Study of Effect of Rise-Span Ratio and Study of Different Hanger Configuration in the Analysis of Bowstring Arch Bridge

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Study of Effect of Rise-Span Ratio and Study of Different Hanger Configuration in the Analysis of Bowstring Arch Bridge

Karnati Vidhatha

G. Phani Ram (Assistant Professor, ( M.Tech Structural Engineering)

Velagapudi Ramakrishna Siddhartha Engineering College

Abstract:- Bowstring arch bridges have significant advantages in economical and atheistic appearance which provide suitable option for bridges of longer spans. Though bowstring arch bridges have different design parameters which effect the performance of bridges. Parameters such as rise-span ratio, various hanger arrangements affect the economy of the bridge. The purpose of this paper is to investigate the influence of different parameters and determining the most suitable solution for a railway bridge. The hangers are significantly prone to premature failure or harm because of fatigue as they endure continual loading with giant variations and ample load cycles. The rise-span ratio has comparatively large effect on stability of structure. Excessively large or small rise-span ratio is drawback for structural stability. The work focuses on comparing the results of different rise-span ratio with each other and the response of the tensile stresses when different hanger arrangements are used. The work focuses on decreasing fatigue stress without increasing bending moments in arch and tie.

INTRODUCTION

Tied arch bridges have been designed and constructed since the late 19th century. Tied arch bridges are both aesthetic and economical alternates to long span bridges holding a place in the hierarchy of major bridges. They fit in a niche between viable and economical plate girder spans and short cable stayed bridge spans. There are several variations of the tied arch with the most common form being those having vertical hangers, stiff tie girders and the tie are strongly influenced by the hanger arrangement. Vertical, fan and network arrangements are the most commonly adopted schemes for hangers. Hanger arrangement is the key issue in determining the structural behavior. Many parameters should be taken into consideration to optimize the design of a tied arch bridge: the bending moment in the arch and tie, the axial force in the hangers, the variation of bending moment in the arch and tie, and the variation of axial force in the hangers. The hangers are significantly prone to premature failure or harm because of fatigue as they endure continual loading with giant variations and ample load cycles. The rise-span ratio has comparatively large effect on stability of structure. Excessively large or small rise-span ratio is drawback for structural stability.

HANGER ARRANGEMENT

Depending on the inclination of hangers for tied arch bridges, in the analysis we considered different arrangements, as follows:

  1. Langer system or vertical hanger system- as in Fig. 1 which requires a deck with high rigidity, who plays the role of a tie for the flexible arches. The deck is suspended by vertical hangers.

    Fig. 1 Tied arch bridge with vertical configuration of hangers

  2. Nielsen system or network hanger system- as in Fig. 2 which consists of a single rigid beam, reinforced with a system of hangers. In this system, the hangers are inclined and work as a variable-section truss with rigid bottom flange

Fig. 2 Tied arch bridge with Nielsen configuration of hangers.

RISE-SPAN RATIO

The rise-span ratio has a relatively large impact on stability of structure. The rise-span ratio is the most important geometric parameter of arch bridges. The rise-span ratio has comparatively large effect on stability of structure. Excessively large or small rise-span ratio is drawback for structural stability

When the rise-span ratio is excessively large, which increases the height of arch rib will lead to increasing of length of arch rib, thereby reducing the structural rigidity and increasing weight, finally leading to reduction of arch stability.

When the rise-span ratio is excessively small, the arch rib will be too flat and straight, so the axial compression force in arch will increase causing the arch to destabilization.

METHODOLOGY:

The Analysis is carried out in STAAD PRO V8I software, where we assume some initial sizes of the bridge components like deck, tie beams, arch etc., and then the structure is made to act upon the dead and live loads to analyze the structure for structural steel. This procedure is repeated until we get economical sections and economical reinforcement.

The criterion for the arch requires the arch member to be shaped to avoid bending moments in the rib for downward loads. Maxima or minima for the internal reactions of a specific arch having a particular circular or parabolic shape may be developed for a unique set of external loads but not for all external loading combinations. That is, for a specific arch shape and loading, the axial thrust may be maximized while the bending moment is minimized. Moreover, fabrication and construction techniques for arches commonly involve connecting straight members on chords to for the best fit to the mathematical arch shape. For this reason, internal bending moments cannot be entirely eliminated in arch structures. As a result, the best outcome is to minimize bending moments in the arch rib for many arch structures including the bow string arch structure.

  • Collecting the geometrical data of Godavari arch bridge.

  • Developing of initial model in STAAD Software and analyzing the model subjected to railway loads.

  • Replacing the model with different rise and span values and comparing results and finding most suitable solution for a railway bridge consisting of two concrete arches, with one lane subjected to railway loads.

  • Comparing the model with different hanger arrangement.

    IDEALISATION OF MAKING OF ANALYTICAL MODEL OF STRUCTURE:

    The dimensions of the different structural elements or members is assumed to some approximate values of the dimensions of the Godavari arch bridge which can be altered once after the analysis is completed according to requirement of safety and serviceability of the structure.

    Once the span and width requirements of the structure are known, we assume the height of the arch to be provided and the arch model is prepared in the auto cad as the arch is a curved member which cannot be drawn or developed in the Staad pro v8i. Importing of the arch member from auto cad to Staad is also not possible, hence we drop vertical coordinates from arch on to the longitudinal girder at regular intervals of relatively lesser values compared to the span (half meter etc.,) and the spacing of the hangers. Now this model which when imported to Staad pro v8i is left with the longitudinal girder and the vertical ordinates dropped. This can be used to develop the arch. Now all the vertical drops are connected at their top ends using beams in the Staad pro to get the arch profile. As the distance between the tips of the adjacent ordinates is very low, the beam connecting them will no longer acts as a linear flat member but in a bulk in the whole arch looks as a curved member due to large scaling. These inter-connected beam members will perfectly resemble an arch profile. Now the ordinates are removed and hanger ordinates are placed at required intervals. This gives us the single arch which is translational repeated and these two arches are connected using lateral bracings at the arch and transversal beams at the longitudinal girders.

    FIG:3 Model of bridge structure.

    FIG 4: Solid view of the model of the structure

    4.2CRSS SECTION DRAWING OF THE GIRDER

    FIG5: CROSS SECTION OF THE GIRD

    CROSS SECTION DRAWINGS

    FIG 6:C SECTION DRAWING

    FIG 7: J SECTION DRAWING

    CROSS SECTION DRAWINGS

    FIG 8: I SECTION DRAWING

    FIG 9: J SECTION DRAWING

    GRILLAGE SECTION

    FIGURE-10: Top view of the grillage section

    LOADING PATTERNS

    Railway bridges: Railway bridges including combined rail and road bridges are to be designed for railway standard loading given in bridge rules. The standards of loading are given for

  • Broad gauge – Main line and branch line

  • Metre gauge – Main line, branch line and Standard C

  • Narrow gauge – H class, A class main line and B class branch line

The actual loads consist of axle load from engine and bogies. The actual standard loads have been expressed in bridge rules as equivalent uniformly distributed loads (EUDL) in tables to simplify the analysis. These equivalent UDL values depend upon the span length. However, in case of rigid frame, cantilever and suspension bridges, it is necessary for the designer to proceed from the basic wheel loads. In order to have a uniform gauge throughout the country, it is advantageous to design railway bridges to Broad gauge main line standard loading.

Loading patterns have been taken according to BRIDGE RULES (Rules specifying the loads for design of super-structure and sub-structure of bridges and for assessment of the strength of existing bridges)

According to BRIDGE RULES specifying the loads for design of super-structure and sub-structure of bridges and for assessment of the strength of existing bridges (APPENDIX II PAGE NO 21)

Modified Broad gauge loading-1987, Broad guage-1676 mm

Equivalent Uniformly Distributed Loads (EUDL) in kilo Newtons (tonnes) on each track

For Bending Moment, L is equal to the effective span in metres. For Shear, L is the loaded length in metres to give the maximum Shear in the member under consideration. The Equivalent Uniformly Distributed Load (EUDL) for Bending Moment (BM), for spans up to 10m, is that uniformly distributed load which produces the BM at the centre of the span equal to the absolute maximum BM developed under the standard loads. For spans above 10m, the EUDL for BM, is that uniformly distributed load which produces the BM at one-sixth of the span equal to the BM developed at that section under the standard loads.

EUDL for Shear Force (SF) is that uniformly distributed load which produces SF at the end of the span equal to the maximum SF developed under the standard loads at that section.

  1. SUPER IMPOSED DEAD LOAD

    Super imposed load refers to a load that is in addition to the dead weight of the bar joists and bridging The weight of the track is considered as 0.4413 kN/m

    SELF WEIGHT

    Self-weight is the load on a structure imposed by its own weight. Self-weight is considered as 1kN/m

    FIG 11: BOW STRING ARCH BRIDGE WITH NETWORK CONFIGURATION OF HANGERS

    Bowstring arch bridge with 94m span and 18.8m (1/6th span-rise ratio) rise with vertical hanger configuration has been analyzed using STAAD software.

    The axial forces in the hangers are examined and tabulated as follows.

    BEAM

    TOTAL LOAD (KN)

    2

    1463.512

    3

    1484.178

    4

    1528.196

    5

    1652.747

    6

    2148.519

    7

    1542.885

    8

    794.189

    9

    1484.181

    10

    1582.211

    11

    1652.736

    12

    2148.501

    13

    1542.866

    14

    794.204

    30

    1463.512

    31

    1484.578

    32

    1528.197

    33

    1652.747

    34

    2148.519

    35

    1542.885

    36

    794.189

    37

    1484.181

    38

    1528.211

    39

    1652.736

    40

    2148.501

    41

    1542.866

    42

    794.204

    BEAM

    TOTAL LOAD (KN)

    2

    1463.512

    3

    1484.178

    4

    1528.196

    5

    1652.747

    6

    2148.519

    7

    1542.885

    8

    794.189

    9

    1484.181

    10

    1582.211

    11

    1652.736

    12

    2148.501

    13

    1542.866

    14

    794.204

    30

    1463.512

    31

    1484.578

    32

    1528.197

    33

    1652.747

    34

    2148.519

    35

    1542.885

    36

    794.189

    37

    1484.181

    38

    1528.211

    39

    1652.736

    40

    2148.501

    41

    1542.866

    42

    794.204

    Loads imposed on the structure

    Bow string arch bridge with 100m span and 30m (0.3 rise-span ratio) rise with vertical hanger configuration is analyzed in STAAD software

    Beam

    L/C

    Node

    Axial Force kN

    49

    5

    58

    951.477

    9

    5

    18

    951.363

    18

    5

    36

    943.065

    58

    5

    76

    942.061

    8

    5

    16

    937.562

    48

    5

    56

    935.69

    17

    5

    34

    912.162

    57

    5

    74

    911.127

    60

    2

    80

    871.839

    20

    2

    40

    871.839

    51

    2

    62

    871.804

    11

    2

    22

    871.804

    50

    2

    60

    827.469

    10

    2

    20

    827.469

    59

    2

    78

    827.467

    19

    2

    38

    827.467

    60

    1

    80

    823.159

    20

    1

    40

    823.159

    11

    1

    22

    823.125

    51

    1

    62

    823.125

    7

    5

    14

    800.395

    50

    1

    60

    781.265

    Axial forces of the hangers

    Bow string arch bridge with 94m span and 18.8m (0.2 rise-span ratio) rise with network hanger configuration is analyzed in STAAD software

    beam

    axial force kn

    2

    20.256

    3

    55.875

    4

    71.057

    5

    84.308

    6

    110.221

    7

    113.011

    8

    111.812

    9

    91.329

    10

    64.292

    Bow string arch bridge with 100m span and 30m (0.3 rise-span ratio) rise with network hanger configuration is analyzed in STAAD software

    Axial forces of the hangers

    Beam

    Axial Force kN

    112

    524.448

    32

    522.941

    110

    507.534

    111

    505.689

    30

    504.641

    31

    503.7

    109

    498.358

    29

    494.036

    108

    470.234

    28

    466.015

    114

    448.058

    34

    447.199

    107

    430.706

    27

    428.026

    115

    412.458

    35

    411.757

    105

    395.424

    CONCLUSIONS

    • The bowstring arch bridge with 94 m span and 18.8m rise (0.2 rise-span ratio) with vertical arrangement of hangers has greater axial forces compared to bowstring arch bridge with 94m span and 18.8m rise (0.2 rise-span ratio) with vertical arrangement of hangers.

    • Bow string arch bridge with 100m span and 30m (0.3 rise-span ratio) rise with network hanger configuration has lesser axial forces than Bow string arch bridge with 100m span and 30m (0.3 rise-span ratio) rise with vertical hanger configuration.

    • In vertical arrangement of hangers, the axial forces on hangers are high and bending moments on arch and tie are high as compared to network configuration of hangers, this is because there is low stiffness of arch plane in the vertical configuration of hangers.

    • This negative effect does not occur in network configuration of hangers because of crossing hangers, which increases arch stiffness.

    • A reasonable rise-span ratio for bow string arch bridge studied here is around 0.25-0.3

    • The rise-span ratio has comparatively large effect on stability of structure. Excessively large or small rise-span ratio is drawback for structural stability.

REFERENCES

  1. Tveit P. Consideration for design of network arches. J Struct Eng 1987;10: 2198207.

  2. Tveit P. The network archAn extended manuscript from 21 lectures in 12 Countries. Grimstad (Norway): Internet Edition; 2001.

  3. Tveit P. The network arch. Bits of manuscript in September 2008 after lectures in 50 Countries. Internet Edition. 2008. http://pchome.grm.hia.no/~ptveit/.

  4. Brunn B, Schanack F. Calculation of a double track railway network arch bridge applying the European standards. Technische Universität Dresden; 2003.

  5. De Zotti A, Pellegrino C, Modena C. A parametric study of the hanger arrangement in arch bridges. In: 5th international conference on arch bridges. ARCH '07. 2007.

  6. Schanack F, Brunn B. Analysis of the structural performance of network arch bridges. Indian Concr J 2009;(1):713.

  7. Pipinato A, Pellegrino C, Bursi OS, Modena C. High-cycle fatigue behavior of riveted connections for railway metal bridges. J Constr Steel Res 2009;65(12): 216775.

  8. Cupani G. Fatigue behaviour of hangers in arch bridges. M.Sc. thesis. University of Padova; 2009 [in Italian].

  9. EN 1991-2. Eurocode 1Actions on structures. Part 2: Traffic loads on bridges. Brussels (Belgium): European Committee for Standardization; 2003.

  10. G+D Computing. Sydney: Straus7 User's Manual; 2005.

  11. Teich S. Fatigue optimization in network arches. In: 4th international conference on arch bridges. ARCH'04; 2004.

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