COMPREHENSIVE RETROFIT EXAMPLE 1 MULTI-SPAN CIP REINFORCED CONCRETE BOX GIRDER BRIDGE

Transcription

1 COMPREHENSIVE RETROFIT EXAMPLE 1 MULTI-SPAN CIP REINFORCED CONCRETE BOX GIRDER BRIDGE 1. Problem Statement Evaluate a six-span cast-in-place reinorced concrete highway overcrossing located in southern Caliornia or seismic retroitting. The structure is supported on monolithic single column bents and has a single expansion joint hinge located in span 3. The bridge was constructed in the early 1960 s and has several obvious seismic deiciencies including substandard transverse column reinorcement and a minimal support length at the interior expansion joint hinge. Use the D method o evaluation. Once an evaluation has been completed and seismic deiciencies identiied and quantiied, develop a retroit strategy that will result in the minimal perormance criteria being met. Design the retroit measures necessary to implement the selected strategy.. Description o As-Built Bridge The bridge, which is located in a seismically active region o southern Caliornia, is on a curved horizontal alignment o 600 t radius and has variable span lengths. It passes over a reeway and parallel surace streets. The site class is Type D. The cross-section o the superstructure is o constant width and consists o ive girder stems with an overhang on one side. A raised curb with emergency sidewalk is provided on the other side. The depth o the superstructure varies rom 7-0 to 3-6 with the transition occurring in span 3. Abutments are seat type supported on 45-ton piles with approach retaining walls provided to contain approach roadway ills. They are oriented normal to the superstructure. The superstructure is supported on elastomeric bearings with concrete shear keys provided to restrain transverse movement. The bearing seat is -6 in width. The internal expansion joint hinge located in span 3 consists o an 8 inch bearing seat with embedded steel angles or bearing. Transverse concrete shear keys are provided, but no longitudinal cable restrainers are in place. Internal bents are single columns o circular cross section supported on pile ootings. Columns at Bents and 3 are 6-0 in diameter while the remaining E1-1

2 columns are 5-0. The main reinorcing steel is lap spliced just above the ootings, and the column transverse steel, consisting o #5 spirals with a 5 pitch, is lap spliced periodically. Pile ootings vary in size depending on the size o the column, and lack upper layers o reinorcing steel to resist negative bending moments. Piles have a design capacity o 45 tons and are eectively pinned at the base o the ooting. The reinorcing steel rom the piles extends into the ooting and can resist the seismic uplit capacity o the piles, which is assumed to be 50% o their ultimate compressive capacity (C u x C design ). A ield inspection o the bridge revealed no deterioration or modiication o the structure. Because o the age o the concrete it is assumed to have an in-situ strength o 5500 psi. Reinorcing steel is Grade 60. The as-built plans or the bridge are shown in Figures E1-1 through E Enhanced Procedure or Method D Seismic Evaluation The procedure described in the manual or Method D is enhanced to include components other than the columns. Step 1 Strength and Deormation Capacities a. Hinge Force and Displacement Capacity The expansion joint hinge orce and displacement capacities are calculated based on the details o the as-built structure. The transverse orce capacity is based on shear riction in the shear keys. The total number o #5 bars crossing the shear plane is 16 and the bars are assumed to be Grade 60 with an expected strength o 66 ksi. The concrete crack surace over each o the two shear keys is 16 inches by 36 inches. Thereore, the shear capacity is given by V u φv n φ ( ca + μ[ A + P ]) ( ( 36 ) + 1.4[ ] ) cv v y c 50 kips The displacement capacity can be calculated as the seat width minus the expansion joint gap plus 100 mm (4 inches). δ c Ns gej c h inches E1-

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6 Table E1-1 - Hinge Force and Displacement Capacities Hinge 1 Transverse Force Kips (KN) 50 (3) Longitudinal Displacement - inches (mm) 3.0 (10) b. Column and Foundation Shear Capacities In the case o column shear capacities, both the initial and inal shear strength is considered. An example o the required calculation or Bent ollows. 1.6ρ A 1.6ρ 0.8A v e v tanθ ΛρtA g ρ ta g A sl ρt.01 A π(36) ρ v c 4A ss sd 0.5 4(.31) (7 4.63) tanθ cot θ tanθ 0.5 [ 0.355] ρ 0.64 ρ π D π (7 4.63) Vs A hyh cot θ (.31)(60) (1.435) s kips 514 KN Λ.875(68.7) Vp P tanα (1157) kips 191 KN g v t 0.5 E1-6

7 The initial and inal contribution o V V Thereore, the initial and inal ultimate shear V V ci c ui u ' π (36) 3.61 ce A e kips 3881 KN ' ce A ( V + V + V ) 0.85( ) s 1468 kips 653 KN ( V + V + V ) 0.85( ) s 850 kips 378 KN e p p 145 kips 645 KN ci c the concrete (V ci and V capacity (V ui c respectively) is : and V u ) is given by : The ollowing table includes the shear capacities or all o the columns. Table E1- - Column Shear Strength Capacity Column Column Length Feet (m) 0.0 (6.10) 4.5 (7.47) 17.0 (5.18) 19.4 (5.91) 1.7 (6.6) Dead Load Axial Load Kips (KN) 1157 (5149) 1069 (4757) 448 (1994) 457 (034) 545 (45) Initial Shear Strength Kips (KN) 1468 (653) 1407 (663) 1006 (4475) 996 (4431) 1001 (4455) Final Shear Strength Kips (KN) 850 (378) 789 (351) 576 (565) 567 (51) 57 (545) Similarly, the oundation shear capacity is calculated based on the capacity o the piles in shear plus the capacity provided by passive pressure on the ace o the pile cap. The ultimate lateral capacity o a single pile is assumed to be 40 kips (178 KN) based on physical testing o similar piles. The shear capacities or Bent and 3 are calculated as ollows: H (piles) N c p 40 5 ( 40) h Hc (cap) Pp W dw kips 1068 KN 1000 kips 4450 KN ( 4 + ) 4 15 E1-7

8 The total shear capacities o all pier oundations are summarized below Table E1-3 - Pier Foundation Capacities Pier Foundation and 3 4, 5 and 6 Shear Capacity Kips (KN) Longit. Trans (5518) (5518) (370) (370) E1-8

9 c. Abutment Force and Displacement Capacities Abutment orce capacities are governed either by the capacity o shear keys or the capacity o the piles and wingwalls. The shear key capacity is calculated in a manner similar to those or the hinge and is summarized below. V u φv n kips ii. i. Shear Keys: φ ( ca + μ[ A + P ]) cv ( ( ) + 1.4[ ] ) v Piles and Wingwalls y c In the case o the piles the calculation or Abutment 1 is perormed as ollows: V N (40) p p 50 kips The wingwall capacity is equal to the capacity o one wingwall in shear. In this case the wingwall is 14 eet high and 1 inches thick (d9 ). Thereore: V w φhd 190 kips ' c V V + V abut p w 710 kips The displacement capacity in the longitudinal direction depends on the geometry o the seat and the nominal amount o expansion (g e 1 ). In this case: δ N g c abut s e c 5 inches Similarly or Abutment 7: V δ abut abut 576 kips 5 inches Table E1-4 - Abutment Force and Displacement Capacities Abut Transverse Force Kips (KN) Shear Piles and Keys Wingwalls Longitudinal Displacement - inches (mm) E1-9

10 (804) (3160) (804) (563) Step Nonlinear Static Pushover Analysis 5.0 (635) 5.0 (635) In a displacement-based approach, the irst step in a nonlinear static pushover analysis is to assess the deormation capacity o various ductile elements such as columns. One method is to perorm moment-curvature computer analyses based on allowable strains. For this problem, simpliied methods presented in the retroit guidelines or determining allowable plastic rotations o the columns are used. These depend on the limit state being investigated. In this bridge, the unconined splices that are typical o bridge construction prior to 1971 must be considered. The transverse spiral reinorcing in the column is lap spliced (a substandard detail) and will be subject to ailure as soon as the outer concrete cover spalls. Thereore, a compression ailure in unconined concrete should be investigated. Shear ailure is another possibility that could limit ductile response. The ollowing calculations are perormed or Bent. φ L L L y p p p y E D 9000 s rad/in 0.08L ε in 0.99 in ( 60) ( 7 ( ) (.69) 1.44) ( 0( 1) ) (.0007)( 1.5) ( ( )) (.0007)( 1.5) P e y 1 c D + 0.5ρt ' ' c 1 A 1 d D c g c D β 1.3α 0.16 by trial and error d c 0.16D 0.16 y b (or transverse bending) (or longitudinal bending) ( 7) in 0.75 The allowable plastic rotation or each o the limit states can now be calculated. E1-10

11 εcu.005 φp φy c rad/in θp φplp ( 30.59) rad (transverse bending) θp φplp ( 0.99) rad (longitudinal bending) The splice section is evaluated as ollows: l s L 0.03 lap 4 in ye ' ce d b in 45 Thereore, this is a "long splice and, by inspection, unconined compression will control. Although the inal shear capacity is suicient to resist shear demands in the transverse direction, shear ailure could occur in the longitudinal direction due to shear capacity degradation resulting rom lexural yielding. The amount o plastic rotation that is allowed will be limited because o this. This is calculated as ollows. The plastic overstrength moment at the dead load axial orce is calculated irst. E1-11

12 E1-1 ( )( ) ( ) ( )( ) ( ) ( ) ( )( )( )( ) 11,091kip t D A A P A P A P A P 1 D A M M Thereore, A P D D K D A M A A 0.5 A P A P A P 5.5 ksi Where A P A P A P A P 1 D A M D A M g ' c g ' c bcc g ' c to g ' c bcc g ' c e g ' c bo po o g ' c bcc ' c su t shape g ' c bo g cc g ' c bcc ' c su t g ' c to g ' c e ' c g ' c bcc g ' c to g ' c bcc g ' c e g ' c bo g ' c po + κ + ρ αβ ρ

13 Thereore, the limitations on lexural yielding based on shear strength or Bent degradation is: V φ θ m p p M Vi Vm 5 φ Vi V rad/in φ p p L p L kips y ( ) ( 0.99) radians (Does not control) The deormation capacity o all as-built columns is summarized below. Column Deormation Capacity (Longitudinal) Column Yield Curvature radians/in (radians/m) (.0075) (.0075) (.00337) (.00337) (.00337) Ultimate Curvature radians/in (radians/m) (.01147) (.0118) (.01336) (.01489) (.014) Plastic Moment Kip t (KN m) (15053) (14874) 711 (9661) 713 (9676) 738 (980) Plastic Hinge Length inches (m).1 (.561) 4.3 (.617) 0.7 (.56) 1.8 (.554).9 (.58) Plastic Rotation radians Column Deormation Capacity (Transverse) Column Yield Curvature radians/in (radians/m) (.0075) (.0075) (.00337) (.00337) Ultimate Curvature radians/in (radians/m) (.01147) (.0118) (.01497) (.01489) Plastic Moment Kip t (KN m) (15053) (14874) 711 (9661) 713 (9676) Plastic Hinge Length inches (m) 31.7 (.805) 36.0 (.914) 8.8 (.73) 31.1 (.790) Plastic Rotation radians E1-13

14 (.00337) (.014) (980) (.848) Once the deormation capacity o the potential plastic hinge has been determined, a longitudinal displacement capacity evaluation o the entire bridge is determined through a longitudinal push-over analysis. In this type o analysis the columns are modeled as non-linear elements. The rame, which is modeled in -dimensions, is incrementally displaced in the longitudinal direction until the maximum allowable plastic rotation is achieved in the plastic hinge zones. The displacement at which this occurs is identiied as the displacement capacity, Δ ci. The transverse displacement capacity is determined by a transverse push-over analysis o each bent. Both the longitudinal and transverse push-over models include non-linear oundation springs or both rotational and translational movement. 1. Longitudinal Push-over Analysis a. Computer Models The computer model used or the longitudinal push-over analysis is shown in Figure E1-4. This model was analyzed using the DRAINDX computer program that was originally developed at the University o Caliornia at Berkeley. The non-linear elements used to model the potential plastic hinges in the reinorced concrete column are based on a tri-linear interaction curve (i.e. Shape Code 3). This tri-linear curve is selected to match the actual interaction curve in the vicinity o the axial load. The actual interaction curve is calculated using the computer program YIELD, one o several that can be used or this purpose. The tri-linear curves used in this analysis are shown in Figures E1-5a and E1-5b. Slaved Nodes at Hinge Rigid Links (Typ) Nonlinear Beam Element (Typ) Nonlinear Foundation Element (Typ) Figure E1-4 DRAINDX Model E1-14

15 Axial Force - kips Tri-linear curve it or DRAINDX Interaction Diagram Nominal Moment - kip t Axial Force - kips Tri-linear curve it or DRAINDX Interaction Diagram Nominal Moment - kip t Figure E1-5a Interaction Diagram - 5 t Column Figure E1-5b Interaction Diagram - 6 t Column The oundations are modeled as non-linear elements or translation and rotation. With respect to rotation, this is done to simulate rocking o the ootings when the pile axial capacities are exceeded. I rocking o the oundations occur prior to the limiting deormation in the column, the oundation will act as a use that may spare the columns signiicant damage. The oundation non-linear rotational springs are calculated as ollows. Bent & 3 Ultimate Compression Capacity o Pile (90) 180 kips Ultimate Tension Capacity o Pile 0.5 Compression Capacity 90 kips P P DL() DL(3) 1157 kips 1069 kips KN KN Ultimate Moment Capacity (See Figure E1-6) N(1) N() 5(-90) -450 kips > -003 KN N(4) N(5) 5(180) 900 kips > 4006 KN N(3) (450) (900) 57 kips > 1144 KN N(3) (450) (900) 169 kips > 75 KN E1-15

16 M M For Ultimate pile capacities are assumed to be reached at a vertical displacement o 1". From this the initial rotational φ k u c c R N(1) 6 + N() 3 + N(4) 3 + N(5) ,150 kip t this example, the ooting rotational response is modelled as perectly elastic/plastic. δ l u ex M φ c u , ,187,000 KN m/rad 16,484 KN m stiness is calculated or input into the DRAINDX program. rad 875,000 kip t/rad P H M N(1) N() N(3) N(4) N(5) Figure E1-6 Pile Footing Free Body Diagram (Bent & 3) Ultimate Translational Capacity E1-16

17 H (piles) N 4450 KN o approximately 1". DRAINDX. k c inch 5 mm ( 40) 1000 kips h Hc (cap) Pp W dw kips 1068 KN ( + 4) Based on past testing, the pile ultimate capacity is reached at Δ u T p Hc (piles) + Hc (cap) Δ 1 U 140 kips/inch 17 KN/mm 4 15 The initial translational stiness is calculated or a displacement input to E1-17

18 Similarly or Bents 4 to 6: k 450,560 KN m/rad (average) k R T M φ H Δ c u c u 6, ,000 kip t/rad 83 kips/inch 146 KN/mm Translational yielding o the piles in this case can mean destruction o the pile heads. This could potentially result in signiicant vertical settlements at the oundation although complete collapse is unlikely. Still it is advisable to avoid this ailure mode. Rotational yielding will usually mean that piles will plunge and pull out o the soil i the pile to ooting connection is suiciently strong. Although this action can limit column orces, there are two issues to be considered. First, the response o the oundation is subject to some uncertainty, and the possibility o oundation over strength makes the using action unreliable unless there is a signiicant dierence between the column and the oundation moment capacities. Thereore, columns should generally be retroitted as a ail sae measure even i the pushover analysis indicates piles will yield irst. Secondly, the amount o plastic rotation to be tolerated in the oundation beore oundation retroitting is mandated is subject to some judgment. Excessive plastic rotation can result in unacceptable oundation settlement as pointed out in Chapter 6. In this case, it is assumed that a plastic rotation o 0.03 radians can be tolerated. Member properties used or the push-over analysis are consistent with those used in the dynamic analysis described below. Appendix E1-1 includes the DRAINDX input iles. b. Computer Results In the longitudinal direction the DRAINDX model is displaced incrementally until the allowable deormation is achieved at the potential plastic hinge zones. The controlling displacement is shown in bold ace type. The ollowing table summarizes the results o all o the non-linear push-over analyses. E1-18

19 Table E1-7 - Displacement Capacity inches (mm) Bent Notes: Longitudinal Ultimate Ultimate (Bottom) (Top) (14) (79) (180) (104) (34) (81) (34) (79) (34) (80) 1. Controlled by column. Controlled by ooting Transverse Ultimate Ultimate (Bottom) (Top) (178) N/A (6) N/A 10.8 (74) N/A 10.8 (74) N/A 10.8 (74) N/A Step 3 Non-Seismic Demands Non-seismic loads to be considered in the Extreme Event 1 loading condition are assumed to be negligible or this example. Step 4 Demand Analysis 1. Response Spectrum Parameters Based on the location o the bridge site, the ollowing seismic loading parameters are determined rom the maps developed by the United States Geologic Survey (USGS). S s.0 S Site actors (or Site Class D) are given in Table 1-4 o the retroit manual. Thereore, F a 1.0 F v 1.5 S DS F a S s 1.0(.0).0 S D1 F v S 1 1.5(1.0) 1.5 E1-19

20 The resulting response spectrum to be used or the demand analysis is shown in Figure E1-7.0 Spectral Acceleration - g's Period - Sec. Figure E1-7 Design Spectra. Member Properties or Analysis The superstructure section properties were calculated using the Section Wizard computer program, which is part o STAAD III. Table E1-8 summarizes these results. Table E1-8 - Superstructure Section Properties t (Metric values shown in parentheses) Section Depth A x I zz I yy I xx Span 1 & Bent & 3 Span 3 A Span 3 B Spans 4-6 Bents (.13) 7.00 (.13) 5.84 (1.78) 4.67 (1.4) 3.50 (1.07) 3.50 (1.07) (4.78) (16.69) (4.4) 43.7 (4.06) (3.70) 93.4 (8.67) (3.40) (6.8) 58.8 (.3) (1.33) (0.68) (0.95) (33.31) (85.78) (30.9) (8.51) (6.10) (47.96) (7.75) (19.70) (5.40) (3.41) (1.85) (.75) E1-0

21 Gross column section properties are modiied to relect the cracking that is likely to occur during a seismic event. The modiication actors are taken rom Table 7-1 in the Bridge Retroit Manual. In the as-built case, the structural details will not accommodate ductile behavior and thus preclude plastic hinging rom taking place. Thereore: For Bents and 3 (6 φ Columns): A g πr (3) πr Ig 4 4 A A.63 m M e n D g (.69) E I e 8.7 t.63 m 4 ( 3) t 65. in m 9386(1) 11,600 k - in (From YIELD computer program) y ' c MnD ,000 Eε 430()(.0007) ksi in 4 0. t m 4 For Bents 4, 5 and 6 (5 φ Columns): A g πr (.5) πr Ig 4 4 A A 1.83 m e g y t 1.83 m 4 (.5) t 0.7 m M n 5836(1) 70,000 k - in D 60 4 (.69) in MnD 70, Ie 13,000 in Eε 430()(.0007) t m 4 3. Elastic Response Spectrum (Demand) Analysis a. Computer Models The SEISAB computer program was used to perorm the elastic response spectrum (demand) analysis. SEISAB automatically models the structural elements o the bridge with beam elements. As a deault, the superstructure spans are modeled using our beam elements, which result in lumped masses at the quarter points o the span. Columns are modeled using 3 beam elements. The pile oundations are modeled using SEISAB pile and ooting data block capabilities. E1-1

22 When using a linear elastic model to simulate the non-linear behavior o a bridge during a strong earthquake it is typical practice to use several computer models to envelope the actual bridge response. In this case, two compression models and one tension model was used. The irst compression model assumed that the expansion joints at Abutment 1 and the hinge were locked up and able to transmit longitudinal orces. The second compression model assumed the hinge and Abutment 7 were locked up. The tension model assumed all expansion joints were ree to move. The worst-case orces and displacements rom each o these models were used to determine seismic demands. The behavior o the longitudinal expansion joints at the abutments depends not only on the expansion joint gap, but also on the non-linear behavior o the ill behind the abutment wall. In the compression models this behavior is usually linearized using a trial and error approach. This is demonstrated in Figure E1-8, which shows the non-linear orce-displacement curve at Abutment 1 plus the linearized displacement actually used in the irst compression model Longituninal Force (kips) k 1.0 Linearized Stiness Longitudinal Displacement (inches) 6.0 Figure E1-8 Abutment 1 Longitudinal Response In this igure the ultimate capacity o the abutment is given as the passive pressure behind the wall. The backwall is assumed to shear o at the level o the bearing seat and engage the ill behind the wall. The displacement at which the ultimate orce is reached includes the displacement required to achieve ull passive pressure (0.0H) plus the expansion joint gap, D g. Thereore, at Abutment 1: E1-

23 H Δ P ult H W Pp W pphw Kips 4803 KN 0.0H + Dg.80 in 71mm For Abutment 7: H P P W p p HW p H W Kips 135 KN Δ ult 0.0H + Dg in 56 mm The actual stiness used in the model must be adjusted until the computed abutment orce demand is within 30% o H p. b. Computer Input Files SEISAB computer input iles or each o the three elastic models used are included in Appendix E1-. c. Computer Results The ollowing tables summarize the maximum results obtained rom the SEISAB computer analyses. Table E1-9 Abutment Forces and Displacements Location Abutment 1 Abutment 7 Forces Kips (KN) Displacements inches (mm) Longitudinal Transverse Longitudinal Transverse (6884) (450) (149) (45) (6684) (395) (145) (4) E1-3

24 Table E1-10 Column Moments and Displacements Bent Location Top Bottom Top Bottom Top Bottom Top Bottom Top Bottom Elastic Moment K t (KN m) Displacement inches (mm) Longit. Trans. Longit. Trans (46360) (147) (185) (977) (7116) (4109) (156) (354) (8305) (46160) (4385) (18) (387) (14030) (361) (6437) (137) (73) (14595) (1500) (791) (143) (154) (13967) (9901) Plastic shear demands on the columns and oundations are limited by yielding o the columns and/or the oundations and are calculated as ollows or Bent in the longitudinal direction: V M L.0(11095) 0 p p c 1110 kips The remaining plastic shear demands are calculated in a similar ashion and are summarized below. E1-4

25 Table E1-11 Column Plastic Shears Bent Plastic Shear Kips (KN) Longit. Trans (4940) (3983) (379) (371) (968) 555 (470) 448 (1994) 36 (1885) 317 (1638) 83 (1486) Hinge orce and displacement demands are obtained rom the worst case SEISAB model. Table E1-1 - Hinge Force and Displacement Demands Hinge Transverse Force Kips (KN) 1076 (4788) Longitudinal Displacement inches (mm) 7.6 (193) Step 5 - Summary o Capacity/Demand Ratios The adequacy o the current structure to resist earthquakes is given by the capacity/demand ratio or the various components o the bridge or dierent types o actions. These are summarized as ollows with inadequate components indicated by bold type. E1-5

26 Table E1-13 Capacity/Demand Ratios Location Response Item Longitudinal Transverse Abutment 1 Force Keys N/A 0.68 Force - Piles N/A 0.77 Displacement 4.41 N/A Abutment 7 Force Keys N/A 0.73 Force - Piles N/A 0.67 Displacement 4.56 N/A Bent Displacement Foundation Shear Bent 3 Displacement Foundation Shear Bent 4 Displacement Foundation Shear Bent 5 Displacement Foundation Shear Bent 6 Displacement Foundation Shear Hinge 1 Displacement 0.53 N/A Force N/A 0.39 Footnotes: 1. Controlled by ailure o unconined concrete in compression.. Controlled by plunging and uplit o oundation piles. Figure E1-9 is a graphical presentation o the as-built seismic deiciencies o the bridge. E1-6

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28 4. Retroit Strategy Evaluation a. Identiication o Retroit Strategy A retroit strategy that addresses the global response o the bridge is shown in Figure E1-10. The strategy, which involves retroitting o all ive columns and both abutments, addresses each deiciency that was identiied by the detailed seismic evaluation perormed above. The hinge is also to be retroitted with seat extenders and longitudinal cable restrainers to prevent unseating. It is also necessary to retroit the oundations at Piers, 3, 5 and 6 to prevent ailure o the pile cap in negative bending and Pier 4 to prevent excessive plastic rotation o the oundation. This strategy is evaluated in the ollowing sections. A less obvious strategy, which relied on Piers 3 and 4 to carry all longitudinal orces, was also investigated. This strategy involved retroitting these two columns with steel or iber shells. Transverse orces would be carried by the two abutments, which were also to be retroitted, and Piers 3 and 4, such that each rame could resist torsional response about the vertical axis. Piers, 5 and 6 would have been allowed to ail under lateral load, but would have been retroitted with light steel shells to preserve axial load capacity at these locations. This strategy could have worked i it weren t or the high ductility demands placed on the retroitted columns. Short o replacing these columns, or strengthening them signiicantly, it was not possible to retroit these columns to gain the ductility necessary to resist ailure o the main reinorcement due to low cycle atigue. Thereore, this trial strategy was ultimately rejected. b. Design o Retroit Measures i. Abutment Retroit 1. CIDH Bolters The existing abutment piles and wingwalls at the abutments do not have the capacity to resist transverse orces. It is necessary to provide additional capacity through large diameter cast-in-drilled hole (CIDH) bolsters. The shear capacity o this bolster must exceed the dierence between the transverse orce demands and the capacity o the existing abutment. Thereore, V bolster ( V V ) d abut For Abutment 1 this is calculated as ollows V bolster kips E1-8

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30 At Abutment 7: V bolster kips Thereore, to simpliy details, design both bolsters to resist the orces at Abutment 7. The minimum diameter o the CIDH bolster is determined based on the maximum shear capacity, which is determined by using the maximum ' allowable shear stress, which is 8 c. Thereore, A A D e V (min) φ 8 bolster bolster A e 0.8 (min) bolster ' c A in in bolster π in π Use D bolster 48 in The top o the pile is detailed with a pinned connection at the level o the abutment ooting. This eliminates the need or the bolster-to-abutment connection to resist large moments. Thereore, the connection need only resist the shear orce o 88 kips. Dowels drilled and bonded into the side o the abutment wall are used or this purpose. According to Caltrans tests, a #7 dowel bonded into a 7 deep, drilled hole with magnesium phosphate grout can saely resist 0.3 kips in tension. Thereore, the number o dowels required to transer the shear orce eccentrically applied at the top o the bolster is: N dowels 1.5V T bolster C #7 ( 88) dowels use 1dowels The 1.5 actor in the above equation accounts or the eccentricity o the load. Such dowels must be spaced at a minimum o 14 inches and must be a minimum o 4 inches away rom the edge o any drilled concrete. The pinned connection at the top o the pile must also be capable o transerring the 88 kip shear orce. The pin is designed using the principals o shear riction. Thereore, the minimum area o concrete is: E1-30

31 A pin Vbolster φ(0.) ' c (0.)(3.6) use a 5 in diameter circle 471in The required area o reinorcing steel crossing the shear plane is: A v V bolster φ μ ca use 7 - #8 dowels y cv (491) in 1.0(60) The moment in the CIDH bolster is calculated with the help o a computer program that models the CIDH pile as a series o beam-column elements and the subsurace lateral soil stiness as p-y curves or each increment o soil depth along the length o the pile. Shear and moment diagrams along the pile can be developed using this technique, and rom these the maximum moment demand can be determined. In this case the maximum moment demand is: M bolster 155 k - t Because plastic hinging in the CIDH bolsters will not be allowed, the bolster is designed or this moment. Based on an interaction analysis, this requires 0 #10 s as main reinorcement around the perimeter o the CIDH pile. This results in ρ t o The inal shear capacity provided by the concrete in the pile is determined as ollows V π 1000 ( 4) ' 0.6 c 0.6 c A e 5 kips Thereore, the shear capacity provided by the transverse reinorcement must be V V φv ( 5) bolster c s φ This requires hoop spacing as ollows D s A v yh cot θ V s 87 kips By assuming θ to be 35 degrees, and #6 hoops, the spacing is as ollows E1-31

32 π s 88 use #6 8" oc ( 0.44)( 60) ( 1.43) This gives a volumetric ratio o ρ bh v A sd (0.44) 8.0(41.1) inches Thereore, the assumption or θ can be checked 1.6 A a tan ρv θ ΛρtA g 35.1degrees e 0.5 ( )( 1448) ( )( 1810) a tan Since this approximately equal to the assumed value or θ, the above shear reinorcement results are acceptable.. Pipe Restrainers The existing shear keys at the abutments are not capable o transerring the transverse shear orces rom the superstructure to the abutments. The existing shear key capacity was previously calculated based on their shear riction capacity. V keys 630 kips Thereore, additional shear capacity must be provided as ollows based on Abutment 1: V V V add d keys 90 kips Pipe shear keys may be used to provide this extra capacity. An A36 pipe illed with concrete is capable o resisting 6 ksi in shear. Thereore a double extra strong 6 diameter pipe will provide 406 kips nominal capacity or 345 kips ultimate capacity ater the application o a 0.85 capacity reduction actor. I one pipe is used, it will provide the required additional shear capacity. A cored hole will be required in the existing concrete in order to place the pipe. The pipe shear key may be placed vertically i provisions are made or longitudinal movement o the superstructure. This design has the advantage o eliminating excavation behind the abutment, but requires complicated details to E1-3

33 provide or longitudinal movement. Alternately, the pipe may be oriented longitudinally. In this case one end o the pipe shear key will pass through the abutment backwall. Because this backwall is not thick enough to provide the necessary bearing area or the pipe, it must be reinorced rom behind, which will require some excavation behind the abutment and potentially more disruption to traic. The required bearing area in either case is calculated as ollows: A V 90 pipe g ' φ( 0.85) 0.9( 0.85)( 3.6) c 105 in The value o A g may include as much as twice the actual contact area on the surace o the pipe i suicient concrete surrounds the cored hole. Thereore, because the pipe will rotate and non-uniorm (i.e. triangular) bearing during an earthquake, it is judged that the pipe must be embedded a minimum o 18 (i.e. approx. 105/x6x1/) to develop the required shear capacity. Pipe embedment can be reduced i supplemental steel bearing plates are provided to distribute concrete bearing stresses. Abutment retroit details are shown in Figure E1-11. ii. Column Retroit 1. Carbon Fiber Jacket Retroit Carbon iber jackets are chosen over steel shells because they add such a small increase in longitudinal strength and thus allow or a longer plastic hinge zone. This increases the amount o plastic rotation that can occur prior to a low cycle atigue ailure o the main reinorcing steel. I suicient coninement is provided with a composite shell, the mode o column ailure will always be low cycle atigue o the main column reinorcement. For the 6 t diameter columns the allowable plastic curvature or this mode o ailure is calculated as ollows: φ where ε p ap φ ε ( d d ) ( N ) ( T ) (.089) ( ) L L ( ) 0.08( 7( 0.77) ) Thereore, the allowable pastic rotations or Bent are as ollows θ θ p p p φ φ p p ap p p n (.1) ( 31.7).0811 radians (transverse) radians (longitudinal) 0.5 Similarly, plastic rotations or the other columns can be determined E1-33

34 These allowable plastic rotation capacities result in the ollowing column displacement capacities assuming over strength and/or retroitted ootings at Bents 4 thru 6 do not yield. E1-34

35

36 Table E1-14 Retroitted Displacement Capacity inches (mm) Bent Longitudinal 6. (173) 8. (08) 6.1 (178) 6.4 (173) 6.8 (183) Transverse 1.5 (7) 17.6 (361) 13.7 (318) 14. (30) 15.0 (35) Notice that all displacement capacities are suicient with the exception o Bent 4 in the transverse direction. Because the displacement capacities listed in Table E1-15 are limited by low cycle atigue ailure, jacketing is not the solution at the bottom o Bent 4. In this case a replaceable hinge retroit is required in order lengthen the plastic hinge and mitigate low cycle atigue ailure. The remaining columns may all be retroitted with composite iber shells. Another alternative may be steel shells or the use o replacement hinges on all columns. The thickness o the carbon iber jackets should be suicient to prevent the occurrence o a compression ailure in the concrete or a shear ailure o the column prior to the low cycle atigue ailure. As an example, consider Bent 3. φ p ε cu use ε radians/inch ( φp + φy )( c d ) ( ) cu ( ) as the target concrete strain capacity Using the simpliied method, the thickness o a passive carbon-iber jacket or coninement is given by t ( ) 31D 31 7 E p j in For lap splice perormance: E1-36

37 t 500D E ( 7)(.3) l p p 0.37 in For shear enhancement v sj ( ) / 0.85 tp πe ε Dcot θ p p ( )( )( )( ) 0.01in Thereore, use t inches at lap zone and t 0.15 inches elsewhere Check ε cu ε where ρ ε ' cc ε cu s du du cu.5ρs ' ( p ) 4 (.15) 4 t D 600 ksi ' ce cc du du ( 5.5) ( )( 600)(.0) ε ksi > OK Similar jackets can be used on the remaining columns. A 0.15 inch thick shell should be used at the upper plastic hinge zone o Bent 4.. Replaceable Plastic Hinge The plastic hinge length at the base o Pier 4 must be o suicient length to accommodate the required plastic rotation. This can be accomplished by using the replaceable hinge detail discussed in Section (b). An example o this type o retroit is shown in Figure 9-4. The irst step is to determine the size o the use bar, which must provide the maximum strength but guarantee yielding beore the existing main column steel. d < d b y su 1.5 ( 60) Use 1-1/8" diameter use bars inches The length o the use bar is the length o the plastic hinge. Thereore, using a plastic rotation demand, θ d, based on a transverse displacement demand o 15. E1-37

38 inches as required rom Table E1-10 and a yield displacement o 6.7 inches obtained rom the transverse DRAINDX output, the ollowing minimum use bar length is obtained. du d θp Lp L Thereore du dy D L θp.0489 L D Use L 66 inches y radians ( N ) ( ) ( ( 7.64) ) inches The next step is to size the connector plate and welds. Assuming E70XX electrodes and 3/16 illet welds: L d su w sw w inches The minimum plate thickness based on AISC LRFD is 5/16 inches. Finally, the transverse reinorcement in terms o ½ inch diameter prestress strand must be determined or concrete coninement, anti-buckling and shear resistance. For concrete coninement ρ ρ ρ s s s ' c U s P 1 e ' c A g + ρ ( 87) t y ' c A A g cc For anti-buckling the transverse reinorcement spacing is limited to 6 inches. For shear resistance ρ ρ s s K shape ρt Λ φ su yh A A g cc tanα tanθ ( )( 1.0) ( 1.0) E1-38

39 Thereore, coninement controls. Use ρ s or ½ strand at 5-1/ cc. iii. Column Foundation Retroit 1. Footing Overlay (Without Additional Piles) Column Footings (pile caps) do not have a top mat o reinorcement. Thereore, they are structurally inadequate or resisting the uplit orces generated in the piles by column overturning. To prevent lexural ailures o the ootings these ootings will be overlayed with 1 inches o concrete that contains horizontal reinorcement to resist negative bending moments. This overlay will be made to act compositely with the existing ooting by drilling and bonding vertical reinorcement into the existing ooting that will act in shear riction to resist horizontal shear stresses. The negative bending moment and shear generated by pile uplit at Bent is given by: M ooting NpTp x p k t de + x p de π 4 V ooting N p T p kips The ultimate moment resistance provided by 16 #6 reinorcing bars is given by: M u a φa sy d k t > 1657 OK The shearing resistance at the interace o the existing ooting and the overlay that is required to develop composite behavior is: ν int erace V ooting Ib Q ( 15.0) k/t Thereore, the resistance provided by #5 dowels drilled and bonded in a 5 inch deep hole is: E1-39

40 ν u φv dowel kips > 5.76 OK A pattern o #5 dowels at 1 inches on center in both directions will be suicient to resist horizontal shear stresses. Similar overlays will be required on the remaining ootings with the exception o Bent 4, which must have piles added or lexural strength. E1-40

41 . Footing Retroit (With Additional Piles) Only at Bent 4 is the oundation rotational displacement capacity inadequate. In this case piles will either plunge or uplit an excessive amount. To prevent this, oundation lexural strength must be increased. This is accomplished by adding 8-16 diameter cast-in-drilled hole (CIDH) piles. Because piles must be installed under the existing superstructure, CIDH piles are used or constructability reasons. This results in more than enough additional lexural capacity, but is the minimum number o piles required to achieve a symmetric pile pattern. The additional piles will increase both the positive and negative moment demands on the ootings. M M pos neg N 348 k t N p1 p1 Cp x Tp x k t de + N de + N p p Cp x Tp x de de π π π 4 π 4 Positive moment will be resisted by the bottom reinorcement. Because additional ooting width will be added to accommodate the 8 new piles, additional bottom bars can be added. Existing bottom bars can be extended into the widened portion o the ooting by exposing the ends o these bars and welding or mechanically splicing an additional length o bar onto the ends o these existing bars. Thereore, check the capacity o the existing bottom bars. M cexist a φa sy d k t There is room to add 6 extra bottom bars in the widened portions o the ooting. The capacity o these additional bars is: E1-41

42 M cnew M a φa sy d 138 M + M k t > 348 OK ctotal cexist cnew k t Negative moment can be resisted with an overlay similar to the one designed or the remaining ootings. Thereore, use 8 new 16 diameter cast-in-drilled hole piles in a ooting enlarged to 17-8 square and 5-0 deep. Use a 1-0 overlay with 16 - #6 bars in each direction, # 5 drilled and bonded dowels at 1 on center in each direction, and 8 additional - #9 bars in each direction at the bottom o the ooting. Details o the column and ooting retroits are shown in Figure E1-1. iv. Hinge Retroit 1. Pipe Seat Extenders The hinge seat is not wide enough to accommodate the longitudinal movement at the expansion joint hinge. In addition, the transverse shear keys are not strong enough to resist the transverse orces developed during the design earthquake. These problems can be overcome by using 8 xx strong pipe seat extenders that were developed by Caltrans ater the 1989 Loma Prieta earthquake. These seat extenders will allow 8 o relative longitudinal displacement at the hinges, which is suicient to accommodate the 7.6 inches o longitudinal displacement demand. In addition, these seat extenders will serve as supplemental transverse shear keys. Test perormed by Caltrans have demonstrated that in addition to accommodating 8 inches o relative displacement, these devises are able to carry 180 kips o horizontal shear. Because it is assumed that the maximum transverse shear demand will not occur at the same time as the maximum relative longitudinal displacement, the existing concrete shear keys will participate in the resistance to transverse orces. Thereore, the additional shear capacity required rom the seat extenders is given by: ( V V ) 1.3( ) 70 kips Vdpipeexten ders L d keys Notice that a load actor o 1.3 was used to account or misalignment tolerances o the individual pipe extender units. The required number o seat extenders is determined as ollows: N pipeextenders V dpipeextenders Use 4 pipe extender units. E1-4

43

44 Expansion joint hinge diaphragm bolsters are used to anchor the pipe seat extenders.. Longitudinal Cable Restrainers Some jurisdictions will use a minimum o two longitudinal cable restrainer units in conjunction with the seat extenders. These are optional unless it is necessary to restrain the relative longitudinal displacements at the hinges. In this example, restrainer units will not be speciied. Figure E1-13 includes details o the expansion joint hinge retroit. E1-44

45

46 Appendix E1-1 E1-46

47 File : RETEX1 FOUNDATION SPRINGS, 1. rotation and horiz. translation > elastic perectly plastic. vert. dir. > Fixed Longitudinal direction, Push Each rame at superstructure level Units: kips, t NOTE : 1. /3/004 rvn *STARTXX retex F EXAMPLE PROBLEM LONGITUDINAL *NODECOORDS NODES or Longitudinal dir Superstructure Bent Bent Hinge Hinge Bent Bent Bent Bent Column and Foundation Bent 3 Column and Foundation Bent 4 Column and Foundation Bent 5 Column and Foundation RETROFIT EXAMPLE 1 - LONGITUDINAL PUSHOVER Bent 6 Column and Foundation C C C *RESTRAINTS S ABUT 1 S BENT SPRINGS S BENT 3 SPRINGS S BENT 4 SPRINGS S BENT 5 SPRINGS S BENT 6 SPRINGS S ABUT 7 *SLAVING S *MASSES *ELEMENTGROUP GROUP 1: SUPERSTRUCTURE SUPERSTRUCTURE stiness types E E E E E E E E09-10E09 HIGH VALUE - NO YIELDING ASSUMED element generation *ELEMENTGROUP GROUP : Bent & 3 Columns COLUMNS stiness types 0

48 1 6.6E rigid links 6.6E columns E09-10E09 RIGID LINK element generation *ELEMENTGROUP GROUP 3: Bent 4 THRU 6 Columns COLUMNS stiness types E rigid links 6.6E columns E09-10E09 RIGID LINK element generation *ELEMENTGROUP GROUP 4: Bent oundation Springs PILE SPRINGS stiness types horizontal springs rotational springs vertical element generation horizontal springs rotational springs vertical springs *RESULTS NSD TOP OF PIER NSD TOP OF PIER 3 NSD TOP OF PIER 4 NSD TOP OF PIER 5 NSD TOP OF PIER 6 E 001 TOP OF COLUMN E TOP OF COLUMN 3 E TOP OF COLUMN 4 E TOP OF COLUMN 5 E TOP OF COLUMN 6 E FOUNDATION SPRINGS *NODALOAD PUS1 FRAME 1 PUSHOVER PATTERN S *NODALOAD PUS FRAME PUSHOVER PATTERN S *PARAMETERS OS *GRAV Gravity Load Analysis I Gravity *STAT Nonlinear pushover analysis N PUS1 D *STAT Nonlinear pushover analysis N PUS D *STOP

49 File : RETEXA FOUNDATION SPRINGS, 1. rotation and horiz. translation > elastic perectly plastic. vert. dir. > Fixed Longitudinal direction, Push Each rame at superstructure level Units: kips, t NOTE : 1. /3/004 rvn. 9/15/004 revised by rvn *STARTXX retexa F EXAMPLE PROBLEM LONGITUDINAL *NODECOORDS NODES or Longitudinal dir Superstructure Bent Bent Hinge Hinge Bent Bent Bent Bent Column and Foundation Bent 3 Column and Foundation Bent 4 Column and Foundation Bent 5 Column and Foundation RETROFIT EXAMPLE 1 - LONGITUDINAL PUSHOVER Bent 6 Column and Foundation *RESTRAINTS ABUT BENT SPRINGS BENT 3 SPRINGS BENT 4 SPRINGS BENT 5 SPRINGS BENT 6 SPRINGS ABUT 7 *SLAVING *MASSES *ELEMENTGROUP GROUP 1: SUPERSTRUCTURE SUPERSTRUCTURE stiness types E E E E E E E E09-10E09 HIGH VALUE - NO YIELDING ASSUMED element generation

50 *ELEMENTGROUP GROUP : Bent & 3 Columns COLUMNS stiness types E rigid links 6.6E columns E09-10E09 RIGID LINK element generation *ELEMENTGROUP GROUP 3: Bent 4 THRU 6 Columns COLUMNS stiness types E rigid links 6.6E columns E09-10E09 RIGID LINK element generation *ELEMENTGROUP GROUP 4: Bent oundation Springs PILE SPRINGS stiness types horizontal springs rotational springs vertical element generation horizontal springs rotational springs vertical springs *RESULTS NSD TOP OF PIER NSD TOP OF PIER 3 NSD TOP OF PIER 4 NSD TOP OF PIER 5 NSD TOP OF PIER 6 E 001 TOP OF COLUMN E TOP OF COLUMN 3 E TOP OF COLUMN 4 E TOP OF COLUMN 5 E TOP OF COLUMN 6 E FOUNDATION SPRINGS *NODALOAD PUS1 FRAME 1 PUSHOVER PATTERN S *PARAMETERS OS *GRAV Gravity Load Analysis I Gravity *STAT Nonlinear pushover analysis N PUS1 D *STOP