Chapter 2 Literature Review
2.3 Extradosed Bridge Technology
2.3.9 Side span length
Akio Kasugaxx stated that due to the similar structural behavior of Extradosed bridges with prestressed box-girder bridges, side spans length should be determined proportionally to them, generally between 0.6 and 0.8 from main span length. However, Chio indicated that for an Extradosed bridge with constant depth deck, the use of ratios (L1/L) higher than 0.60, produces high deflections, strainer strengths and tension increases on deck in comparison to closer side spans. According to Chio , side span length variation (L1) has relevant effects on deck flexural moments in the side span, which decrease as long as ratio (L1/L) goes down.
23 | P a g e
Chapter 3
Structural Components of PC Extradosed Bridge, Naluchi
PC Extradosed Bridge is composed of the following major structural components;
1. Prestressed concrete PC girder 2. Reinforced concrete deviator 3. Pier
4. Foundation: Shinso foundation 5. Stay cable
3.1. Substructure and Foundation of P3 Pier (Main Bridge)
xxiA comparative study was conducted by JICA (Japan International Cooperation Agency) to consider two alternatives (the Shinso type foundation with a span of 120m and spread footing foundation with a span of 128m) for the river pier foundation. Based on the study, the result shows that the Shinso type foundation is preferable due to cost reduction and reliability under seismic forces.
Figure 3.1-Shinso Foundationxxii
24 | P a g e Figure 3.1 shows the Shinso Foundation in construction phase. Shinso Foundation is protected by a Coffer Dam which is built to protect to the Shinso Foundation during the Construction and also to ensure its safety after the construction phase during its serviceability.
Shinso Foundation is Hollow and Pier 3 is Projected from its bottom.
Figure 3.2-Pier3 projecting From the Shinso Foundation
3.2. P3 Pier
3.2.1 Configuration of Deviator
Pier 3 is Octagonal in shape at the bottom and Rectangular in the top most section. Due to its variation in shape with length it is constructed by Slip Farm technology .This section is chosen because of its less construction cost, structural aspect, and minimum construction duration as the most optimum solution.
Design Strength of 30 MPa and maximum permissible water-cement ratio of 0.50 and cover of 100 mm. According to the Building Code Requirements for Structural Concrete (ACI-318-05), minimum required strength of pier concrete is 27 N/mm2 and maximum permissible water cement ratio is 0.50 if the pier is partially under water during flood. Hence it satisfies the durability requirement.
The deviator also called the pylon basically functions as a deviating support. The top level of pylon of PC Extradosed Bridge is about 80m from the foundation and about 24 m from deck
25 | P a g e surface to top level. The shape of pylon as a tower on the river is determined by structural and architectural aspects.
Figure 3.3 shows the Pier 3.
Figure 3.3-Pier 3 3.2.2 Saddle
Saddle support is type of support in which stay cable passes through the pylon in continuity. In this support system, anchorages are not required at the pylon hence exposure to atmosphere is not likely and thus it is selected for the project.
The structural characteristics of saddle support are:
1. No hollow space in the pylon (filled with concrete)
2. The stay cables pass through the pylon, and the tension in both sides of the cables will be balanced.
26 | P a g e Figure 3.4 -Cables passing through Pylon
3.3 Stay Cable
3.3.1 Stay Cable Layout
In the Extradosed bridge, stay cables have two functions, one to minimize bending moment by up lifting self weight of the girder and second to resist the forces developed due to live loads.
The pylon (deviator) height is an important parameter for determining the stay cable layout because it controls the magnitude of negative moment. Another parameter to be considered is the amount of PC tendons. This calculation is based on the necessary tensile force and the stress range. The appropriate stay cable layout is determined by considering cost optimization by alternate study for the pylon height (20-26m), which are 1) H=20m; H/L=1/11.9, 2) H=23m;
H/L=1/10.4, 3) H=26m; H/L=1/9.2. The results showed differences in the number of PC tendons amongst the cases considered in comparative study.
The 7 inner cables near the support have 19 strands having diameter 15.2 mm while outer 7 cables have 27 strands having the same diameter 15.2 mm.
27 | P a g e Figure 3.5--Stay Cable Layoutxxiii
3.3.2 Selection of Cable
Originally, twisted PC strand were developed for the PC cable stayed bridges and also as inner cables for the PC girders.
For almost all Extradosed bridges, twisted PC strands are applied.
Figure 3.6 – Twisted Cable Strands
3.3 Anchorage of Stay Cable
3.4.1 Stay Cable Anchorage
Stay cable anchorages are constructed in order to transfer the tension of stay cables to main girders efficiently. Anchors are reinforced by either PC tendons or by reinforcing bars against local stress caused by tension of the stay cables. Stay cable anchorage area is surrounded by large tensile stress from the stay cables. The anchorage zone on the main girder is an important structural component that supports the main girder. Therefore, these parts have to be
28 | P a g e reinforced by PC tendons or reinforcing bars against shear forces and the local stress which occurs due to the tensioning force induced by stay cable.
Figure 3.7 – Stay Cable Anchorage 3.4.2 Wind Vibration
While designing stay cable and anchorages of Extradosed bridge, it is desirable to conform to
“Wind-Resistance Design Handbook for Highway Bridges” Japan Road Association. It is evident that wind and moving vehicles cause vibrations of stay cables. The vibrations of stay cables include nominal vibration and self-excited vibration. Nominal vibrations due to vortex excited oscillation arise from winds of relatively low speed and create vibrations of constant amplitude.
If the stay cable is anchored by fixity, a lateral force arises repeatedly near the anchorage zone of the stay cable.
The vibration due to moving vehicles is an irregular vibration. Considering this, stay cable anchorages have to be a flexible structure which can sufficiently absorb the vibrations.
Additionally, the stay cable and stay cable anchorage must be water proof and received sufficient rust-proofing treatment.
Also, at the anchorage area, it is desirable to install protection facilities at the surface of girder deck to prevent damage to stay cables even if automobiles collide with it. Protection facilities, which are buffers or vibration isolators or dampers, have to be provided.
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3.5 Prestressed Concrete Girder
3.5.1 Number of Cells
The highly rigid box girder is necessary as a girder type because it can accommodate longer clear span, i.e.120 m or more for the PC Extradosed Bridge. A box type which is hung transversally by both ends with stay cable is selected while considering the deck width of 13.3m.
While selecting box girders, there is a choice between a single cell or a 2-cell box girder. Though single cell box girder is easy in construction and maintenance but two-cell box girder is structurally more durable and rigid. Unlike the 2 cell girder, the prestress tendons and rebar requirement in transverse direction in case of single cell box girder are proportionately increased due to longer unsupported span of box girder. Hence, it is finally concluded that 2-cell type is the most appropriate girder type in this case.
3.5.2 Dimension of girder
A 2-cell box girder has a sectional scheme consisting of upper and lower flanges and three webs. In the cross-section, the upper and lower flanges occupy a large area, so the girder can resist large compressive stresses due to bending moments. PC tendons or reinforcing bars should be placed so as to resist bending moment, tensile stress and shear stress due to working loads. On the other hand, the girder has large torsion stiffness and it is desirable due to eccentric distribution of live loads.
3.5.3 Arrangement of Inner Cables
Resisting bending moment due to working load is accomplished by effective arrangement of inner PC cables with appropriate eccentricity with respect to the centroidal axis of the box girder section
30 | P a g e Figure 3.8 –Cable arrangement of slab
3.6 Specifications
Following Specifications were followed by the design Engineer for the Design Purposes, however we have only used ‘’Standard Specifications for Highway Bridges”, 17th Edition, AASHTO 2004
1. Standard Specifications for Highway Bridges”, 17th Edition, AASHTO 2004 2. Designing of Bridge on National Highways”, NHA-JULY/2006
3. Standardization of Bridge Superstructure” NHA-MARCH/2005 4. Pakistan Code of Practice for Highway Bridges, PEC, 1996 5. Specifications for Highway Design” Japan Road Association
3.7 Materials
Materials Strength and Properties to be used in the Construction of bridge are as follow 3.7.1 Concrete:
Deck & Pylon Ec = 33430 MPa, fc’ = 40 MPa Abutments, Pilecaps, Footing Ec = 26430 MPa , fc’ = 24 MPa
Where fc’ is the specified compressive strength of concrete at 28 days 3.7.2 Reinforcing Steel
Reinforcing Steel conform to deformed and plain billet steel bars. ASSHTO M31 (ASTM A615) GRADE 420 with minimum yield strength fy = 420 MPa and minimum tensile strength fpu = 620 MPa
3.7.3 Prestressing Steel (Strand):
The properties of steel used in cables and prestressing tendons are as follows and are used as input parameters in SAP2000s
Ultimate Strength fs’ = 1860 MPa Yield Strength fpy = 1670 MPa Elastic Modulus of Strand Es = 195000 MPa
Allowable Jacking Stress fsj = 73.5% of Ultimate Strength
31 | P a g e Wobble coefficient k = 0.0007 m-1
Draw-in at anchorage 8 mm 3.7.4 Support Stiffness’s of Naluchi Bridge:
U1(X) U2(Y) U3(Z)
P2 Pier 5,280,000 5,620,000 110,000,000
P3 Pier 14,000,000 14,000,000 103,000,000
P4 Pier 2,170,000 2,170,000 71,700,000
Table 3.1xxiv These stiffness are to be used in Dynamic Analysis.
3.8 Design Loads
3.8.1 Construction Loads
The construction loads considered is : Weight of form traveler =100 tons 3.8.2 Dead Load And Superimposed Dead Load :
The dead load shall consist of the weight of the entire structure, including the roadway, sidewalks, car tracks, pipes, conduits, cables, and other public utility services.
Reinforced Concrete : 24.5 kN/m3 Superimposed dead load :
1. Barrier & Railing : 20.63kN/m (two sides) 2. Asphalt : 8.0 ~ 17.7cm = 33.85kN/m 3.8.3 Creep And Shrinkage :
Structural calculations shall take into account the time dependent effects on materials, i.e.
creep, shrinkage of concrete and prestressing losses (instantaneous and long term losses).
Software uses CEB-FIP 1990 Model Code. Relative humidity of ambient temperature RH = 70%.Creep coeffiecent calculated by Design engineers is 1.4
32 | P a g e 3.8.4 Prestressing force:
Prestressing losses due to friction, creep, shrinkage, taken into account the construction stages shall be considered in computation models. Prestressing force of 444 KN is applied in each tendon
3.8.5 Live Load
The live load consist of the weight of the applied moving load of vehicles, cars and Pedestrians We will use HS 20-44 as recommended by AASHTO and is available in SAP2000.
3.8.5.1 H Loading
The H loadings consist of a two-axle truck or the corresponding lane loading as illustrated in Appendix B. The H loadings are designated H followed by a number indicating the gross wesight in tons of the standard truck.
3.8.5.2 HS Loading
The HS loadings consist of a tractor truck with semitrailer or the corresponding lane load as illustrated in Appendix A. The HS loadings are designated by the letters HS followed by a number indicating the gross weight in tons of the tractor truck. The variable axle spacing has been introduced in order that the spacing of axles may approximate more closely the tractor trailers now in use. The variable spacing also provides a more satisfactory loading for continuous spans, in that heavy axle loads may be so placed on adjoining spans as to produce maximum negative moments.
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Chapter 4
Structural Analysis of Naluchi Bridge
Structural analysis is a process to analyze a structural system to predict its responses and behaviors by using physical laws and mathematical equations. The main objective of structural analysis is to determine internal forces, stresses and deformations of structures under various load effects.
Structural modeling is a tool to establish three mathematical models,
(1) Structural model consisting of three basic components: structural members or components, joints (nodes, connecting edges or surfaces), and boundary conditions (supports and foundations)
(2) Material model (3) Load model.
4.1 Modeling Discretization
Formulation of a mathematical model using discrete mathematical elements and their connections and interactions to capture the prototype behavior is called Discretization. For this purpose: a) Joints/Nodes are used to discretize elements and primary locations in structure at which displacements are of interest. b) Elements are connected to each other at joints. c) Masses, inertia, and loads are applied to elements and then transferred to joints.
4.2 Elastic Analysis:
Service and fatigue limit states should be analyzed as fully elastic, as should strength limit states, except in the case of certain continuous girders where inelastic analysis is permitted, inelastic redistribution of negative bending moment and stability investigationxxv When modeling the elastic behavior of materials, the stiffness properties of concrete and composite members shall be based upon cracked and/or uncracked sections consistent with the anticipated behavior (LRFD 4.5.2.2, AASHTO 2007). A limited number of analytical studies have been performed by Caltrans to determine effects of using gross and cracked moment of inertia.
34 | P a g e The specific studies yielded the following findings on prestressed concrete girders on concrete columns:
1) Using Igs or Icr in the concrete columns do not significantly reduce or increase the superstructure moment and shear demands for external vertical loads, but will significantly affect the superstructure moment and shear demands from thermal and other lateral loads .Using Icr in the columns can increase the superstructure deflection and camber calculations xxvi Usually an elastic analysis is sufficient for strength-based analysis.
4.3 Static Analysis:
Static analysis mainly used for bridges under dead load, vehicular load, wind load and thermal effects. The influence of plan geometry has an important role in static analysis xxvii.One should pay attention to plan aspect ratio and structures curved in plan for static analysis.
4.4 Methodology of modeling in SAP 2000:
The following are the general steps to be defined for analyzing a structure using SAP2000/CSI:
1. Geometry (input nodes coordinates, define members and connections)
2. Boundary Conditions/ Joint Restraints (fixed, free, roller, pin or partially restrained with a specified spring constant)
3. Material Property (Elastic Modulus, Poisson’s Ratio, Shear Modulus, damping data, thermal properties and time-dependent properties such as creep and shrinkage) 4. Loads and Load cases
5. Stress-strain relationship
6. Perform analysis of the model based on analysis cases
In this section, we create a SAP2000/CSI model for the Example Bridge using the Bridge Wizard (BrIM-Bridge Information Modeler). The Bridge Modeler has 13 modeling step processes which are described below:
4.4.1 Layout line
The first step in creating a bridge object is to define highway layout lines using horizontal and vertical curves. Layout lines are used as reference lines for defining the layout of bridge objects and lanes in terms of stations, bearings and grades considering super elevations and skews.
35 | P a g e 4.4.2 Deck Section
Various parametric bridge sections (Box Girders & Steel Composites) are available for use in defining a bridge. User can specify different Cross Sections along Bridge length.
4.4.3 Abutment Definition
Abutment definitions specify the support conditions at the ends of the bridge. The user defined support condition allows each six DOF at the abutment to be specified as fixed, free or partially restrained with a specified spring constant. Those six Degrees of Freedom are: U1- Translation Parallel to Abutment U2- Translation Normal to Abutment U3- Translation Vertical R1- Rotation about Abutment R2- Rotation About Line Normal to Abutment R3- Rotation about Vertical For Academy Bridge consider U2, R1 and R3 DOF directions to have a “Free” release type and other DOF fixed.
4.4.4 Bent Definition
This part specifies the geometry and section properties of bent cap beam and bent cap columns (single or multiple columns) and base support condition of the bent columns.
The base support condition for a bent column can be fixed, pinned or user defined as a specified link/support property which allows six degrees of freedom.
4.4.5 Diaphragm Definition
Diaphragm definitions specify properties of vertical diaphragms that span transverse across the bridge. Diaphragms are only applied to area objects and solid object models and not to spine models. Steel diaphragm properties are only applicable to steel bridge sections.
4.4.6 Hinge Definition
Hinge definitions specify properties of hinges (expansion joints) and restrainers. After a hinge is defined, it can be assigned to one or more spans in the bridge object
4.4.7 Parametric Variation Definition
Any parameter used in the parametric definition of the deck section can be specified to vary such as bridge depth, thickness of the girders and slabs along the length of the bridge. The variation may be linear, parabolic or circular.
36 | P a g e 4.4.8 Bridge Object Definition
The main part of the Bridge Modeler is the Bridge Object Definition which includes defining bridge span, deck section properties assigned to each span, abutment properties and skews, bent properties and skews, hinge locations are assigned, super elevations are assigned and pre-stress tendons are defined. Since we calculate the pre-pre-stress jacking force from CTBridge, we use option to input the Tendon Load force.
4.4.9 Update Linked Model
The update linked model command creates the SAP2000/CSI object-based model from the bridge object definition. l. There are three options in the Update Linked Model including:
1. Update a Spine Model using Frame Objects 2. Update as Area Object Model
3. Update as Solid Object Model 4.4.10 Bridge Results & Output
Analysis result and outputs are in the form of 1. Influence Lines and Surfaces
2. Forces and Stresses Along and Across Bridge 3. Displacement Plots
4. Graphical and Tabulated Outputs 4.5 Naluchi Bridge Model:
4.5.1 Geometry Description
The bridge to be modeled is 246m long with two span. The deck is 15.6m wide and varies linearly. It has two lanes 5m wide each. This is a T-shape girder and pier structure along with deviators (pylon) from which stay cables are hanging the box girder deck.
After providing section geometry data, all the sectional properties of the can be formulated.
Using this information, the different sections of bridge are designed and for this purpose a bridge model with non-prismatic segments is created.
To create a non-prismatic member, starting and ending section, the length of the segment and how the properties were varied over the segment are specified. Non prismatic members may
37 | P a g e have any number of segments and are defined using starting and ending sections and the segment properties may be varied in linear parabolic and cubic manner.
Non prismatic sections, these may be assigned to the line diagram of the bridge deck as per drawings of the initial design in similar preposition and alignment.
4.5.2 Imaginary Diaphragm Modeling
The section for the imaginary diaphragm (rigid zone element) is defined by assigning it the high moment of inertia values while keeping its mass and weight zero
4.5.3 Stay Cables Modeling
Stay cable section was defined by specifying the diameter of the stay cable selected, material, number of linear segments and tension at the two ends.
The initial tension in stay cables could be applied properly when the cable element is applied.
However, by applying frame element is successfully used in the analysis and initial tension is applied as strain in the frame element. Strain calculation is shown in the Table 4.1
Nos. of location as, the restraints according to “Initial Design Final Draft”. Non prismatic section for P3 Pier is defined as per drawings of Initial Design and a fixed support at its base is assigned to it.
Cross beams and deviators are also modeled after defining their sections according to the drawings of Initial Design
38 | P a g e 4.5.5 Loading Description
4.5.5.1 Dead Load:
Self Weight of the girder, anchorage load and surface load are included in the dead load case.
To incorporate the effect of initial tension in the cables, the strain produced due to initial tension is calculated and is defined in another load case
To incorporate the effect of initial tension in the cables, the strain produced due to initial tension is calculated and is defined in another load case