Performance Evaluation of Different Types of Cable Stayed Bridges

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Performance Evaluation of Different Types of Cable Stayed Bridges

Lekshmi Priya R

Department of Civil Engineering Younus College of Engineering and Technology

Kollam,Kerala

Mrs Raji R

Department of Civil Engineering Younus College of Engineering and Technology

Kollam,Kerala

Abstract – In our country, bridges play a vital role because of undulated topography, steeper terrains and so many rivers flow. Among different types of bridges, cable stayed bridges are very popular bridge type for long span bridges. Cable stayed bridges have good stability, optimum use of structural materials, aesthetic, relatively low design and maintenance costs, and efficient structural characteristics. These are indeterminate structures which behaves as a continuous beam elastically supported by the cables, which are connected to one or two towers. This study investigates the performance evaluation of different types of cable stayed bridges by varying the pylons shapes and arrangement of cable stays. The nonlinear dynamic behavior of cable stayed bridge decks due to different load combinations and earthquake forces are done. Here the study is carried out for cable stayed bridges for four lane of total span 900 m, which includes 500 m main span and 200 m side spans. IRC Class A loading is used for the study. The superstructure of the cable stayed bridges are analyzed and designed by using SAP 2000 version 14 software. This work includes the determination of deck displacement, time period, frequencies for different types of cable stayed bridges using SAP 2000.

Keywords- Cable stayed bridges, deck deflection, pylon, stay cables

  1. INTRODUCTION

    Cable stayed bridges have emerged as a dominant structure for long span bridge for the past fifty years because of their good stability, optimum use of structural materials, aesthetic, relatively low design and maintenance costs, and efficient structural characteristics. Therefore, this type of bridges are becoming more and more popular and are usually preferred for long span crossings compared to suspension bridges.

    The superstructure behaves as a continuous beam elastically supported by the cables, which are connected to one or two towers. The main structural elements of a cable stayed bridges are the bridge deck, piers, towers and the stays. The deck supports the loads and transfers them to the stays and to the piers through bending and compression. The stays transfer the forces to the towers, which transmit them by compression to the foundations. The interrelation of these components makes the structural behavior of cable- stayed bridges efficient for long-span structures, in addition to providing an aesthetic pleasant solution. The cable-stayed system has become a very effective and

    economical system during the last century. It is mainly used to cover large spans. The development of this structural system is due to advances in materials, engineering analysis and design, and construction methodology. In terms of cable arrangements, the most common type of cable stayed bridges are fan, harp, and semi harp bridges. Typical shapes for bridge towers are H- shaped, A-shaped and Y-shaped towers.Because of their large size and nonlinear structural behaviour, the analysis of these types of bridges is more complicated than conventional bridges. Up to a span length of 1100 metres, the cable stayed system is considered as an economical solution. To achieve the increase span length and more slender girders for future bridges, accurate procedures need to be developed that can lead to a thorough understanding and a realistic prediction of the structural response to not only wind and earthquake loads but also traffic loads.

  2. STRUCTURAL DESCRIPTION

    The structural systems can be varied by changing tower shapes and the cable arrangements. The configurations of cable-stayed bridge are stiffening girder, cable system, towers and foundations. The stiffening girder is supported by straight inclined cables which are anchored at the towers. These pylons are placed on the main pier so that the cable force can be transferred down to the foundation system. Three basic cable arrangements are harp system, fan system and semi harp system. The role of tower or pylon is also very important in cable-stayed bridge. The towers are the most visible elements of a cable-stayed bridge. The primary function of the pylon is to transmit the force arising from anchoring the stay and these forces will dominate the design of the pylon. Many varied types of the pylon are H-type, Atype and Spread pylon Y-type are used.

    The proposed bridge is a long-span cable-stayed bridge with double plane with three span. The bridge with the total length of 900 m comprises of three spans: a 500 m main span between two pylons, and two side spans each with a length of 200 m has been modeled. The bridge deck is a steel box girder 14 m wide and 3.1 m high. The cross sectional area and the modulus of elasticity of the deck are

    3.36 m2 and 1.9 x 108kN/m2 respectively. There are two pylons 500 m apart consisting of hollow concrete section of 6 x 6 m, above and below the deck levels. The modulus of

    elasticity and area of cross section of concrete pylon are

    3.35 kN/m2 and 11 m2 respectively. The pylons are fixed to the ground level. New parallel wire strands are used for proposed bridge models. New PWS cable with an outer diameter of 0.15m has a metallic cross-section of 0.0177 m2 corresponding to a void ratio of 0.3 has been used. The deck section are attached to the pylons with 160 cables of varying length with 20 cables on each side of the pylon. The support ends of the bridge are hinged.

  3. MODELLING

    A cable stayed bridge model has been created by using the software SAP 2000. The modelling has been done by assuming the above values. And also various values are taken from the IS and IRC Codes for the modeling. Some of the IS codes used are IS 456:2000 , IS 800 : 2007 , IS 1893 : 2000 , IS 875 : 1967, IRC 6:2000 etc. Long-span

    cable-stayed bridge is modeled by changing the pylon shapes and the cable arrangements and analyzed by using SAP-2000 Software.

  4. ANALYSIS RESULTS

    In this study, the cable stayed bridges are analyzed for four different shapes of pylon on SAP 2000 software. The models of cable stayed bridges are A – Fan Arrangement, A

    – Harp Arrangement, A – Semi Harp Arrangement, H – Fan Arrangement, H – Harp Arrangement, H – Semi Harp Arrangement, Y – Fan Arrangement, Y – Harp Arrangement, Y – Semi Harp Arrangement. The girder deflection is studied based on the various load conditions, load combinations, seismic load Response spectrum and Time history Analysis and Modal Analysis. Deflection is the vertical displacement of a member subjected to loading. The allowable deflection for cable stayed bridge is L/400, where L is the main span length of proposed bridge.

    1. Results due to load combinations

      The displacements of the girder along the bridge length due to different load combinations are shown in their respective tables and figures.

      TABLE 1 TABLE SHOWING DEFLECTIONS DUE TO DEAD LOAD +MOVING LOAD

      Span (m)

      Deck deflection (m)

      A Fan

      A harp

      A semi harp

      H Fan

      H Harp

      H Semi harp

      Y Fan

      Y Harp

      Y Semi harp

      0

      0

      0

      0

      0

      0

      0

      0

      0

      0

      100

      0.0004

      0.0000

      0.0004

      0.0004

      0.0003

      0.0005

      0.0001

      0.0003

      0.0002

      200

      0.0004

      0.0000

      0.0004

      0.0004

      0.0004

      0.0005

      0.0001

      0.0003

      0.0002

      300

      0.0427

      0.0974

      0.0707

      0.0410

      0.0858

      0.0667

      0.0362

      0.0831

      0.0636

      400

      0.0645

      0.0958

      0.0726

      0.0623

      0.0836

      0.0835

      0.0562

      0.0639

      0.0653

      500

      0.0645

      0.0958

      0.0726

      0.0623

      0.0831

      0.0835

      0.0562

      0.0648

      0.0653

      600

      0.0427

      0.0974

      0.0707

      0.0410

      0.0853

      0.0667

      0.0362

      0.0853

      0.0636

      700

      0.0004

      0.0000

      0.0004

      0.0004

      0.0004

      0.0005

      0.0001

      0.0003

      0.0002

      800

      0.0004

      0.0000

      0.0004

      0.0004

      0.0003

      0.0005

      0.0001

      0.0003

      0.0002

      900

      0

      0

      0

      0

      0

      0

      0

      0

      0

      DEAD LOAD + MOVING LOAD

      DEAD LOAD + MOVING LOAD

      0.12

      0.1

      0.08

      0.06

      0.04

      0.02

      0

      0.12

      0.1

      0.08

      0.06

      0.04

      0.02

      0

      0 100 200 300 400 500 600 700 800 900

      SPAN LENGTH (M)

      0 100 200 300 400 500 600 700 800 900

      SPAN LENGTH (M)

      A Fan A harp

      A semi harp H Fan

      H Harp

      H Semi harp

      Y Fan

      A Fan A harp

      A semi harp H Fan

      H Harp

      H Semi harp

      Y Fan

      Y Harp

      Y Harp

      DECK DEFLECTION (M)

      DECK DEFLECTION (M)

      Fig.1 Graph showing deck deflections of different models

      TABLE 2 TABLE SHOWING DEFLECTIONS DUE TO DEAD LOAD + LIVE LOAD

      Deck deflection (m)

      an (m)

      A Fan

      A harp

      A semi harp

      H Fan

      H Harp

      H Semi harp

      Y Fan

      Y Harp

      Y Semi harp

      100

      0.039

      0.101

      0.083

      0.074

      0.191

      0.159

      -0.103

      0.124

      0.070

      200

      0.134

      -0.043

      -0.010

      -0.020

      -0.015

      -0.015

      0.144

      -0.013

      -0.010

      300

      0.554

      -0.518

      -0.166

      -0.140

      -0.320

      -0.250

      0.706

      -0.218

      -0.139

      400

      0.982

      -1.119

      -0.459

      -0.414

      -0.858

      -0.839

      1.524

      -0.508

      -0.393

      500

      0.982

      -1.119

      -0.459

      -0.414

      -0.857

      -0.839

      1.524

      -0.510

      -0.393

      600

      0.554

      -0.518

      -0.166

      -0.140

      -0.318

      -0.250

      0.706

      -0.222

      -0.139

      700

      0.134

      -0.043

      -0.010

      -0.020

      -0.015

      -0.015

      0.144

      -0.013

      -0.010

      800

      0.039

      0.101

      0.083

      0.074

      0.190

      0.158

      -0.103

      0.127

      0.070

      900

      0

      0

      0

      0

      0

      0

      0

      0

      0

      an (m)

      A Fan

      A harp

      A semi harp

      H Fan

      H Harp

      H Semi harp

      Y Fan

      Y Harp

      Y Semi harp

      100

      0.039

      0.101

      0.083

      0.074

      0.191

      0.159

      -0.103

      0.124

      0.070

      200

      0.134

      -0.043

      -0.010

      -0.020

      -0.015

      -0.015

      0.144

      -0.013

      -0.010

      300

      0.554

      -0.518

      -0.166

      -0.140

      -0.320

      -0.250

      0.706

      -0.218

      -0.139

      400

      0.982

      -1.119

      -0.459

      -0.414

      -0.858

      -0.839

      1.524

      -0.508

      -0.393

      500

      0.982

      -1.119

      -0.459

      -0.414

      -0.857

      -0.839

      1.524

      -0.510

      -0.393

      600

      0.554

      -0.518

      -0.166

      -0.140

      -0.318

      -0.250

      0.706

      -0.222

      -0.139

      700

      0.134

      -0.043

      -0.010

      -0.020

      -0.015

      -0.015

      0.144

      -0.013

      -0.010

      800

      0.039

      0.101

      0.083

      0.074

      0.190

      0.158

      -0.103

      0.127

      0.070

      900

      0

      0

      0

      0

      0

      0

      0

      0

      0

      Sp

      dead load + live load

      dead load + live load

      2.000

      1.500

      1.000

      0.500

      0.000 100 200 300 400 500 600

      700 800

      900

      2.000

      1.500

      1.000

      0.500

      0.000 100 200 300 400 500 600

      700 800

      900

      -1.500

      SPAN LENGTH (M)

      -1.500

      SPAN LENGTH (M)

      -0.500

      -1.000

      -0.500

      -1.000

      A Fan A harp

      A semi harp H Fan

      H Harp

      H Semi harp

      Y Fan

      Y Harp

      Y Semi harp

      A Fan A harp

      A semi harp H Fan

      H Harp

      H Semi harp

      Y Fan

      Y Harp

      Y Semi harp

      Deck deflection (m)

      Deck deflection (m)

      Fig.2 Graph showing deck deflections of different models

      TABLE 3 DEFLECTIONS DUE TO DEAD LOAD +MOVING LOAD+WIND LOAD

      Span (m)

      Deck deflection (m)

      A Fan

      A harp

      A semi harp

      H Fan

      H Harp

      H Semi harp

      Y Fan

      Y Harp

      Y Semi harp

      100

      0.0003

      0.0000

      0.0003

      0.0003

      0.0003

      0.0004

      0.0001

      0.0003

      0.0002

      200

      0.0003

      0.0000

      0.0003

      0.0003

      0.0004

      0.0004

      0.0001

      0.0003

      0.0002

      300

      0.0360

      0.0000

      0.0596

      0.0346

      0.0724

      0.0563

      0.0305

      0.0701

      0.0537

      400

      0.0544

      0.0822

      0.0612

      0.0526

      0.0705

      0.0704

      0.0474

      0.0539

      0.0551

      500

      0.0544

      0.0809

      0.0612

      0.0526

      0.0701

      0.0704

      0.0474

      0.0547

      0.0551

      600

      0.0360

      0.0809

      0.0596

      0.0346

      0.0720

      0.0563

      0.0305

      0.0720

      0.0537

      700

      0.0003

      0.0822

      0.0003

      0.0003

      0.0004

      0.0004

      0.0001

      0.0003

      0.0002

      800

      0.0003

      0.0000

      0.0003

      0.0003

      0.0003

      0.0004

      0.0001

      0.0003

      0.0002

      900

      0

      0

      0

      0

      0

      0

      0

      0

      0

      DEAD LOAD + MOVING LOAD + WIND LOAD

      DEAD LOAD + MOVING LOAD + WIND LOAD

      0.1000

      0.0800

      0.0600

      0.0400

      0.0200

      0.0000

      A Fan A harp

      A semi harp H Fan

      H Harp

      H Semi harp

      0.1000

      0.0800

      0.0600

      0.0400

      0.0200

      0.0000

      A Fan A harp

      A semi harp H Fan

      H Harp

      H Semi harp

      100 200 300 400 500 600 700 800 900

      SPAN LENGTH (M)

      100 200 300 400 500 600 700 800 900

      SPAN LENGTH (M)

      Y Fan

      Y Harp

      Y Fan

      Y Harp

      DECK DEFLECTION (M)

      DECK DEFLECTION (M)

      Fig.3 Graph showing deck deflections of different models

      TABLE 4 TABLE SHOWING DEFLECTIONS DUE TO DEAD LOAD +MOVING LOAD + EARTHQUAKE LOAD (RS)

      Span (m)

      Deck deflection (m)

      A Fan

      A harp

      A semi harp

      H Fan

      H Harp

      H Semi harp

      Y Fan

      Y Harp

      Y Semi harp

      100

      0.0036

      0.0035

      0.0052

      0.0036

      0.0047

      0.0046

      0.0033

      0.0049

      0.0057

      200

      0.0001

      0.0035

      0.0001

      0.0001

      0.0001

      0.0001

      0.0001

      0.0001

      0.0001

      300

      0.0085

      0.0001

      0.0139

      0.0083

      0.0154

      0.0129

      0.0079

      0.0153

      0.0135

      400

      0.0129

      0.0163

      0.0146

      0.0128

      0.0148

      0.0170

      0.0126

      0.0119

      0.0145

      500

      0.0129

      0.0152

      0.0146

      0.0128

      0.0148

      0.0170

      0.0126

      0.0114

      0.0145

      600

      0.0085

      0.0152

      0.0139

      0.0083

      0.0153

      0.0129

      0.0079

      0.0153

      0.0135

      700

      0.0001

      0.0163

      0.0001

      0.0001

      0.0001

      0.0001

      0.0001

      0.0001

      0.0001

      800

      0.0036

      0.0001

      0.0052

      0.0036

      0.0047

      0.0046

      0.0033

      0.0046

      0.0057

      900

      0

      0

      0

      0

      0

      0

      0

      0

      0

      DEAD LO AD + M O VING LO AD + EQ LO AD ( RS)

      0.0200

      0.0150

      0.0100

      0.0050

      0.0000

      DEAD LO AD + M O VING LO AD + EQ LO AD ( RS)

      0.0200

      0.0150

      0.0100

      0.0050

      0.0000

      100 200 300 400 500 600 700 800 900

      SPAN LENGTH (M)

      100 200 300 400 500 600 700 800 900

      SPAN LENGTH (M)

      A Fan A harp

      A semi harp H Fan

      H Harp

      H Semi harp Y Fan

      Y Harp

      A Fan A harp

      A semi harp H Fan

      H Harp

      H Semi harp Y Fan

      Y Harp

      DECK DEFLECTION (M)

      DECK DEFLECTION (M)

      Fig.4 Graph showing deck deflections of different models

      TABLE 5 TABLE SHOWING DEFLECTIONS DUE TO DEAD LOAD +MOVING LOAD + EARTHQUAKE LOAD (THA)

      Deck deflection

      (m)

      Span (m)

      A Fan

      A harp

      A semi harp

      H Fan

      H Harp

      H Semi harp

      Y Fan

      Y Harp

      Y Semi harp

      100

      0.0002

      0.0047

      0.0128

      0.0104

      0.0103

      0.0102

      0.0075

      0.0109

      0.0146

      200

      0.0002

      0.0047

      0.0002

      0.0002

      0.0001

      0.0001

      0.0001

      0.0001

      0.0002

      300

      0.0200

      0.0002

      0.0202

      0.0143

      0.0208

      0.0196

      0.0118

      0.0212

      0.0216

      400

      0.0101

      0.0184

      0.0254

      0.0181

      0.0222

      0.0271

      0.0179

      0.0189

      0.0270

      500

      0.0142

      0.0176

      0.0181

      0.0199

      0.0193

      0.0251

      0.0204

      0.0155

      0.0179

      600

      0.0185

      0.0181

      0.0209

      0.0128

      0.0209

      0.0184

      0.0125

      0.0214

      0.0218

      700

      0.0102

      0.0196

      0.0001

      0.0002

      0.0001

      0.0001

      0.0002

      0.0001

      0.0001

      800

      0.0129

      0.0002

      0.0113

      0.0102

      0.0093

      0.0112

      0.0072

      0.0100

      0.0126

      900

      0

      0

      0

      0

      0

      0

      0

      0

      0

      D E A D L O A D + M O VI N G L O A D + E Q L O A D ( T H A )

      D E A D L O A D + M O VI N G L O A D + E Q L O A D ( T H A )

      0.0300

      0.0250

      0.0200

      0.0150

      0.0100

      0.0050

      0.0000

      A Fan A harp

      A semi harp H Fan

      H Harp

      H Semi harp Y Fan

      0.0300

      0.0250

      0.0200

      0.0150

      0.0100

      0.0050

      0.0000

      A Fan A harp

      A semi harp H Fan

      H Harp

      H Semi harp Y Fan

      100 200 300 400 500 600 700 800 900

      SPAN LENGTH (M)

      100 200 300 400 500 600 700 800 900

      SPAN LENGTH (M)

      Y Harp

      Y Semi harp

      Y Harp

      Y Semi harp

      DECK DEFLECTION (M)

      DECK DEFLECTION (M)

      Fig.5 Graph showing deck deflections of different models

    2. Results due to Seismic load Response Spectrum Analysis

      The displacements of the girder along the bridge length based on Response spectrum analysis are shown in their respective tables and figures.

      TABLE 6 TABLE SHOWING DEFLECTIONS DUE TO RESPONSE SPECTRUM ANALYSIS

      Span (m)

      Deck deflection (m)

      A Fan

      A harp

      A semi harp

      H Fan

      H Harp

      H Semi harp

      Y Fan

      Y Harp

      Y Semi harp

      0

      0

      0

      0

      0

      0

      0

      0

      0

      0

      100

      0.0036

      0.0046

      0.0045

      0.0035

      0.0035

      0.0051

      0.0032

      0.0048

      0.0057

      200

      0.0001

      0.0000

      0.0000

      0.0001

      0.0001

      0.0000

      0.0001

      0.0001

      0.0001

      300

      0.0032

      0.0047

      0.0045

      0.0031

      0.0042

      0.0050

      0.0034

      0.0049

      0.0056

      400

      0.0051

      0.0044

      0.0066

      0.0048

      0.0032

      0.0055

      0.0056

      0.0039

      0.0063

      500

      0.0051

      0.0044

      0.0066

      0.0048

      0.0032

      0.0055

      0.0056

      0.0033

      0.0063

      600

      0.0032

      0.0047

      0.0045

      0.0031

      0.0042

      0.0050

      0.0034

      0.0046

      0.0056

      700

      0.0001

      0.0000

      0.0000

      0.0001

      0.0001

      0.0000

      0.0001

      0.0001

      0.0001

      800

      0.0036

      0.0046

      0.0045

      0.0035

      0.0035

      0.0051

      0.0032

      0.0045

      0.0057

      900

      0

      0

      0

      0

      0

      0

      0

      0

      0

      RESPONSE SPECTRUM ANALYSIS

      RESPONSE SPECTRUM ANALYSIS

      0

      0

      0 100 200 300 400 500 600 700 800 900

      SPAN (M)

      0 100 200 300 400 500 600 700 800 900

      SPAN (M)

      0.007

      0.006

      0.007

      0.006

      H fan

      H harp

      H Semi Harp

      H fan

      H harp

      H Semi Harp

      0.005

      0.005

      A Fan

      A Fan

      0.004

      0.004

      A Harp

      A Harp

      0.003

      0.002

      0.001

      0.003

      0.002

      0.001

      A Semi harp

      Y Fan Y Harp

      Y Semi Harp

      A Semi harp

      Y Fan Y Harp

      Y Semi Harp

      DECK DEFLECTION (M)

      DECK DEFLECTION (M)

      Fig.6 Graph showing deck deflections of different models

    3. Results due to Seismic load Time History Analysis

      The displacements of the girder along the bridge length based on Time History analysis are shown in their respective tables and figures. Here, the values of El-Centro earhquake is taken for the analysis.

      TABLE 7 TABLE SHOWING DEFLECTIONS DUE TO TIME HISTORY ANALYSIS

      Span (m)

      Deck deflection (m)

      A Fan

      A harp

      A semi harp

      H Fan

      H Harp

      H Semi harp

      Y Fan

      Y Harp

      Y Semi harp

      0

      0.0000

      0.0000

      0.0000

      0.0000

      0.0000

      0.0000

      0.0000

      0.0000

      0.0000

      100

      0.0103

      0.0103

      0.0102

      0.0101

      0.0047

      0.0128

      0.0074

      0.0109

      0.0146

      200

      0.0001

      0.0000

      0.0000

      0.0002

      0.0002

      0.0001

      0.0001

      0.0001

      0.0001

      300

      0.0092

      0.0100

      0.0113

      0.0089

      0.0062

      0.0114

      0.0073

      0.0109

      0.0136

      400

      0.0104

      0.0117

      0.0166

      0.0104

      0.0056

      0.0163

      0.0109

      0.0109

      0.0189

      500

      0.0122

      0.0089

      0.0147

      0.0120

      0.0062

      0.0090

      0.0134

      0.0074

      0.0097

      600

      0.0077

      0.0102

      0.0101

      0.0075

      0.0074

      0.0121

      0.0079

      0.0108

      0.0138

      700

      0.0002

      0.0000

      0.0000

      0.0002

      0.0002

      0.0001

      0.0002

      0.0000

      0.0001

      800

      0.0101

      0.0093

      0.0111

      0.0101

      0.0047

      0.0112

      0.0072

      0.0100

      0.0126

      900

      0.0000

      0.0000

      0.0000

      0.0000

      0.0000

      0.0000

      0.0000

      0.0000

      0.0000

      TIME HISTORY ANALYSIS

      TIME HISTORY ANALYSIS

      0.0200

      0.0180

      0.0160

      0.0140

      0.0120

      0.0100

      0.0080

      0.0060

      0.0040

      0.0020

      0.0000

      A Fan

      A harp

      0.0200

      0.0180

      0.0160

      0.0140

      0.0120

      0.0100

      0.0080

      0.0060

      0.0040

      0.0020

      0.0000

      A Fan

      A harp

      0 100 200 30

      400 500

      SPAN (M)

      0 100 200 300

      400 500

      SPAN (M)

      A semi harp

      A semi harp

      H Fan

      H Harp

      H Semi harp Y Fan

      Y Harp

      Y Semi harp

      H Fan

      H Harp

      H Semi harp Y Fan

      Y Harp

      Y Semi harp

      600 700 800 900

      600 700 800 900

      DECK DEFLECTION (M)

      DECK DEFLECTION (M)

      Fig.7 Graph showing deck deflections of different models

    4. Results due to Modal Analysis Period

      The displacements of the girder along the bridge length based on Modal analysis are shown in their respective tables and figures. The variation of period and frequency of the 9 models are given.

      TABLE 8TABLE SHOWING DEFLECTIONS DUE TO PERIOD

      Mode number

      Period in seconds

      H fan

      H harp

      H Semi Harp

      A Fan

      A Harp

      A Semi harp

      Y Fan

      Y Harp

      Y Semi Harp

      1

      9.892

      9.701

      20.751

      9.5

      9.702

      9.4

      9.169

      9.2103888

      9.106

      2

      6.664

      5.364

      8.838

      3.499

      5.49

      3.436

      4.606

      4.6073905

      4.375

      3

      6.664

      5.364

      5.536

      3.201

      3.853

      3.421

      4.598

      4.5237647

      4.369

      4

      6.664

      5.336

      5.536

      2.649

      3.618

      2.873

      3.498

      3.5506197

      3.513

      5

      6.664

      5.297

      5.536

      2.587

      2.384

      2.52

      2.861

      3.2635109

      3.255

      6

      3.623

      3.818

      5.536

      2.471

      2.377

      2.481

      2.259

      2.9551999

      2.802

      7

      3.145

      3.565

      4.92

      1.787

      2.339

      1.766

      1.747

      1.7439271

      1.745

      8

      2.449

      3.044

      3.881

      1.212

      1.936

      1.607

      1.456

      1.7267059

      1.574

      9

      1.796

      1.827

      3.25

      1.16

      1.818

      1.268

      1.456

      1.3594558

      1.247

      10

      1.194

      1.761

      2.941

      1.023

      1.521

      1.15

      1.218

      1.3421149

      1.154

      11

      1.167

      1.396

      2.45

      0.859

      1.317

      0.854

      1.168

      1.3157417

      1.097

      12

      1.007

      1.15

      2.07

      0.859

      1.177

      0.853

      1.151

      1.156899

      1.097

      M O DAL ANALYSIS – PERIO D

      M O DAL ANALYSIS – PERIO D

      0

      1

      2

      3

      4

      5

      6

      7

      8

      9 10 11 12

      Y Harp

      Y Semi Harp

      0

      1

      2

      3

      4

      5

      6

      7

      8

      9 10 11 12

      Y Harp

      Y Semi Harp

      MODE NUMBER

      MODE NUMBER

      25

      20

      15

      25

      20

      15

      H fan

      H Semi Harp H harp

      A Fan

      H fan

      H Semi Harp H harp

      A Fan

      10

      10

      A Harp

      A Harp

      A Semi harp

      A Semi harp

      5

      5

      Y Fan

      Y Fan

      PERIOD IN SECONDS

      PERIOD IN SECONDS

      Fig.8 Graph showing deck deflections of different models

    5. Results due to Modal Analysis – Frequency

    TABLE 9 TABLE SHOWING DEFLECTIONS DUE TO FREQUENCY

    Mode number

    Frequency in Hz

    H fan

    H harp

    H Semi Harp

    A Fan

    A Harp

    A Semi harp

    Y Fan

    Y Harp

    Y Semi Harp

    1

    0.101

    0.103

    0.048

    0.105

    0.103

    0.106

    0.109

    0.108573

    0.11

    2

    0.15

    0.186

    0.113

    0.286

    0.182

    0.291

    0.217

    0.2170426

    0.229

    3

    0.15

    0.186

    0.181

    0.312

    0.26

    0.292

    0.217

    0.2210548

    0.229

    4

    0.15

    0.187

    0.181

    0.377

    0.276

    0.348

    0.286

    0.281641

    0.285

    5

    0.15

    0.189

    0.181

    0.387

    0.419

    0.397

    0.35

    0.3064185

    0.307

    6

    0.276

    0.262

    0.181

    0.405

    0.421

    0.403

    0.443

    0.3383866

    0.357

    7

    0.318

    0.28

    0.203

    0.56

    0.428

    0.566

    0.572

    0.5734185

    0.573

    8

    0.408

    0.328

    0.258

    0.825

    0.516

    0.622

    0.687

    0.5791374

    0.635

    9

    0.557

    0.547

    0.308

    0.862

    0.55

    0.789

    0.687

    0.7355885

    0.802

    10

    0.838

    0.568

    0.34

    0.977

    0.657

    0.869

    0.821

    0.7450927

    0.866

    11

    0.857

    0.716

    0.408

    1.164

    0.759

    1.171

    0.856

    0.7600276

    0.911

    12

    0.993

    0.869

    0.483

    1.164

    0.85

    1.172

    0.869

    0.8643797

    0.912

    MODAL ANALYSIS – FREQUENCY

    MODAL ANALYSIS – FREQUENCY

    MODE NUMBER

    MODE NUMBER

    1.4

    1.2

    1

    1.4

    1.2

    1

    H fan

    H harp

    H Semi Harp

    H fan

    H harp

    H Semi Harp

    0.8 A Fan

    0.6 A Harp

    0.8 A Fan

    0.6 A Harp

    0.4

    0.4

    A Semi harp

    A Semi harp

    0.2

    0

    0.2

    0

    1

    1

    2

    2

    3

    3

    4

    4

    5

    5

    6

    7 8

    7 8

    9 10 11 12

    9 10 11 12

    Y Fan

    Y Harp

    Y Semi Harp

    Y Fan

    Y Harp

    Y Semi Harp

    FREQUENCY IN HZ

    FREQUENCY IN HZ

    Fig.9 Graph showing deck deflections of different models

  5. CONCLUSIONS

In this study, the cable stayed bridge of span length of 900m is analyzed by varying the pylons shapes and arrangement of cable stays. Therefore, this study would give some knowledge ofanalysis and design of three-span cable-stayed bridge. The analysis results conclude that the maximum deformation of the bridge deck occurs at the midpoint of the main span. Also, all the cable stayed bridges falls in the permissible range of allowable deck deflection and hence serviceability problems does not occur. The bridge models were analysed based on the different load combinations and seismic loads.

For the load combination of DL+ML, Y shaped Fan arrangement showed minimum deck deflection, for the load combination DL+ LL -Y shaped Semi Harp arrangement exhibits minimum deflection, for the load combinationDL + ML+ WL – Y shaped fan arrangement showed minimum deflection, for the load combinationDL

+ ML+ EQL(RS) – Y shaped fan arrangement showed minimum deflection, for the load combinationDL + ML+ EQL(THA) – A shaped harp arrangement exhibits minimum deflection at the mid point of the main span. In response spectrum analysis, H shaped semi harp arrangement exhibits maximum deflection and A shaped harp arrangement exhibits minimum deflection. In Time History Analysis, Y shaped Semi harp arrangement exhibits maximum deflection and A shaped harp arrangement exhibits minimum deflection. From the modal analysis From Modal Analysis, the period decreased from the mode number 1 to 12 and the frequency increased from the mode number 1to 12.

REFERENCES

  1. AlessioPipinato (2012) Coupled Saftey Assessment of Cable Stay Bridges Canadian center of Science and Education.

  2. Atul K. Desai (2013) Seismic Time History Analysis for Cable- Stayed Bridge Considering Different Geometrical Configuration For Near Field Earthquakes World Academy of Science, Engineering and Technology Vol:7 2013-07-2

  3. AzitaAzarnejad, Ken McWhinnie (2011) Cable-Stayed Bridge as an Alternative for Medium and Short Span Bridges Annual Conference of the Transportation Association of Canada Edmonton,

    Alberta

  4. Azzaro.D, C Gentile, (2001) Bridges with spatial cable systems: effects on static and dynamic behavior , 26th Conference on Our World in Concrete & Structures: Singapore

  5. Li Y. Zhang (2007) Static and Seismic Analysis of a Retrofitted Single-Tower Concrete Cable-Stayed Bridge in China ATLSS Reports Civil and Environmental Engineering

  6. O., Rageh (2013) Non-Linear Static and Modal Analysis of Three Types of Cable- Stayed BridgesMathematical Theory and Modeling ISSN 2225-0522 Vol.3, No.12, 2013

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