CHAPTER 1

INTRODUCTION

GENERAL

Bridge structures are used to carry vehicular load to bypass some obstruction on the path. A bridge may be simply supported on girders, balancedcantilever or it may be a cable strayed. This study focuses on simply supported bridges consisting of a bridge deck, bearings, girders, bent, column and abutments. Spans are considered to be straight and with varying length of this study. India has its own code provision regarding the design of I and box bridge girders. So, to improve and meet the international standards specified by AASTHO (STD and LRFD) and EN1991-2, the IRC live loads can be proportioned accordingly. Since this code allows to adjust the loading, if the design vehicles are dissimilar to the above code vehicle. It is noted that the vehicular design loads vary with countries. Since it depends on the vehicle characteristics and traffic condition on bridges of various countries. So, this study will also offer fundamental data for further growth of standard loading for bridge design in India.

Thus, this paper aimed to quantitatively compare the responses of simple beam bridges due to Indian truck loadings with the American and European standard live loadings. Additionally, the maximum ratios of bridge responses, shear and bending moment, due to American and European loadings were compared with those from Indian trucks. The dynamic impact effects and reduction in load intensity due to improbable coincident of simultaneous loaded lanes were separately incorporated in the analysis for each standard. For bridge design practice in India, these ratios could be applied as multiplier to those standard loadings; hence, the maximum shear and bending moment of simple beam bridge caused by those proportioned standard loadings and Indian truck are comparable. In addition, the results of this study would be employed as the basic data for further development of standard loadings for bridge design and IS code practices in India.

HISTORY

Girder bridges have existed for millennia in a variety of forms depending on resources available. The oldest types of bridges are the beam, arch and swing bridges, and they are still built today. These types of bridges have been built by human beings since ancient times, with the initial design being much simpler than what we enjoy today. As technology advanced the methods were improved and were based on the utilization and manipulation of rock, stone, mortar and other materials that would serve to be stronger and longer. In Rome, the techniques for building bridges included the driving of wooden poles to serve as the bridge columns, and then filling the column space with various construction materials. The bridges constructed by Romans were at the time basis; however, very dependable and strong while serving a very important purpose in everyday societal life. As the industrial revolution came and went, new materials with improved physical properties were utilized; and wrought iron was replaced with steel due to steel’s greater strength and larger application potential. Also RCC became popular depending upon the availability and site conditions.

GIRDER AND ITS TYPES

A girder bridge, in general, is a bridge that uses girders as the means of supporting the deck. A bridge consists of three parts: the foundation (abutments and piers), the superstructure (girder, truss, or arch), and the deck.

A beam may be made of concrete or steel – many shorter bridges, especially in rural areas where they may be exposed to overtopping and corrosion, will utilize concrete box beams. The term “girder” is typically used to refer to a steel beam. In a beam or girder bridge, the beams themselves are the primary support for the deck, and are responsible for transferring the load down to the foundation. Material type, shape, and weight all affect how much weight a beam can hold. Due to the properties of inertia, the height of a girder is the most significant factor to affect its load capacity. Longer spans, more traffic, or wider spacing of the beams will all directly result in a deeper beam.

TYPES OF GIRDERS

A rolled steel/RCC girder is a girder that has been fabricated by rolling a blank cylinder of steel through a series of dies to create the desired shape. These create standardized I-beam and wide flange beam shapes up to 100 feet in length. This shape can also be cast in concrete which is being used in our study.

A plate girder is a girder that has been fabricated by welding plates together to create the desired shape. The fabricator receives large plates of steel in the desired thickness, then cuts the flanges and web from the plate in the desired length and shape. Plate girders can have a greater height than rolled steel girders and are not limited to standardized shapes. The ability to customize a girder to the exact load conditions allows the bridge design to be more efficient. Plate girder can be used for spans between 10 meters and more than 100 meters (33 feet to more than 330 feet). Stiffeners are occasionally welded between the compression flange and the web to increase the strength of the girder.

A box girder (concrete or steel) or “tub girder” is, as the name suggests, a box shape. They consist of two vertical webs, short top flanges on top of each web, and a wide bottom flange connecting the webs together. A box girder is particularly resistant to torsion and, while expensive, are utilized in situations where a standard girder might succumb to torsion or toppling effects.

RESEARCH OBJECTIVE

Parametric analysis on bridge girders of various shapes for normal and special cases and checking serviceability criteria.

Comparing 3 codes of AASTHO(STD AND LRFD), EUROCODE1991-2,IRC-6 2014 for various bridge loadings.

SCOPE OF THE STUDY

Comparing codes for different loadings to calculate shear, torsion and moment ratio.

With the help of the above ratios giving a factor of multiple.

Conditional assessment of various shapes of bridge girder. Also giving the difference in the responses given by I and BOX girders.

A Parametric study by calculating fundamental frequencies, torsion, SF, BM with varying shapes, no. of lanes and span length.

Fundamental Frequency will give serviceability criteria for various girders.

ORGANISATION OF THESIS

Chapter 1, this introductory chapter presents the background, history, girder and its types, objectives and scope of the project.

Chapter 2, discusses details about various methods, loadings and concepts related to comparison, analysis and serviceability criterion in order to achieve the desired results.

Chapter 3, deals with the details of modelling of structure, its material properties and cross-sectional properties.

Chapter 4, discusses about loading in various standards,i.e. IRC, ASSTHO and EUROCODE.

Chapter 5, deals with the analysis procedure, types of analysis and example on how to do analysis using CSi bridges 2015.

Chapter 6, discusses about the results obtained and shows tables and graphs related to that.

Finally, in Chapter 7conclusion are drawn based on obtaining results.

CHAPTER 2

LITERATURE REVIEW

Various studies have been done to do a general assessment of bridge girders using European, American and other international standards. Also a study describing the bridge response due to Indian load condition is available. The differences in the Box and I girder is also available as a comparative study with different loading and criteria. Dynamic study giving the fundamental frequency helps to access the serviceability criteria for different bridge responses. So, this study helped a lot in giving a factor for calibrating the Indian loading with the international standards. Also checking the serviceability criteria and general assessment of bridge girder responses.

Hatem M. Seliemcompared old Egyptian code(ECP 201-2003) with the new ECP 201-2012(based on traffic load on the bridges of EN 1991-2)by taking concrete I shaped, box shaped and composite girder. The new VLL and load combinations introduced in ECP-201:2012 are fundamentally different than those presented in previous versions of the code. The impact of these new loads and load combinations on the design of new bridges or the structural safety of the existing bridges that have been designed according to ECP-201:2003 or ECP-201:1993 has not been fully addressed for the different bridge deck systems. Three different bridge deck systems, i.e. concrete I-shaped girders, composite steel plate girders, and concrete box-girders with different spans were numerically modelled using a two-dimensional grillage analogy. The bridge decks were analyz ed under main gravity loads using VLL according to ECP-201:2012 and ECP-201:2003. The internal forces of individual load cases, total un-factored load combination, and total factored load combination of ECP-201:2012 and ECP-201:2003 were compared. The study shows that concrete box-girders designed according to ECP-201:2012 and ECP- 201:2003 using the ultimate limit state method yield almost the same demand. Despite the increase in the VLL of ECP-201:2012, and consequently the live load forces, concrete I-shaped girder bridges will be subjected to less total factored internal forces in comparison to ECP-201:2003 This is attributed to the interaction between the live to dead loadratio and the load combinations. Design of composite steel plate girder bridges according to ECP-201:2012 using the allowable stress design method yields over designed sections.

Magdy Samaan studied the curved continuous multiple box girder bridges and applied finite element method to evaluate the mode shapes and natural frequency. This experimental investigation along with a parametric study gave the variation of fundamental frequency with a variety of parameters. The fundamental frequency decreases by 20% for each span length increment, the torsional mode shapes decrease with the increase in span length, fundamental frequency decreases with bridge curvature and also span to depth ratio increases with the fundamental frequency.

Suniti Suparpstudied that, for the Bridge design practice in Thailand, engineers have to calibrate the design live loads obtained from these international Standards with the existing Thai truck weight limits in order to achieve the same level of bridge safety. This article Comparatively studied the load-carrying behaviour of simple beam bridges with the span length ranging from 5 to 60 meters Due to Thai truck loads against the AASHTO(STD;LRFD) and EN1991-2 design live loads defined by the American and European standards, respectively. The objective of this study was to compare the maximum shear and bending moment of the Simple beam bridges due to various types of loadings. The proper ratios of the shear, also bending moment, between the AASHTO(STD;LRFD) and EN1991-2 loads against Thai truck loads were proposed. The results showed that, in each span, the maximum shear and bending moment were caused by various types of trucks. Additionally, the heaviest truck produced The maximum responses for some analysis cases. From the comparative analysis, the shear ratios and the moment ratios were Proposed associated with various bridge span lengths. For bridge design practice in Thailand, these ratios could be applied as Multipliers to the AASHTO(STD;LRFD) or EN1991-2 loads; therefore, the bridge responses were conformable to those of Thai truck loads. Theseare the base for recent paper which helped in comparing the Indian code with the International specifications. She gave an idea about international loading standards. The moment and shear force ratio can be used to calibrate Indian standards with the international one’s.

Supriya Madda did a parametric study ofthe dynamics of bridge girder with span length ranging from 15 to 35 m. The IRC Class A loading gives a variation of bending moment and deflection with an increase in span length. For two lane bridge, all the bridge spans, except 35m, give reasonable results of the deflection/span ratio, which are acceptable. But for span 35m (2.51×10-3), it isvery close to the permissible limit (2.66×10-3) which may lead to serviceability problems in future. The same will be situation for similar kind of bridge beyond a span of 35 m. For four lane bridge, Deflection/span ratiovalues for shorter spans, i.e.up to 30 m are within permissible limit for all the combinations of longitudinal girders. But for 35 m span, of 3 LG (2.665×10-3) and 5 LG (2.19×10-3) systems, there is nomarginal difference between actual the and permissible value (2.66×10-3). Hence, it is quite possible that, they may lead to serviceability problems. Vehicle frequency is considered between 3 – 5 Hz. Hence, frequency of bridge superstructure should not fall in the vehicle frequency band to avoid resonance. However, the frequency for span 25m and 30m of two lane bridge fall in the vehicle frequency band of 3 – 5 Hz. Hence, there may arise issues relatedto vibration. It may be safe to state that, all other spans will not pose any vibration related problems.

Eiki Yamaguchistudied the Mid Niigata Prefecture Earthquake in 2004, the damage of a bridge pier was found mitigated by the collision between a girder and an abutment. Therefore, in the seismic response analysis, it is important to include the effect of the collisions. A simple and practical method of simulating the collision in the analysis is the introduction of a spring where the collision occurs. However, the constant of such a collision spring is yet to be formulated well. In this study, appropriate collision-spring constants are investigated for simulating the collisions between girders and between a girder and an abutment. The response analysis of a bridge under seismic loading is then conducted to see the influence of the collision.

CHAPTER 3

MODELLING

GENERAL

The bridge structure is modelled and analyzed using CSI bridges 2015 software. For designing a new structure, connection details and support conditions shall be made as close to the computational models as possible. For an existing structure evaluation, structures shall be modelled as close to the actual as-built structural conditions as possible. The correct choice of modelling and analysis tools/methods depend on: a) Importance of the structure b) Purpose of structural analysis c) Required level of response accuracy. Based on this, The models are prepared for 2 lane and 4 lane bridge girders. The frame section properties, bearing properties, girder and deck section properties are defined in the components window. The box and I girder section details are given according to its design capacity. Foundation springs are assigned for analysis purpose. The loads are assigned according to the different codes for various bridge spans. Vehicle class of CLASS A TR , HSn-44 ,HL-93 and LM1 are loaded over the bridge deck according to IRC6, AASTHO(STD),AASTHO(LRFD) and EN1991-2 respectively. Figure 3.1 and figure 3.2 Shows the 3D view of I and Box bridge girders respectively.

Fig. 3.1 3D sectional view of I bride girder model.

Fig. 3.2 3D sectional view of BOX bride girder model.

All the external load factors were automatically taken as per the respective code followed. The bridge girder span length ranges from 20 to 60 m for both I and box girder. The springs are installed on supports to get the actual response of the bridge girder. The moving load analysis is done to receive shear, torsion and bending moments for worst condition. The modal analysis gives mode shapes and fundamental frequency for bridge responses. The loads are considered to receive the maximum response from bridge girder. The truck type and their loading are different for different loads. It depends on the transport facility and traffic condition of various countries.

MATERIAL PROPERTIES AND MODELLING

Different types of materials are used for bridge structural members such as concrete, steel, pre-stressing tendons, etc. The material properties that are usually used for an elastic analysis are: modulus of elasticity, shear modulus, Poisson’s ratio, the coefficient of thermal expansion, the mass density and the weight density. One should pay attention to the units used for material properties. For linear elastic materials, stresses are linearly proportional to strain(? = E?) as described by Hooke’s Law. The Hooke’s Law is applicable for both homogeneous and isotropic materials. For a simple linear spring, the constitutive law is given as: Fs = k? where ? is the relative extension or compression of the spring, while Fs and k represent the force in the spring and the spring stiffness, respectivelyConcrete grade of M30 and steel reinforcement Fe415 is used. Their concrete and steel properties are shown in fig. 3.3 and fig. 3.4 respectively.

Fig.3.3 concrete grade properties for bridge girder.

A bridge structure is discretized with finite-size elements. Element characteristics are derived from the constituent structural materials The importance of the structure, experience of the designer and the level of needed accuracy affects type of model, location of joints and elements within the selected model, and number of elements/joints to describe the geometry of the structure. For example, a horizontally curved structure should be defined better by shell elements in comparison with straight elements. The other factors to be considered are: a) Structural boundaries – e.g., corners b) Changes in material properties c) Changes in element sectional properties d) Support locations e) Points of application of concentrated loads.

Fig.3.4 Steel grade properties for bridge girder.

GIRDER AND DECK SECTION PROPERTIES

Total 40 combinations were analyzed.The models are prepared for 2 lanes and 4 lane bridge girder. The cross sectional properties and 3D view of their section can be seen in fig. 3.5 to fig.3.7. The frame section properties, bearing properties, girder and deck section properties are defined in the components window.Foundation springsare assigned for analysis purpose. Vehicle class of CLASS A TR , HSn-44 ,HL-93 and LM1 are loaded over the bridge deck according toIRC6,AASTHO(STD),AASTHO(LRFD) and EN1991-2 codes respectively in all the cases one by one. Moving further towards the cross sectional properties of I and Box girder. It is necessary to define the individual girder sectional properties and also the deck sectional properties of the bridge. It can be seen the girder section and deck section are defined separately since they are cast separately and as a result assigned separately. On the other hand, the Box sectional property act monolithically with the deck section property as they act and defined monolithically.So fig. 3.5 and fig.3.6shows the I girder section and deck section properties respectively.

Fig.3.5 I section properties for bridge girder.

Fig.3.6 Deck section properties for I bridge girder.

So all this sectional property has been taken according to the length and shape of the girder. AASTHO even provide predefined Box girder sectional properties for varying lengths. Fig. 3.7shows the Box girder deck section properties.

Fig.3.7 Deck section properties for Box bridge girder.

In this way 2 and 4 lanes I and Box girders are modelled and analyzed to get desired results.

CHAPTER 4

DIFFERENT CODE REVIEW ON BRIDGE LOADING

Loading of IRC-6

IRC-6 was revised in the year 2014 to include loads and load combination for LSM (Limit State Method). But now Indian Road Congress has withdrawn codes IRC-18 (post-tensioned bridge design) and IRC-21 (concrete bridge design), which have WSM (Working Stress Method) of the design. Although IRC-18 and IRC-21 is now replaced with IRC-112-2011 which have only Limit State Method for bridge design, the bridge designers are using WSM for the design of bridges in India. Overloading is also a problem in India and there is no legislation at present to stop it. To transit from Working Stress Method to Limit State Design Method, the issue of overloading on bridges become more important to be discouraged through a legislation. LSM is now practiced in most of the countries and for the harmonization of the code; Indian Codes are following the trend. But Quality control and strict supervision must be ensured as LSM may be economical in terms of reduction in concrete consumption in bridge elements when compared to WSM. Limit State Method is definitely a superior version of the design as it guides to designing a structure considering all eventualities and all overall structural failure conditions.

So based on this IRC loading is taken and in this study combination with CLASS A TR vehicles are preferred. According to this the nose to tail distance between successive trains shall not be less than 18.5m. For single lane bridges having carriageway width less than 5.3m, one lane of CLASS A shall be considered to occupy 2.3m, remaining width of carriage width shall be loaded with 500 kg/m2. Also for multi-lane bridges, each CLASS A loading shall be considered to occupy a single lane for design purpose. The ground contact area of the wheels can be seen intable no. 4.1 The minimum clearance f, between outer edge of the wheel and the roadway face of the kerb and the minimum clearance g, between the outer edges of passing or crossing vehicles on multi-lane bridges can be seen as given in table no. 4.2.

Table 4.1ground contact area of the wheels for CLASS A loading

Table 4.2clear carriageway width for CLASS A loading

Fig 4.1 CLASS A train of vehicles.

Since this study consecrates on 2 and 4 lanes. So fig. 4.3 and 4.2 Gives the load combinations respectively.

Fig. 4.2 IRC 6-2014 load combination for 4 lanes.

Fig. 4.3 IRC 6-2014 load combination for 2 lanes.

Loading of ASSTHO(STD)

The AASHTO standard specifications, AASHTO(STD), stipulates four classes of truck loadings and equivalent lane loadings; H20, H15, HS20 and HS15. The weights of loading H15 and H20 are 75% of HS15 and HS20, respectively. The heaviest loadings are designated as HS20-44 comprising of a tractor truck with a semitrailer or a corresponding lane loading as shown in fig. 4.4. The dynamic effects are to be added in both cases of loading by the formula given as 15.24/(L+38) where L is the span length in meters. The standard truck or lane loadings shall be assumed to occupy a width of 3.00 m. In view of improbable coincident loadings, the probability of the maximum stresses occurs in any member by loading any number of traffic lanes simultaneously, the reduction in load intensity shall be applied at 90% and 75% of the resultant live loads for three lanes and more than three lanes, respectively. There is, however, no reduction intensity for up to two lanes of traffic loaded.

Loading of ASSTHO(LRFD)

The AASHTO developed the new bridge standard loading called HL-93 (Highway Loading, developed in 1993). This model consists of three distinctive different live loads; i.e., (1) design truck (2) design tandem and (3) design lane as shown in Table 4.4 HL-93(Tandem) represents the combination of distinctive live loads of design tandem and the design lane load. Likewise, HL-93(Truck) represents the combined loads of design truck and the design lane load. HL-93(Continuous) represents the bridge live loads consisting of two design truck loads and design lane load, all scaled by 90%. For continuous beam systems, HL-93(Continuous) is only used for negative superstructure moments over the supports and reactions at interior supports. For typical structural components in the limit states other than fatigue and fracture, a dynamic load allowance may be presented as the additive percentage of 33% directly added to all concentrated axle loads but the uniform lane load is not affected. The HL-93 live loads also occupy a width of 3.00 m. As indicated in AASHTO(STD). The extreme live loads shall be determined by multiplying with the multiple presence factors which are taken into account for the improbable coincident loadings. These factors are 1.2, 1.0, 0.85 and 0.65 for the number of loaded lanes of 1, 2, 3 and greater than 3, respectively.

Fig. 4.4 AASTHO(STD and LRFD) 2007 loading.

Loading of Eurocodes (EN1991-2)

The Eurocodes were developed as provisional standards under the responsibility of the Commission of European Communities. The Structural Eurocodes program comprised of many standards; i.e., Eurocodes, Eurocodes 1 to 9, had been developed in series since 1990. EN1991-2 is one of them involves the traffic loads on bridges. Four models of vertical loads denoted LM1 to LM4 are defined for serviceability and ultimate limit state verification except fatigue verification. However, the main characteristic load model LM1, comprising of the tandem system of two concentrated loads and uniformly distributed load as shown in Figure 4.5, is applicable to all bridges. The characteristic values of tandem system and uniformly distributed loads on lane No. i are denoted Qi,Qik, qi,qik ,Qi, qi , are taken into account for various types of traffic on the bridges. For first class road bridges, these values are generally equal to 1.0. The characteristic values of the loads for LM1 are given inTable 4.3 It can be seen that, for greater than three loaded lanes, the tandem system loads are neglected, but the uniformly distributed load shall be remained with 2.5 kN/m2. Both of two loadings occupy a width of 3.00 m. for each lane. The dynamic effects are already included in the characteristic values of loadings.

Fig. 4.5 Load Model No. 1 (LM1) for EN1991-2 loading.

Table 4.3Characteristic Values of Loadings for Load Model No. 1

CHAPTER 5

ANALYSIS

GENERAL

The analysis consists of static linear analysis of dead loads. The moving load analysis responds to a variety of vehicle class load given under different country codes. A modal analysis is also conducted to calculate the mode shapes and the fundamental frequencies.All the three analyses have been simultaneously done to come across the torsion, bending moment and shear force of different bridge girder response to a variety of codes. Selecting the proper boundary condition has an important role in structural analysis. Effective modelling of support conditions at bearings and expansion jointsrequires a careful consideration of continuity of each translational and rotationalcomponent of displacement. For a static analysis, it is common to use a simplerassumption of supports (i.e. Fixed, pinned, roller) without considering the soil/foundation system stiffness. For specific projects, the nonlinear modelling of the system can be achieved byusing nonlinear spring/damper bearings are kept freely in all directions to calculate the mode shapes This will help in compiling data for performing comparative studies on girder loading by various vehicle load classes.

STEPS TO ANALYSE A STRUCTURE IN CSi BRIDGES 2015

The following are the general steps to be defined for analyzing a structure using CSiBridge:

Geometry (input nodes coordinate, define members and connections)

Boundary Conditions/ Joint Restraints (fixed, free, roller, pin or partially

restrained with a specified spring constant).

Material Property (Elastic Modulus, Poisson’s Ratio, Shear Modulus,

damping data, thermal properties and time-dependent properties such as

Creep and shrinkage)

Loads and Load cases

Stress-strain relationship

Perform analysis of the model based on analysis cases

Bridge Designers can use CSiBridge templates for generating Bridge Models, Automated Bridge Live Load Analysis and Design, Bridge Base Isolation, Bridge Construction Sequence Analysis, Large Deformation Cable Supported Bridge Analysis, and Pushover Analysis. The user can either model the structure as a Spine Model (Frame) or a 3D Finite Element Model.

ANALYSIS AND ITS TYPES

Structural Analysis provides the numerical mathematical process to extract structure responses under service and seismic loads in terms of structural demands such as member forces and deformations. Thisstudy concentrates on 3 types of analysis and those are as follows.

LINEAR STATIC ANALYSIS

In the linear relation of stress-strain of a material, Hooke’s law is valid for smallstress-strain range. For linear elastic analysis, sets of loads acting simultaneously canbe evaluated by superimposing (adding) the forces or displacements at the particularpoint. Static analysis mainly used for bridges under dead load, vehicular load, windload and thermal effects. The influence of plan geometry has an important role instatic analysis,one should pay attention to plan aspect ratio andstructures curved in plan for static analysis.

MOVING LOAD ANALYSIS

Vehicles such as trucks and trains passing bridges at a certain speed will cause dynamic effects. The dynamic loads for moving vehicles on bridges are counted for by a dynamic load allowance. Impact factor increases as vehicle speed increases, impact factor decreases as bridge span increases. Under the condition of “Very good” road surface roughness (amplitude of highway profile curve is less than 0.4 in.) the impact factor is well below the design specifications. But the impact factor increases tremendously with increasing road surface roughness from “good” to “poor”. Field tests indicate that in the majority of highway bridges, the dynamic component of the response does not exceed 25% of the static response to vehicles with the exception of deck joints. For deck joints, 75% of the impact factor is considered for all limit states due to hammer effect, and 15% for fatigue and fracture limit states for members vulnerable to cyclic loading such as shear connectors.

Dynamic effects due to moving vehicles may be attributed to two sources:

Hammering effect is the dynamic response of the wheel assembly to riding

surface discontinuities, such as deck joints, cracks, potholes and delamination’s.

Dynamic response of the bridge as a whole to passing vehicles, which may

be due to long undulations in the roadway pavement, such as those caused by settlement of fill, or to resonant excitation as a result of similar frequencies of vibration between bridge and vehicle.

The magnitude of dynamic response depends on the bridge span, stiffness and surface roughness, and vehicle dynamic characteristics such as moving speed and isolation systems.

MODAL ANALYSIS

The Analysis assumes a sinusoidal mode shape can be used for the analysis of the superstructure and calculating the fundamental frequencies of slab beam bridges. For long span bridges or low speed moving load, there is little amplification which does not result in much dynamic responses. Maximum dynamic response happens when load frequency is near the bridge fundamental frequency. The aspect ratios of the bridge deck play an important role. When they are less than 4.0 the first mode shape is dominant, when more than 8.0, other mode shapes are excited.

a) Cycle: When a body vibrates from its initial position to its extreme positive position in one direction, back to extreme negative position, and back to initial position.

b) Frequency: If a system is disturbed and allowed to vibrate on its own, without external forces and damping (free Vibration). A system having n degrees of freedom will have, in general, n distinct natural frequencies of vibration.

? = distance/time

? = 2?f

c) Period (T): Is the time taken to complete one cycle of motion. It is equal to

the time required for a vector to rotate 2? (one round).

d) Frequency (f): The number of cycles per unit time, f = 1/T (H.Z).

5.4 ANALYSIS EXAMPLE ON 2 LANE BOX GIRDER

Now out of 40 models, let’s take an example for 2 lane box girder (20 m) under ASSTHO(LRFD) loading and see how to analyse it.

Define the lane data- the lane definition can be understand by fig.5.1.

Fig. 5.1 Bridge lane data for box girder.

Define different components (material and sections) which we already discussed in modelling (CHAPTER 3)

Define vehicle- the vehicle definition can be understood in fig. 5.2.

Define vehicle class- the vehicle class is defined in fig 5.3.

Analysis cases – this is defined infig. 5.4.

Fig. 5.2 Bridge vehicle class data for 2 lane box girder under AASTHO(LRFD) loading

Fig. 5.3 Bridge vehicle data for 2 lane box girder under AASTHO(LRFD) loading.

Fig. 5.4Analysis case in two lane loaded .

Results-

Display Bridge Forces at an entire bridge width for 2 lane loaded from Spine Model.

Maximum moment and shear force for 2 lane Box girder can be seen in fig. 5.5andfig 5.6 It is not necessary that maximum response is due to the entire section. It can be due to any of the girder.

The modal analysis results areshown as mode shape 2 in fig. 5.7

This shows an example how to analyze any load case in CSi bridges. Similarly, all the cases are analyzed, i.e. for 2 and 4 lane I and Box girder with IRC, ASSTHO(LRFD and STD) and EUROCODE loadings. Keeping in mind that we have to change bridge lane data depending on 2 or 4 lane. Also taking Vehicle class of CLASS A TR, HSn-44,HL-93 and LM1 for IRC6, AASTHO(STD),AASTHO(LRFD) and EN1991-2 respectively.

Fig. 5.5 showing maximum moment due to entire section for AASTHO(LRFD) loading.

Fig. 5.6 showing maximum shear force due to entire section for AASTHO(LRFD) loading.

Fig. 5.7 showing mode shape 2 at frequency of 3.9 Hz.

CHAPTER 6

RESULTS AND DISCUSSION

6.1 MAXIMUM BENDING, SHEAR AND TORSION RESPONSE

The parametric and comparative analysis of I and Box Girder results in bending moment, shear force, torsion and fundamental frequencies from various standards.The values of all the above parameters are given in table 6.1 to 6.6 for I and Box Girder separately. Also their graphs are plotted from fig. 6.8 to 6.13. The maximum bending moment and shear force due to LM1 and Class A loading are for 2 lane and 4 lane I girder respectively. The maximum moment due to LM1 and HL-93 are for 2 lane and 4 lane Box girder respectively.LM1 and Class A loading gives maximum shear force for 2 and 4 lane Box girder respectively. Class A shows maximum torsion for both 2 lane and 4 lane I and box girder. It has been noticed that HSn-44 leads to lowest values for shear, moment and torsion in all the cases, except torsion in 2 lane I girder. The bending moment values are nearly similar for both 2 lane HL-93 and Class A I-Girder and box girder span between 10 to 60m.but for 4 lane I-girder bending moment for 20m, Class A and LM1 gives nearby values whereas for 60 m Class A and HL-93 gave closer values. Also, for 4 lane Box girder Class A , HL-93 and LM1 loading shows almost similar moment values throughout all the spans. Shear force data shows IRC Class A and LM1 loading have closer value at 20 m span in 2lane I-Girder whereas value of LM1 decreases while moving towards 60 m in 4 lane I and Box girders. In case of torsion IRC shows maximum value except for 2 lane Box girder in which it shows close value with LM1 at 20 m then increases and again came closer to LM1 value at 60m.

6.2 SERVICEABILITY CRITERION DUE TO FUNDAMENTAL FREQUENCY

A modal analysis produces bridge mode shapes and frequencies due to varying length and lanes. A maximum fundamental frequency of 6.21 is given by 4 lane box girder at 20 m then it gradually decreases, also a minimum fundamental frequency of 0.731 is given by 2, 4 lane I girder at 60m. Since vehicle frequency lies in the range of 3-5 Hz. Hence, 2 and 4 lane I girder with 20m span may give vibration problems because its fundamental frequency lies in that range. Also in case of 2 lane box girder with 20 m span and 4 lane box girder with 30,40 m span there may be serviceability problem due to resonance.

6.3 MULTIPLICATION FACTOR FOR BENDING, SHEAR AND

TORSION OF VARIOUS CODES

For better comparison and to meet the calibre of international standards a ratio of code specified loading against a response due to IRC loading is required. Therefore, the ratio of shear force, bending moment and torsion for both 2 lane and 4 lane I and Box girder is generated and a graph is plotted against the varying span length and given from figure 6.2 to 6.7. It has been noted that for 2 lane box girder maximum response is given by LM1 at 60 m and for 4 lanes it is given by LM1 at 20m. Also in case of I girder maximum response is LM1 for both 2 and 4 lanes at 20m. Here minimum reaction is given by 4 lane HS-44 for I girder and 2 lane HS-44 for Box girder. So it has been seen that LM1 gives maximum response as ratios above 1 and HS-93 shows nearby value to 1 and below 1,whereas HSn-44 shows a lesser value always below 1. Thus this can be used as an multiplier with LM1,HSn-44,HL-93 to meet their standards. Also,it provides basic data for further development of Indian code.

Table-6.1 maximum bending moments with various span for I girder.

2 Lane I girder(kN-m) 4 Lane I girder(kN-m)

Span

(m) CLASS A loading HL-93 loading HSn-44 loading LM1 loading CLASS A loading HL-93 loading HSn-44 loading LM1 loading

20 3896.14 3690.27 2886.53 4326.79 4551.02 4204.02 3182.58 4641.3

30 7972.78 7388.2 6237.84 8520.9 8781.6 8345.6 6844.8 8538.8

40 13013.45 12317.47 10843.07 13716.47 14070.89 13631.46 11707.69 13438.09

50 19043 18523.7 16687.5 20031.56 20757.82 20168.16 17839.35 19583.87

60 26204.62 26116.03 23914.6 27656.6 28655.43 28205.6 25542.3 27157.5

Table-6.2 maximum shear force with various span for I girder.

2 Lane I girder(kN) 4 Lane I girder(kN)

Span

(m) CLASS A loading HL-93 loading HSn-44 loading LM1 loading CLASS A loading HL-93 loading HSn-44 loading LM1 loading

20 911.35 792.13 635.35 943.81 1031.992 877.4 689.7 1012.7

30 1158.7 1047.32 888.6 1249.08 1333.8 1169.4 968.6 1268.61

40 1406.9 1307 1144.6 1440.21 1603.18 1456.56 1245.17 1528.76

50 1643.16 1561.2 1398.67 1682.4 1850.48 1732.89 1516.37 1777.67

60 1881.66 1815.4 1652.73 1930.5 2093.6 2006.78 1786.7 2025.6

Table-6.3 maximum torsion with various span for I girder.

2 Lane I girder(kN-m) 4 Lane I girder(kN-m)

Span

(m) CLASS A loading HL-93 loading HSn-44 loading LM1 loading CLASS A loading HL-93 loading HSn-44 loading LM1 loading

20 167.898 87.918 62.648 127.978 185.28 134.019 86.597 166.487

30 220.233 121.183 92.613 175.235 235.409 177.64 120.98 203.82

40 271.12 165.72 124.09 228.6 267.27 213.26 151.63 221.14

50 324.828 221.098 166.588 297.678 293.245 256.444 188.315 250.366

60 377.322 278.062 214.757 364.252 335.28 311.93 235.65 288.12

Table-6.4 maximum bending moments with various span for box girder.

`2 Lane box girder(kN-m) 4 Lane box girder(kN-m)

Span

(m) CLASS A loading HL-93 loading HSn-44 loading LM1 loading CLASS A loading HL-93 loading HSn-44 loading LM1 loading

20 5022.6 4561.899 3483.435 5783.419 5847.59 5819.38 4549.11 6145.72

30 9223.59 9090.14 7504.683 10438.05 12167.25 12100.65 10169.21 12075.95

40 14730.32 15081.92 12983.16 16503.16 20154.2 20292.5 17717.4 19709.87

50 28333.66 29124.84 26509.34 30569.71 29782.3 30443.08 27234.6 29123.4

60 39749.7 41222.39 38060.35 45558.34 48888.44 50357.64 46556.74 48198.86

Table-6.5 maximum shear force with various span for box girder.

2 Lane box girder(kN) 4 Lane box girder(kN)

Span

(m) CLASS A loading HL-93 loading HSn-44 loading LM1 loading CLASS A loading HL-93 loading HSn-44 loading LM1 loading

20 1088.49 925.89 745.52 1180.96 1031.992 877.4 689.7 1012.7

30 1409.61 1248 1061.18 1495.47 1373.5 1187.58 955.4 1346.12

40 1709.92 1569.87 1378.55 1809.069 1768.1 1578.24 1337.31 1706.7

50 2580.4 2434.43 2238.468 2675.92 2125.8 1957.4 1708.2 2051.86

60 2971.57 2859.66 2661.32 3156.8 2462.07 2325.44 2070.38 2385.67

Table-6.6 maximum torsion with various span for box girder.

2 Lane box girder(kN-m) 4 Lane box girder(kN-m)

Span

(m) CLASS A loading HL-93 loading HSn-44 loading LM1 loading CLASS A loading HL-93 loading HSn-44 loading LM1 loading

20 621.608 505.923 413.695 598.55 428.352 301.465 206.892 304.762

30 864.5 711.725 602.801 814.785 867.925 682.525 582.905 650.271

40 1091.85 926.889 810.331 1027.628 1200.3 1004.3 873.56 911.725

50 986.37 827.464 739.328 963.825 1568.92 1386.21 1223.21 1230.26

60 1103.09 967.464 877.349 1099.133 2095.4 1961.289 1775.9 1758.7

Fig.6.1 fundamental frequency for 2,4 lane I and box girder.

Fig. 6.2 maximum moment ratios for 2,4 lane I girder from all specified loads

Fig.6.3 maximum shear ratios for 2,4 lane I girder from all specified loads.

Fig. 6.4 maximum torsion ratios for 2,4 lane I girder from all specified loads

Fig. 6.5 maximum moment ratios for 2,4 lane box girder from all specified loads.

Fig. 6.6 maximum shear ratios for 2,4 lane box girder from all specified loads

Fig. 6.7 maximum torsion ratios for 2,4 lane box girder from all specified loads.

Fig. 6.8 I girder bending moment for 2 and 4 lane

Fig. 6.9 I girder shear force for 2 and 4 lane

Fig. 6.10 I girder torsion for 2 and 4 lane

Fig. 6.11 Box girder bending moment for 2 and 4 lane

Fig. 6.12 Box girder shear force for 2 and 4 lane

Fig. 6.13 Boxgirder torsion for 2 and 4 lane

CHAPTER 7

CONCLUSION

This study compared the bridge response due to IRC loading against American and European loading standards under different parameters. All the Indian loading were taken from IRC6-2014. The specific load from each code is taken with its dynamic allowances. The analysis shows the bridge response due to different loading from various codes and helps to conclude the following results-

This helps in providing a comparative idea of maximum and minimum responses by all the three codes against IRC load.

The maximum bending moment, shear force and torsion resulted from various international standards with Indian code has been compared and concluded.

The bridge reaction for span varying from 20 to 60 m with 2 and 4 lane I and Box girder were analyzed and given in the form of shear, moment and torsion ratio. This ratio helps in differentiating the IRC loading with the other standards. Also,it helps in analyzing the difference in bridge reactions of various codes.

The ratio may be used as a multiplier to calibrate Indian standards against the international standards.

It provides the basic data for further development of the code.

This study also concentrates on responses due to I and box shaped girders. Thus, given the difference between both of them.

The modal analysis provides the fundamental frequency which has already been discussed and helps in providing serviceability criteria for bridges.

Now to relate and to make use of above obtained results one by one. First, let’s see how to use various obtained multiplication factors. Referring to fig. 6.2if we want to calibrate maximum bending moment ratio of 2LSTD to 2LIRC loading for I girder then, according to graph a multiplication factor of 0.9 should be multiplied with IRC loading for a 60 m span length. Similarly, referring to fig 6.3 if we want to calibrate maximum shear force ratio of 2LSTD to 2LIRC loading for I girder then, according to graph a multiplication factor of 0.85 should be multiplied with IRC loading for a 60 m span length. Again, referring to fig 6.4for the same case of torsion in I girder a multiplication factor of 0.65 is required.

The conditional assessment, i.e. maximum bending moment, shear force and torsion at varying span length due to various codes has already been discussed(CHAPTER 6, 6.1) and can be analyzed from fig. 6.8 to fig. 6.13.

The serviceability condition for various span lengths and lanes can be taken from fig. 6.1.Since it is known that vehicle frequency lies between 3-5 Hz, so it can be seen from the graph that the span length and no. of lanes coming in the range of 3-5 Hz will give serviceability problems. So we have to choose accordingly.

REFERENCES

IRC:6-2014. Indian road standards for loading.

IRC 112-2011. Indian bridge design code.

AASHTO16-AAC load handbook on LRFD and STD specifications.

EN 1991-2. European standards for bridge loads.

“Assessment of vehicular live load and load factors for design of short-span bridges according to the new Egyptian Code” Hatem M. Seliem ,Mostafa Eid, Alaa G. Sherif

“Static Test Analysis of a Bridge Structure in Civil Engineering” Jiamei Zhao a,b,, Tao Liu c, Yuliang Wang.

“Seismic Response Analysis of Yachi River Super-large Bridge” Wen-xiu Liua, Bing Zhub, Zhang-liang Yuc and Xing Hand

“Dynamic Analysis of Curved Continuous Multiple-Box Girder Bridges” Magdy Samaan1; John B. Kennedy, F.ASCE2; and Khaled Sennah,

Use of I-Beam Grillages and Box Girders in High Speed Railway Projects Marco Rosignoli

“Analysis of Bridge Performance under the Combined Effect of Earthquake and Flood-induced Scour” Swagata Banerjee1 and Gautham G. Prasad2

“A Study on Simple Beam Bridge Responses Due to Thai Truck Loads” Suniti Suparpa, Panuwat Joyklada

“Finite element analysis of curved steel girders with tubular flanges” Jun Donga,Richard Sause

“Dynamic analysis of T-Beam bridge superstructure ” Supriya Madda1, Kalyanshetti M.G

CSi bridges 2015, “Structural Analysis Program”, Integrated software for structural analysis and design.

CSI Analysis Reference Manual for CSi bridges®.