknown degree of freedom. r {} x& net k i then decompoed to form the global incremental enddeformation vector r {} d & for each egment. Hence, if Π i the decompoition operator that depend on the connectivity array of the degree of freedom at the end of the egment, then r r {} d & {} x& net Π =. (32) k Baed on the new deformation profile updated uing the node coordinate at the end of the diplacement tep r, the net global incremental end-deformation and the coordinate tranformation [ T ] (a in Eq.(34)) are updated. The net incremental deformation vector r {} u& in local coordinate (Figure 8) for each egment, i obtained a where r r {} {} u& {} u [ T] r {} d& & =, (33) T u & = = u& 1 u& 2 u& 3 u& 4 u& 5 u& 6. (34) f Uing thi, the net incremental axial train ε& in fibre f at a normal ditance y from the centroidal axi of the gro cro-ection of the egment before deforming, i calculated a f ( u& 1 u& 4 ) + ( u& 3 u& 6 ) y ε & =. (35) L Given the tate of the fibre at the end of the previou diplacement tep (r-1) and the net incremental axial train f ε&, the new tre tate f σ of the fibre i obtained uing the cyclic contitutive law of teel and concrete decribed previouly. From the tree of all the fibre in the cro-ection of the egment, the total internal reitance, namely the axial reitance P c and the bending moment calculated from M c reited by the ection (egment ), are P c = N fc N f c c σ i Ai + σ j i = 1 j = 1 A j, and (36) 19

20 M c = N fc i = 1 σ c i A c i y i + N f j = 1 σ j A j y j, (37) and the total hear r V c r V c reited by the egment in the diplacement tep r from ( u& u& ) ( u& & ) (r β + = ) Vc + GA 1 + β L 2 1 u6, (38) where (r 1) V c i the egment hear force at the end of the previou diplacement tep. Thu, the component of the end-force vector r { r } in local coordinate for the egment are obtained a P c r 1 = (39a) r = r 2 V c (32b) r 3 r = Vc L Mc 2 (32c) r4 = P c (32d) r 5 = r V c (32e) r 6 r = Vc L Mc 2 (32f) Uing thi, the egment end-force vector in global coordinate, { } p i computed a where r {} [ T] T r {} r [ ] p =, (40) a b b a T =. (41) a b b a The aembly of thee { p } vector of each egment reult in the updated complete member reidual force vector { p }. Collecting the force along the unknown degree of freedom { p u}, the reidual force vector { r } i then computed a { r } = { fu} { pu}. (42) The above procedure i reiterated until the reidue { r } i within pecified tolerance. Upon convergence, the global coordinate of the node and the egment end 20

21 force are updated. The target deformed geometry for the next diplacement tep (r+1) i computed baed on the next lateral increment at the tip of the cantilever pier (Figure 9). The above internal reitance calculation procedure i repeated with additional diplacement increment until the pier reache failure. Thu, the full lateral load-lateral diplacement repone i traced. From thi, the flexural overtrength-baed hear demand where max V Ω on the RC pier bending in ingle curvature i extracted a max Ω Hmax, (43) V = H max i the maximum internal reitance of the pier at it tip during the entire diplacement loading hitory (Figure 10). 7. Numerical Study The adequacy of trength deign proviion a per Interim IRC: i invetigated for mot commonly ued olid and hollow RC pier of circular and rectangular cro-ection. Pier of typical 5 m height are deigned a per the trength deign methodology outlined in IRC: The approximate initial choice of ection ize (cro-ectional area) and probable load on the pier are taken from field data of exiting bridge pier. In thi tudy, a 2-lane upertructure i conidered. The weight of the upertructure i taken a kn/m. Hence, for a pan of 40 m, the pier are ubjected to a upertructure gravity load of 6500 kn. The lateral and vertical eimic load on the pier are calculated a outlined in IRC: for eimic zone V, with importance coefficient of 1.5 on rocky or hard oil ite. The nomenclature ued to deignate bridge pier tudied i decribed a follow. The firt character (i.e., C or R ) indicate pier of circular or rectangular cro-ection. The econd character (i.e., S or H ) indicate olid or hollow ection. The third character (i.e., W or S ) indicate pier without and with hear deign. The fourth character (i.e., G, L or P ) indicate type of invetigation undertaken on the pier, namely effect of geometry, lenderne or axial load. The fifth et of number in the invetigation on effect of lenderne (i.e., 2 or 6 ) indicate lenderne of the pier, while that in the invetigation on effect of axial load level (i.e., 05, 10, 30 ) indicate the axial load ratio. Becaue there i no proviion for hear deign of pier or compreion member in IRC: , only nominal tranvere reinforcement a required by IRC: i provided in firt et of four pier (one each of olid circular, olid rectangular, hollow 21

22 circular and hollow rectangular cro-ection). Thee are named a CSWG, RSWG, CHWG and RHWG. However, proviion for hear deign in beam and lab are outlined in IRC: Hence, a econd et of four more pier (namely CSSG, RSSG, CHSG and RHSG) i deigned for hear in line with thee hear deign proviion. The overtrength baed hear demand of thee eight pier are etimated from their monotonic lateral load-diplacement repone. Alo, the nominal deign hear capacitie of the ection are computed a per IRC: wherein both concrete and tranvere teel are conidered to contribute to the deign hear trength. Next, the effect of pier lenderne on overall repone i invetigated. A et of eight pier i deigned for two lenderne ratio, namely 2 and 6. The pier (namely CSWL-2, CSWL-6, RSWL-2, RSWL-6, CHWL-2, CHWL-6, RHWL-2 and RHWL-6) are deigned for the ame upertructure gravity load of 6500 kn, and a tranvere load in accordance with Eq.(2) with nominal tranvere reinforcement a per IRC: In all pier, the cro-ectional area i kept at approximately 4.6 m 2, giving a compreion force of about ' f c A. Puhover analyi i performed for all the twelve pier to g compare the overtrength hear demand with the nominal hear capacity at the critical ection. Then, the effect of level of axial load on the overall repone of pier i invetigated. For thi, a 10 m long olid circular pier of diameter 2 m i deigned for upertructure gravity load of 5050 kn and lateral load of 1032 kn. The pier ha nominal tranvere reinforcement in the form of circular hoop of diameter 8 mm at 300 mm centre. The pier i then ubjected to axial compreion load of 0.05 f c A g, 0.10 f ' c A g and.30 f ' c A g 0 and lateral puhover analyi i performed (analyi cae CSWP-05-1, CSWP-10-1 and CSWP-30-1). The circular hoop in the pier are the enhanced to 12 mm diameter at 100 mm centre, and the lateral load-deformation repone for the three axial load level are obtained for thee additional tranvere reinforcement type alo (analyi cae CSWP-05-2, CSWP-10-2 and CSWP-30-2). In all numerical tudie, concrete cover of 40 mm and concrete grade of 40 MPa are ued. All tudie are performed for major axi bending, i.e., in the tranvere direction (normal to traffic flow). For all the pier, ince the reultant tenion due to direct compreion and bending under deign load exceed permiible tre given in IRC: , cracked ection analyi wa carried out to arrive at the amount of 22 '

23 longitudinal teel a required by IRC: The permiible tree ued in deign are increaed by 50% while uing eimic load-combination, a per recommendation of IRC: Reult The reult of the puhover analye are hown in Figure 11 to 13. In thee, the flexural overtrength baed hear demand in the pier are normalied with repect to the deign hear force and are plotted againt the percentage drift capacity of the pier. The invetigation with different cro-ection hape or geometrie how that in all cae, the flexural overtrength baed hear demand i more than (2.2 to 3.8 time) the deign hear. Thi i primarily due to the afety factor ued in the deign. Alo, in all cae, the hear demand i more than the hear capacity of the ection (Table 7), implying poible hear failure in thee pier. Further, hort pier (with lenderne ratio of ) with olid ection and hear reinforcement perform better than the pier with hollow ection with approximately ame cro-ectional area, and height (Figure 11). Hollow ection have larger ection dimenion and therefore draw more lateral force. In pier with circular cro-ection, thi increae the overtrength-baed eimic hear demand without any appreciable increae in deformability. In pier with rectangular cro-ection, the pier with hollow cro-ection how increaed deformability, apart from the expected increaed hear demand (Figure 11). Thi i due to the IRC: requirement that, in rectangular ection, every corner and alternate longitudinal bar be laterally upported by the corner of a tie, and that no longitudinal bar be farther than 150 mm from uch a laterally upported bar. Thi force additional intermediate tie in both direction in the hollow rectangular ection, which enhance the effective confinement of concrete (compare volumetric ratio of tranvere reinforcement in Table 8) and therefore increae the maximum train that concrete can utain. Thi alo reult in increaed deformability of the hollow rectangular ection compared to the olid rectangular ection with only nominal tranvere reinforcement. On the other hand, pier with olid cro-ection with deign tranvere hear reinforcement have better pot-yield behaviour in the form of enhanced deformability and diplacement ductility. Thi ignifie the importance of tranvere reinforcement on the overall repone of pier. The hear capacitie of circular and rectangular ection, both olid and hollow, 23

24 with nominal tranvere reinforcement a recommended by IRC: are inufficient for the hear demand due to flexure for thee hort pier (Table 7 and 8). Premature brittle hear failure of pier i expected before the full flexural trength i achieved. Of the four type of pier having ame height and imilar cro-ectional area, and ubjected to the ame axial compreion, the olid circular pier have the leat hear capacity. Thi i attributed to the preence of only a ingle circular hoop in olid circular pier. In rectangular ection, the intermediate tie in both the direction enhance the hear capacity. Thu, the ratio of tranvere reinforcement required (to prevent hear failure) to that provided i maximum (15.69) in pier with olid circular ection and leat (1.87) in pier with hollow rectangular ection (Table 8). Further, the minimum volumetric reinforcement ratio a required in the current international practice (a per AASHTO, NZS and PWRI code) i much higher than the nominal reinforcement requirement pecified in the IRC code (Table 9); the IRC requirement i at leat 2-20 time maller. Alo, in hollow ection, the IRC: requirement of minimum area of tranvere teel of 0.3% of wall cro-ection exceed the IRC: reinforcement requirement. However, even thi tranvere teel i inadequate to reit the overtrength moment-baed hear demand in hort pier (Table 8). In mot pier, epecially where only nominal tranvere reinforcement i provided, buckling of longitudinal reinforcement occurred (Table 7), reulting in udden lo of load carrying capacity. Thi i due to the large pacing of tranvere reinforcement adopted along the member length; the pacing adopted i a per IRC: which i the minimum of (a) 12 time the diameter of mallet longitudinal reinforcement bar, and (b) 300 mm (becaue the leat lateral dimenion i alway much larger than 300 mm). The invetigation on the effect of pier lenderne reveal that the nominal tranvere reinforcement requirement are inadequate for hort pier (lenderne ratio of 3), except for pier with rectangular hollow ection. On the other hand, for lender pier (lenderne ratio of 6), the nominal deign hear capacity i higher than the demand (Table 10 and 11). Thu, lender pier exhibit a ductile behaviour. In large hollow rectangular pier, better ditribution of longitudinal teel and enhanced concrete confinement due to intermediate link reult in uperior pot-yield repone than in the other three type of ection conidered in thi tudy (Figure 12). Alo, with 24

25 increae in lenderne, the hear demand reduce and the deformability increae. Thi i due to greater flexibility of pier with increaed lenderne. Thu, the target deformability of a pier eem to be a function of it lenderne. However, a in the firt tudy, failure i primarily initiated by buckling of longitudinal teel (Table 10). The invetigation on effect of axial load how that with increae in axial load level, ductility reduce while the hear demand increae (Figure 13). With increae in axial load, tenion yielding of teel i delayed increaing the yield diplacement, while the ultimate diplacement i reduced due to leer reidual flexural train capacity of the fibre. Thi caue a reduction in ductility. In addition, with increae in axial load level, flexural cracking of concrete fibre i delayed, thereby increaing the net uncracked ection area. Thi increae the ection rigidity and thu draw in more lateral hear, thereby increaing the hear demand. In addition, with increae in amount of tranvere reinforcement, the deformability increae (Figure 13). Thi i again due to increae in confinement of concrete and correponding increae in ultimate train capacity. Thee obervation ugget that with increae in axial load level, for an expected drift capacity, higher amount of tranvere reinforcement i required to prevent hear failure (Table 12 and 13). 9. Obervation A number of important point are brought to attention through the review of IRC: , IRC: and IRC: eimic bridge deign proviion in light of ome international practice relating to capacity deign approach and the Interim IRC: proviion, and through the numerical invetigation of ingle-column type RC pier baed on deign methodologie in exiting Indian tandard. Thee are: a) The extreme low value of eimic force a per IRC: are eliminated in the Interim proviion and the new proviion provide a more rational bai for eimic force calculation including the effect of tructural flexibility. b) The Interim proviion account for repone reduction factor in eimic deign. Thu, in eence it advocate nonlinear repone of pier. However, the recommended repone reduction factor of 2.5 may not be ued in the deign of connection. c) For pier deigned for deign force level a per IRC:6-2000, the deign longitudinal reinforcement i inufficient to reit the effect of increaed horizontal force level a per Interim proviion, if working tre deign philoophy enumerated in IRC:21-25

26 2000 i ued. d) Increae in concrete trength and tain capacitie due to confinement by tranvere reinforcement and train hardening of longitudinal teel i not accounted for in hear deign of RC pier a per IRC: ; thi reult in much higher flexural overtrength baed hear demand than deign hear level and hence make the bridge vulnerable to brittle hear failure. e) Poibility of platic hinge formation in an extreme eimic event i not accounted for in the deign procedure outlined in IRC code; capacity deign i not performed. f) Nominal tranvere teel requirement a given in IRC: are inadequate in preventing brittle hear failure in hort pier (of lenderne ratio of 3) under force level a per Interim IRC: g) Pier with hollow ection how enhanced deformability and have higher hear capacity compared to the olid one with approximately ame cro-ectional area owing to preence of larger nominal tranvere reinforcement. h) Due to preence of additional intermediate tie, pier with rectangular ection have larger hear and deformability capacity compared to thoe with circular ection. i) Buckling of longitudinal reinforcement i not prevented by the exiting proviion on pacing of tranvere reinforcement; buckling i common in pier reulting in rapid trength lo. j) Increaing the amount of tranvere reinforcement (from 2.43 to time the current amount) increae diplacement ductility of pier and produce improved pot-yield repone. k) Pier under higher axial compreion require more tranvere reinforcement for expected diplacement ductility; tranvere reinforcement requirement in IRC code can be made a function of the probable maximum axial load on the pier and the required diplacement ductility. 10. Concluion Thi tudy on the eimic deign of RC bridge pier deigned a per the current Indian code proviion ugget that the following change be urgently brought into the IRC proviion: a) The deign of RC member a given in IRC: need to be revied in line with the deign philoophy of inelatic action of pier intended in the Interim IRC: proviion. Currently, the IRC ue two different deign philoophie, the inelatic 26

27 behaviour philoophy for calculating the eimic load uing a repone reduction factor (greater than unity) implying nonlinear repone, and the elatic behaviour philoophy for deigning pier by the elatic working tre method. The two need to be calibrated for each other, ele a conitent inelatic deign approach may be adopted. b) The deign for hear of lender vertical RC bridge member need to be baed on capacity deign concept. Alo, a formal deign bai i required for calculation of deign hear trength V c of concrete depending on the confinement, level of axial load, and impoed ductility under cyclic loading. c) The contribution of tranvere reinforcement in confining the core concrete and preventing buckling of longitudinal bar, hould be included. Table 1: Horizontal eimic coefficient α a per IRC: Seimic Zone I II III IV V Horizontal Seimic Coefficient α Table 2: Soil-foundation ytem factor β a per IRC: Soil-Foundation Sytem Factor β Type of Soil mainly contituting the foundation Type I :: Hock or Hard Soil (for N>30) Type II :: Medium Soil (for 10<N<30) Type III :: Soft Soil (for N<10) Bearing Pile reting on Soil Type I, or Raft Foundation Note: N = Standard Penetration Tet Value Bearing Pile reting on Soil Type II & III, Friction Pile, Combined Footing or Iolated RCC Footing with Tie Beam Iolated RCC Footing without Tie Beam, or Unreinforced Strip Foundation Well Foundation

28 Table 3: Seimic Zone factor Z a per Interim IRC: Seimic Zone II III IV V Seimic Zone Factor Z Table 4: Average Repone Acceleration Coefficient Interim IRC: S a g (for 5% damping) a per Soil Type Rocky or Hard Soil Medium Soil Soft Soil Average Repone Acceleration Coefficient S a g 2.50 ; 0.00 T ; 0.40 T 4.00 T 2.50 ; 0.00 T ; 0.55 T 4.00 T 2.50 ; 0.00 T ; 0.67 T 4.00 T Table 5: Deign Seimic Coefficient a per IRC: and Interim IRC: for eimic haking in the tranvere and longitudinal direction of the bridge IRC: Seimic α 2000 Interim IRC: α Interim Ratio α Interim Zone (Longitudinal α 2000 and Tranvere) Longitudinal Tranvere Longitudinal Tranvere V IV III II I

29 Table 6: Maximum recommended pacing of tranvere reinforcement et in pier. Specification Maximum Spacing Outide Potential Platic Within Potential Hinge Region Platic Hinge Region AASHTO Min [b; 300 mm] Min [b/4; 100 mm] CALTRANS --- Min [b/5; 6 db ; 220 mm] NZS (fully-ductile) Min [b/3; 10 db ] Min [b/4; 6 db ] NZS (partially-ductile) Min [b/3; 10 db ] Min [b/4; 10 db ] PWRI > 150 mm 150 mm Note: b = Leat cro-ectional dimenion of the pier d = Leat nominal diameter of longitudinal reinforcement b Table 7: Reult of analye of four type of 5 m long pier comparing hear capacity and demand, and howing final form of failure. Pier Section Area Reinforcement Shear Failure Capacity Demand Mode (L=5 m) (m) (m 2 ) LongitudinalTranvere (kn) (kn) CSWG 2.00 φ Y28 Y8@ Buckling of long. teel CSSG 2.00 φ Y28 Y12@ Buckling of long. teel RSWG Y28 Y8@ Buckling of long. teel RSSG Y28 Y8@ CHWG CHSG 2.6(OD), 1.6(ID) 2.6(OD), 1.6(ID) Y25 Y12@ Buckling of long. teel Y25 Y12@ Buckling of long. teel Y20 Y10@ RHWG (OD), (ID) RHSG (OD), Y20 Y10@ (ID) 29

30 Table 8: Tranvere reinforcement requirement to prevent hear failure in 5 m long pier of four type of cro-ection in invetigation on effect of geometry. Pier Shear Volumetric Ratio of Tranvere Ratio Reinforcement (10-3 ) r p ρ ρ Capacity Demand p r Provided ρ Required ρ (kn) (kn) CSWG CSSG RSWG RSSG CHWG CHSG RHWG RHSG Table 9: Minimum tranvere reinforcement requirement in platic hinge region a per Indian and international code Pier Minimum Volumetric Ratio of Tranvere Reinforcement (10-3 ) Provided Required IRC: AASHTO 1998 NZS 1995 PWRI 1998 CSWG CSSG RSWG RSSG CHWG, CHSG RHWG, RHSG

31 Table 10: Reult of analye of four type of pier of two lenderne ratio comparing hear capacity with demand, and howing final form of failure. Pier L Section Area Reinforcement Shear Failure Name Long Tran Capacity Demand Mode (m) (m) (m 2 ) (kn) (kn) CSWL φ Y28 Y8@ Buckling of long. teel CSWL φ Y28 Y8@ Buckling of long. teel RSWL Y28 Y8@ Buckling of long. teel RSWL Y28 Y8@ Buckling of long. teel CHWL (OD), 2.4(ID) Y25 Y12@ Buckling of long. teel CHWL (OD), 2.4(ID) Y25 Y12@ Buckling of long. teel RHWL (OD), Y20 Y12@ (ID) RHWL (OD), Y20 Y12@ (ID) Table 11: Tranvere reinforcement requirement to prevent hear failure in pier in invetigation on effect of lenderne. Pier Shear Volumetric Ratio of Tranvere Ratio Reinforcement (10-3 ) r p ρ ρ Capacity Demand p r Provided ρ Required ρ (kn) (kn) CSWL CSWL RSWL RSWL CHWL CHWL RHWL RHWL

32 Table 12: Reult of analye of olid circular pier with three axial load ratio and two different circular hoop with percentage lateral drift. Pier Section Area Diameter Reinforcement Long. Tran. Shear Axial Lateral Load Drift Capacity Demand Ratio (kn) (kn) (%) (L=10.0m) (m) (m 2 ) CSWP Y CSWP Y CSWP Y CSSP Y32 Y12@ CSSP Y32 Y12@ CSSP Y32 Y12@ Table 13: Tranvere reinforcement requirement to prevent hear failure in pier in invetigation on effect of axial load. Pier Shear Volumetric Ratio of Tranvere Ratio Reinforcement (10-3 ) r p ρ ρ Capacity Demand p r Provided ρ Required ρ (kn) (kn) CSWP CSWP CSWP

33 Figure 1: Seimic Zone and Zone Map of India [IS:1893 (Part 1), 2002]. Tranvere Direction Traffic Direction (Longitudinal Direction) Bridge Vibrating Unit ELEVATION Minor Axi Major Axi Traffic / Longitudinal Direction PLAN SECTION OF PIER Figure 2: Single pier bridge vibration unit with typical orientation of the pier ection. 33