Balance cantilever bridge analysis & design

2013

BALANCED CANTILEVER BRIDGE DESIGN FOR

R Prabu, Md. Riaz & Ranjil P Ramath

8/31/2013

BALANCED CANTILEVER BRIDGE DESIGN 1)

By R. Prabu, Design Engineer, 2) Mohammed Riaz, Design Engineer, 3) Ranjil P Ramath, PM/Team Leader

ABSTRACT: This paper describes about the analysis and design of two balanced cantilever bridges designed to carry metro rail over it and crossing a railway line underneath (Rail over Bridge – RoB). Since the bridge is crossing the main and live railway line, only option for constructing the bridge it is in pre-cast and that too balanced cantilever construction. To accommodate the roadway underneath one of the internal support became a monolithic portal with superstructure. The balance cantilever thus had to rest on portal beam at one support and on free bearing at other pier support. As the bridge is on curve, it demanded bridge builder method of construction, which resulted in the stabilising frame concept for the transfer of unbalanced moments during construction. The maximum toe reaction (point load) from bridge builder was around 2200kN during lifting and empty weight was around 350kN. This extreme bandwidth of load posted a colossal challenge of proportioning the prestress design for no tension at any part. The box section has been designed to carry these loads. Substructure and foundation has been designed for all load cases as per DBR and importantly for the stability during construction and secondary effects due to prestressing at the monolithic portal. Bearing loads are estimated meticulously to ascertain no-tension condition, at any service stage to avoid tension bearings.

1.0 STRUCTURAL ARRANGEMENT: The span arrangement of the two bridges has been listed below in the table and the schematic views developed in-house of the two bridges is as shown below,

S. No. 1.

Location Bridge 1

Span Configuration 36.0 + 52.0 + 31.5m

Alignment In Transition

Superstructure Type Prestressed Box Girder

2.

Bridge 2

30.0 + 50.0 + 40.0m

In 128m Radius of Curvature

Prestressed Box Girder

Perspective View of Balanced Cantilever Bridges

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2.0 STAGES OF ANALYSIS & DESIGN: Various stages of design has been shown below,

Balanced Cantilever Design Load data as per DBR Construction Load Input

Using Staad Pro & In-house program Section Design Construction Stage Analysis Service Stage Analysis

Cycle of design process

Superstructure Transverse Analysis

Prestress Design Using MIDAS Civil 2012 & STAAD Pro Bearing Load Calculation Substructure Design Stability and Design of Supporting Frame Foundation Design

3.0 SOFTWARE USED: The following software is used for analysis & designs of the two balanced cantilever bridges.

1) 2) 3) 4) 5) 6)

MIDAS-Civil 2012 – For Stage Analysis, Prestress design and Camber detailing.

STAAD Pro V8i – For Stage analysis Checks, Transverse Analysis, Portal frame analysis.

Auto CAD 2D/3D - For Concept views, Cable profiling, Detailed drawings.

In-House excel program developed for transverse & longitudinal superstructure design.

In-House excel program developed for substructure & foundation design.

In-House excel program developed for movement of live load on curved path in STAAD-Pro V8i.

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4.0 CONSTRUCTION METHODOLOGY / CONSTRUCTION LOADS: This balanced cantilever bridge has been planned to be constructed by erecting the precast segment with varying sizes of weight ranging from 200kN to 450kN, with the help of bridge builder system to lift and transfer the segment while prestressing is done in sequence as dictated by the design.

Lifting is permitted only along the axis of the bridge to avoid torsional stresses. This stage wise process will be continued until all the precast segment has been erected either side of the two pier head. After this the key segment will be brought in and will be stitched to form the cantilevers into a single continuous structure, for further loadings.

During construction stage analysis the following construction loads has been considered as per the Design Basis Report and as per the loading details shared by the contractor for the construction stages, and they are a) b) c) d) e)

Bridge Builder weight – Loaded & Empty at each stages Construction impact effect – 10% of segment weight.

Segment shifting trolley weight Accidental load at tip - 100kN Point load Construction live load on deck surface - 1.0kN/m2.

Conceptual 3-Dimensional views of the bridges have been prepared in Auto CAD 3D to appreciate the bridge architecture, investigate mandatory clearances, any construction issues. One of such created conceptual views is as shown below,

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Perspective View of Balanced Cantilever Bridge 2 – During Construction in Progress 5.0 ANALYSIS OF SUPERSTRUCTURE: The structure has been modelled and analysed using MIDASCivil_2012, for various stages of construction and service. A detailed construction scheme has been prepared, with clear demarcation of the loading and unloading schedules along with the prestressing requirements.

The span to depth ratio for both the superstructure has been chosen as shown below, S. No.

Location

Main Span

Span to Depth Ratio At Support At Mid span

1.

Bridge 1

52.0m

17

25

2.

Bridge 2

50.0m

16

24

The substructure consists of Fixed pier (Monolithic with superstructure), Free pier (L Type), Cantilever pier caps and the foundation is of open foundation at Bridge 1 location with a safe bearing capacity 750.0kN/m2, and pile of 1.0m diameter at Bridge 2 location with maximum vertical load capacity of 5000kN/pile & lateral load capacity of 400kN/pile.

The structure can be subjected to two boundary case loading during its construction stages,

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1) Structure with loaded bridge builder with all construction loads, 2) Structure with empty bridge builder with no construction loads.

Hence the analysis needs to simulate these governing construction boundary cases. Hence two separate models have been generated with each case to investigate the stress distribution.

For service case, the completed construction stage model is used and for the following load the structure is designed, 1) Super imposed Loads 2) Vertical Train Load with CDA as per Indian Railway Standard (IRS) Bridge Rules, 3) Centrifugal force, 4) Braking & Traction, 5) Derailment loads, 6) Overall temperature, 7) Differential temperature, 8) Long welded rail (LWR), 9) Nosing force, 10) Wind load, 11) Seismic force Z-II, 12) Differential Settlement, 13) Vehicle collision load Live load analysis has been done for 6Car, 3Car, 2Car train loading with an axle load of 170kN.

Live Load Details Since the span in the structure is varying from 30.0 to 52.0m, to get the governing forces, the above combination of cars have been generated in model and analysed. Envelope function of MIDAS-Civil 2012 has been used to identify the maximum at each section, during the incremental of live load movements.

5.1 TRANSVERSE ANALYSIS & DESIGN: The Bridge has been analysed & designed as per the DBR for all applicable loads mentioned above. Effects of derailment, construction loads, lifting loads, stacking loads are also checked. Since the bridge builder transfer a heavy point load and it is directly supported over the box girder deck slab, the same has been checked for flexure, shear and punching additionally. A 3D FEM Model using plates is created in STAAD-Pro V8i and the stresses are checked and the RCC section is designed for the stresses.

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Stress Distribution – With Bridge Builder Loads

5.2 CONSTRUCTION STAGE LONGITUDINAL ANALYSIS: Since the construction of the superstructure is done by stages and a detailed construction stage analysis is done using the MIDAS-Civil 2012. Each construction stages have been briefly explained as shown below, RP2 and RP3 denotes the respective piers.

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Stage – 1: Pier Head completed + Segment 1 Erection at RP2 & RP3 RP1

RP2

RP3

CL of pier/Bearing (Fixed)

CL of pier/EJ 36000*

RP4

CL of pier/Bearing (Free) 31500*

52000*

CL of pier/EJ

Bridge builder (Typ)

7500

7500

7500

S1

7500

S1

Pier head-cast-in-situ portion (Typ)

S1

RB

RB

Temporary support (Typ)

Piercap (Typ)

Railway portion

Span-1

Open foundation(Typ)

Span-1

S1

0 - 30 days

Pier (Typ)

Span-2

Span-2

STAGE-1 Pier head completion+segment 1 erection RP2 and RP3

Stage – 2: Seg-1 Erected+Seg-2 Erection RP2 & RP3 RP1

RP2

RP3

36000*

52000*

10500

10500

10500

S2 S1

S1 S2

Railway portion

Span-1

Span-1

10500

S1

RB

RB

Stabilizing frame

Open foundation(Typ)

CL of pier/EJ

S2

S1

S2

RP4

CL of pier/Bearing (Free) 31500*

CL of pier/Bearing (Fixed)

CL of pier/EJ

31 - 34 days

Span-2

Span-2

STAGE-2 Segment 2 erection RP2 and RP3

Stage – 3: Seg-2 Erected+Seg-3 Erection RP2 & RP3 RP1

RP3

RP2

CL of pier/EJ

CL of pier/Bearing (Fixed) 52000*

36000*

13500

13500

13500

S3 S1

S3

S2

S3

Stabilizing frame

Open foundation(Typ)

Span-1

Span-1

S2 S1

S1 S2

Railway portion

35 - 38 days

S3

Span-2

STAGE-3 Segment 3 erection RP2 and RP3

7

13500

RB

RB

S2 S1

RP4

CL of pier/Bearing (Free) 31500*

Span-2

CL of pier/EJ

Stage – 4: Seg-3 Erected+Seg-4 Erection RP2 & RP3 RP1

RP2

CL of pier/EJ

RP3

CL of pier/Bearing (Fixed) 36000*

52000*

16500

S4

16500

S4

S2 S3 RB

S1

S4

CL of pier/EJ

16500

S3 S2 S1

S1 S2 S3

RB

16500

S3 S2 S1

RP4

CL of pier/Bearing (Free) 31500*

S4

Railway portion Stabilizing frame

Span-1

Open foundation(Typ)

39 - 42 days

Span-1

Span-2

Span-2

STAGE-4 Segment 4 erection RP2 and RP3

Stage – 5: Seg-4 Erected+Seg-5 Erection RP2 & RP3 RP2

RP1 CL of pier/EJ

RP4

RP3

CL of pier/Bearing (Fixed) 52000*

36000*

CL of pier/EJ

CL of pier/Bearing (Free) 31500*

Bridge builder (Typ) 19500

S4

19500

S3 S2 S1

S1

S5

S5

19500

S2 S3 S4

S1 S2 S3

S4

RB

RB

S5

19500

S4 S3 S2 S1 Railway portion

S5

Stabilizing frame

Open foundation(Typ)

Span-1

Span-1

43 - 46days

Span-2

Span-2

STAGE-5 Segment 5 erection RP2 and RP3

Stage – 6: Seg-5 Erected+Seg-6 Erection RP2 only RP1

RP2

CL of pier/EJ

RP3

36000*

52000*

22500

22500

22500

S6 S4

S3 S2 S1

S1

S5

RB

S6

S2 S3 S4 S5

S4 S3 S2 S1

22500 S1 S2 S3

RB

S5

RP4

CL of pier/Bearing (Free) 31500*

CL of pier/Bearing (Fixed)

Railway portion Stabilizing frame

Open foundation(Typ)

Span-1

Span-1

47 - 50 days

STAGE-6 Segment 6 erection on RP2

8

Span-2

Span-2

S4 S5

CL of pier/EJ

Stage – 7: Seg-6 Erected and stressed at RP2 only RP2

RP1 CL of pier/EJ

25500

25500

S3 S2 S1

S1

22500

S2 S3 S4 S5

S6

S5

Span-1

Span-1

22500

S4 S3 S2 S1

S4 S5

S1 S2 S3

Railway portion

Stabilizing frame

Open foundation(Typ)

CL of pier/EJ

RB

RB

S4

CL of pier/Bearing (Free) 31500*

52000*

36000*

S6 S5

RP4

RP3

CL of pier/Bearing (Fixed)

51 - 54 days

Span-2

Span-2

STAGE-7 Segment 6 erected and stressed on RP2

Stage – 8: Seg-6 Erected on RP3 RP1

RP2

CL of pier/EJ

RP3

36000*

52000*

25500

25500

S3 S2 S1

S1

22500

S2 S3 S4 S5

S6

S6 S5

CL of pier/EJ

22500

S4 S3 S2 S1

S1 S2 S3

S4 S5 S6

RB

S4

RB

S6 S5

RP4

CL of pier/Bearing (Free) 31500*

CL of pier/Bearing (Fixed)

Railway portion Stabilizing frame

55 - 58 days

Span-1

Span-1

Open foundation(Typ)

STAGE-8 Segment 6 erection on RP3

Span-2

Span-2

Stage – 9: Key Segment Erection from RP3 RP1

RP2

CL of pier/EJ

RP3

CL of pier/Bearing (Fixed) 36000*

RP4

CL of pier/Bearing (Free) 31500*

52000*

Bridge builder (Typ) 25500

S3 S2 S1

S1

S2 S3 S4 S5

S6

24500

S6 S5

S4 S3 S2 S1

24500

S1 S2 S3

RB

S4

RB

S6 S5

KS

25500

Railway portion Stabilizing frame

Open foundation(Typ)

Span-1

Span-1

59th day

Span-2

ACTIVITY-1 : Key segment erection from RP3 STAGE-9

9

Span-2

S4 S5 S6

CL of pier/EJ

Stage – 10: Stressing of Continuity Cables RP1

RP2

CL of pier/EJ

RP3

CL of pier/Bearing (Fixed) 36000*

RP4

CL of pier/Bearing (Free) 31500*

52000*

CL of pier/EJ

1816 25500

S6 S5

S4

25500

S3 S2 S1

S1

24500

S2 S3 S4 S5

24500

S6 KS S6 S5

S1 S2 S3

S4 S5 S6

RB

RB

EQ EQ

S4 S3 S2 S1 Stitch concrete - 1 Stitch concrete - 2

Railway portion Span-1

Open foundation(Typ)

63 - 66 days

Span-1

STAGE-10 Stressing continuity cables

Span-2

Span-2

Stage – 11: Cast of RP1 & RP2 cast-in-situ portion by Full Staging Method (FSM) RP1

RP2

CL of pier/EJ

RP3

36000*

RP4

CL of pier/Bearing (Free) 31500*

CL of pier/Bearing (Fixed) 52000*

CL of pier/EJ

FSM - Left 10486

FSM - Right 6985

S6 S5

S4

S3 S2 S1

S1

S2 S3 S4 S5

S6 KS S6 S5

S4 S3 S2 S1

S1 S2 S3

S4 S5 S6

RB

RB

Railway portion

Open foundation(Typ)

Span-1

Span-1

67 - 100 days

Span-2

Span-2

STAGE-11 Cast FSM at RP1 and RP4

Stage – 12: Complete Structure – Checked for its design life considering 120 years RP1

RP2

CL of pier/EJ

RP3

CL of pier/Bearing (Fixed) 36000*

S6 S5

S4

52000*

S3 S2 S1

S1

S2 S3 S4 S5

S6 KS S6 S5

RP4

CL of pier/Bearing (Free) 31500*

S4 S3 S2 S1

S1 S2 S3

Open foundation(Typ)

Span-1

Span-1

RB

RB

Railway portion

100th day

STAGE-12 Completed structure

10

Span-2

Span-2

S4 S5 S6

CL of pier/EJ

5.3 PRESTRESS DESIGN: 5.3.1 PERMANENT PRESTRESSING DESIGN: Since construction is in stages, during each construction stage of construction of cantilever, the top cable at each segment is Prestressed to take care of the hogging moment coming at each stage. After construction of the cantilever arm, the key segment has been attached and the continuity cable has been Prestressed to take care of both the sagging and hogging moment coming over the section. At last after completion of RP1 & RP4 piers the soffit cable has been stressed to take care of the sagging moment coming over the segment. Layout of the above listed cable profile has been shown below. 3D view of the bridge with all cables is developed and the clash checks have been done.

Cable stressing end

Cable stressing end

Cable stressing end

Cable stressing end

Cable stressing end

Cable stressing end

Cable stressing end

Cable stressing end

RP2

Cable stressing end

Cable stressing end

Cable stressing end

Cable stressing end

Cable dead end

Cable stressing end

52000

36000

RP1

RP3

CL of Pier/Bearing

S6

S5

S4

S3 S2

S1 S1

S2

Cable stressing end

Cable stressing end

S3

S4

S5

S6

Cable stressing end

Cable stressing end

Cable dead end

RP2 Cable stressing end

Cable stressing end

Cable stressing end

Cable stressing end

Cable stressing end

Cable stressing end

Cable stressing end

Cable stressing end

Cable stressing end

of box girder

CL of Pier/Bearing

S6

S5

S4

S2

S3

S1

S1

S2

S3

S5

S4

S6

Top Prestressing Cable RP2

RP1 36000

52000

RP3

CL of Pier/Bearing

CL of Pier CL of Bearing Cable dead end

Cable stressing end

Cable stressing end

Cable dead end

Y S6 S5

S4

S3

S2

S1

S1

CL of Pier CL of Bearing

S2

S3

CL of Pier/Bearing

Cable dead end

Cable stressing end

Cable stressing end

S1

S2

S6

S5

S4

S3

S2

S1

PLAN SCALE 1:75

Continuity Cable between – RP1 & RP2

11

S3

of box girder

Cable dead end

RP2

RP3

36000

RP1

52000

Cable stressing end

S3

CL of Pier/Bearing

RP3

Cable stressing end

Cable stressing end

S1

S1

S2

31500

CL of Pier/Bearing

Cable stressing end

S2

S3

S4

S5

S6

KS

S6

S5

S3

S4

S1

S2

S1

S3

S2

Cable stressing end

CL of Pier/Bearing

of box girder

Cable stressing end

S3

S2

CL of Pier/Bearing

S1

S2

S1

S3

S4

S5

S6

KS

S6

S5

S4

S3

S2

Cable stressing end

S1

S1

Cable stressing end

S2

S3

Z=-1821

Continuity Cable Between – RP2 & RP3 RP2

RP3

36000

31500

52000 Cable stressing end

CL of Pier/Bearing

Cable stressing end

Cable stressing end

Cable stressing end

S1

Cable stressing end

CL of Pier/Bearing

Cable stressing end

S2 S3

S4

S5

S6

KS

S6

S5

S4

S3

S1 S2

CL of Pier/Bearing

of box girder

RP1

Cable stressing end

Cable stressing end

S1

Cable stressing end

S2

Cable stressing end

S3

S4

S5

S6

KS

S6

S5

S4

S3

S2

PLAN SCALE 1:75

Soffit Cable Between – RP2 & RP3 CL of box girder

CROSS SECTION OF PRESTRESS CABLES

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Cable stressing end

S1

Cable stressing end

CL of Pier/Bearing

RP3

3D-View of Cable Profile for clash checks

Schematic View of Cable Profile at Support location (Blister not shown) – At RP2 & RP3 5.3.2 TEMPORARY PRESTRESSING DESIGN: As mentioned earlier, as the permanent top prestress has been proportioned in advance for the upper boundary of the construction loads, the lower boundary loads when placed along with this prestressing was creating tensile stresses at soffit of the structure. To avoid this tensile stress temporary sequential prestressing using, high strength restrained bars are used. These bars are placed at top and bottom of the box section and stressed to provide an axial stress equal to 0.8MPa (average).

These bars are untied and reused in a forwarding sequence, in batches. To control the bottom tension over supports, external short cables (19T15) are used. The arrangement of the temporary stressing bar has been as shown below,

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CL of pier/Bearing (Fixed) 3000

3000

15000 In situ portion Jacking end

Dead end

Jacking end

Dead end

350

S1

S1

Stitch concrete

Stitch concrete

CL of box girder

Dead end

Jacking end

S2

S1

Temporary Prestressing Details

5.4 PRESTRESS DESIGN RESULTS FROM MIDAS-CIVIL: The stress diagram of the superstructure during complete construction of the structure has been shown below. In which the maximum compressive stress attained in the section shows as -12.76MPa < the allowable stress 20.00MPa. And there is no tension in the section.

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Stress diagram showing stresses â&#x20AC;&#x201C; (During Construction Stage â&#x20AC;&#x201C; 12) Similarly during service stage, the stresses have been checked for all possible load combination and all the stresses are within the limit. The governing load case stresses has been shown below,

Stress diagram showing stresses â&#x20AC;&#x201C; (During Governing Service Stage) The stresses have been checked for both case of loaded and empty bridge builder. As explained earlier due to the upper and lower boundaries of loads, each cases show substantial variation in the in the design forces. To satisfy both the cases using same prestress, a number of design trials have been performed using the permanent and temporary prestress, and an optimum solution has been worked out. Bending Moment Diagram (BMD) in the construction stages (CS9 for example) is shown below,

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Bending Moment Diagram â&#x20AC;&#x201C; During Construction Stage With Loaded Bridge Builder

Bending Moment Diagram â&#x20AC;&#x201C; During Construction Stage with Empty Bridge Builder The section has been checked for ultimate load for the governing ultimate load case and it has been done through in-house excel program.

6.0 ANALYSIS & DESIGN OF SUBSTRUCTURE AND FOUNDATION: 6.1 STABILIZING FRAME FOR UNBALANCED MOMENT: As explained above, since the superstructure is supported over bearing, to make the structure a stable during construction the stabilizing frame is used to make the cantilever arm a stable one as shown below. The bridge builder is of steel structure designed to erect a segment weight of 450kN. It is not practically possible to erect both the segments simultaneously, and thus will have unbalanced moments, which will vary from stage to stage and will also transfer tension and compression (alternate) in the bridge builder legs.

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Bridge Builder Arrangement

Stabilizing Frame Arrangements As shown above is the case where the segment is erected from only one (left)side of cantilever. Due to this unsymmetrical loading left side leg of stabilizing frame will have full compression and the right side leg of stabilizing frame will have full tension. But to avoid this tension, a permanent compression is applied by anchoring a temporary restrained bar from superstructure to the stabilizing frame. In this case the restrained bar should be always in compression, during all stage of construction, and thus for varying range of loads subjected to. Allowance shall be given for the fatigue and elastic recoveries.

As per the calculation by considering all stages, the structure stability and stresses are checked for unbalanced moments. Places at portal location, these frames are fixed to the ground using rock anchors.

6.2 DESIGN OF FOUNDATION & SUBSTRUCTURE: The foundation & Substructure has been designed as an RCC section fully adhering the DBR, and detailed drawings have been prepared. In the design of L pier,

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the foundation has been kept eccentrically to reduce the permanent transverse moment generated in the pier.

In pile design, possible reversal load cases have been checked for both favourable and unfavourable cases due to permanent longitudinal and transverse moments using in house program. Since the ROB GADs has been finalised by the contractor and got approved from the Railways prior to the initiation of the detail designs, there existed restrictions in the foundation sizes and hence it required many trials to maintain the sizes near that or acceptable to railways. In the bridge at Bridge 2 location where one of its substructure is portal and the superstructure alignment was very close to the right leg of the portal, due to which the maximum vertical forces has been attracted by the right leg of portal, hence the left leg of portal foundation was governed by the minimum load and corresponding moment case. This has induced complication to adhere to the foundation size as per approved GAD. But to avoid tension at left leg of the portal, the stiffness of the pier has been reduced in transverse direction, due to which the transverse moment attracted by the foundation due to gravity loads got reduced and the same foundation size has been followed. Substructure has been designed for the 37 load cases with all possible reversible.

7.0 CONCLUSION:  The bridge is a special type and first in India where the bridge is integrated to a portal beam, and constructed as balanced cantilever.  The entire definitive design of the two bridges has been delivered to the client with in a period of 3 months’ time frame.  Many conceptual views have been developed and have been well appreciated by client. This has showcased team’s capacity to deliver projects with customer satisfaction.  Simulation of cable profiling in 3D-views helped to check the cable clashes and check for minimum cover to the concrete, and thus reaffirmed the workability of sleeker sections.  The bridge has been proportionated to have an optimal design with an average thickness of 0.62m and prestress to superstructure concrete quantity equal to 55 kg/m3, which is challenging achievement for this sort of complex structure, and within this short time frame of designs.  By doing this special and complex type of structural design, team has also been exposed to the international experiences of senior technical advisor, and has equipped the team to do similar and more challenging type of structure in future.  This project involves three levels of independent checking’s and internal peer review, which the design team has successfully undergone and delivered the designs.  This is also the first time that Indian team has delivered this sort of complex bridge project (balanced cantilever technique), by its local resource’s skill sets.  Finally we shall confidently conclude that, with this sort of service, we are rightly sailing towards our vision of becoming the consultant of choice in the global market, and we could find the positive reflections in clients approach too.

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