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MODAL ANALYSIS OF VERTICALLY CURVED CONCRETE FLYOVER BRIDGES
ABSTRACT
The effectiveness and sensitivity of vertically curved concrete flyover bridge (VCCFB) profile is presented. Modal analysis was conducted on three VCCFB models; one for a profile achieved using horizontal beams, profile achieved using slightly curved beams and a profile achieved using combination of straight and curved beams. Twelve vibration mode shapes were recorded with corresponding natural frequencies for each model. In each mode, a model with a profile using straight beams were found to have higher natural frequencies with major differences in modes 2, 6 and 8 corresponding to 2.26, 3.01 and 2.87% differences from the model with curved beams respectively. Also, major differences were recorded in modes 2, 3 and 5 corresponding to 6.31, 5.51 and 4.24% differences in natural frequencies from model with combine beams when using CSiBridge (2015) software. Three vehicles were simulated each passing the bridge for a period of 10 seconds per lane at the same speed of 10, 20, 30, 40, 50km/h and at varying vehicular speeds of 45, 50, 60km/h and 60, 65,70km/h respectively. The response spectrum from time history analysis conducted for the three (3) vehicles moving on each of the model were plotted. The vertical component of acceleration was compared with the Irwin (1979) base curve for human perceptibility threshold. The profile achieved using a combination of straight and curved beams were found to induce less vibration compared to profiles achieved using straight and slightly curved beams. These result thus indicate that profiles of VCCFB achieved using combination of straight and slightly curved beams at the cusp induced less vibration compared to profiles achieved with straight or slightly curved beams. As such the use of combine geometry precast beams should be encouraged in achieving vertical profiles for this class of bridges.
TABLE OF CONTENT DECLARATION iv CERTIFICATION v DEDICATION vi ACKNOWLEDGEMENT vii ABSTRACT viii TABLE OF CONTENT ix LIST OF FIGURES xiii
LIST OF TABLES xiiCHAPTER ONE: INTRODUCTION 11
1.2 Problem Statement and Justification 3
1.2.1 Problem Statement of Research 3
1.2.2 Justification of study 3
CHAPTER TWO: LITERATURE REVIEW 5
2.2.1 Structural Dynamics of a Single Degree of Freedom (SDOF) System 7
2.3.2 Structural Dynamics of a Multiple Degree of Freedom System 9
2.6 Natural Frequencies of Bridges 13
2.7 Causes of Dynamic Motion of Civil Engineering Structures 14
2.8 Overview of Code Provisions for Vibration 14
2.8.3 International Organisation for Standardisation Codes 14
2.8.4 British Standards Codes 15
2.9 Human Perceptibility to Traffic-Induced Bridge Vibrations 16
2.10 Finite Element Method: The Big Picture 18
CHAPTER THREE: MATERIALS AND METHODS 19
3.1 Description of Bridge Model 19
3.3.1 Finite element analysis 20
3.4 Steps in Creating Bridge Object Model in CSiBridge Software 20
3.5.1 Definition of Basic properties 23
3.6 Bridge Component Properties 24
3.7 Lane and Vehicle Definitions 24
3.7.2 Bridge object definition 25
3.9.2 Time History Analysis 26
3.9.3 Response Spectrum Analysis 26
3.10 Bridge Response to Varying Vehicular Speed 27
CHAPTER FOUR: RESULTS AND DISCUSSIONS 29
4.1 Results of Modal, Time history and Response Spectrum analysis 29
4.1.1 Modal Analysis Result 29
4.1.2 Bridge-Vehicle response to varying vehicular speed 42
4.1.3 Human perceptibility to vehicular vibration 53
4.2.2 Bridge- vehicle response to vehicular speed 56
4.2.3 Response spectrum curves 56
4.2.4 Human perceptibility to vibration due vehicular speed 56
CHAPTER FIVE: CONCLUSION AND RECOMMENDATIONS 58
CHAPTER ONE INTRODUCTION
1.1 General
The use of Vertically Curved Concrete Flyover Bridge (VCCFB) at interchanges of highway systems is becoming increasingly popular because of increasing demand for curved roadway alignment for the passage of congested traffic as well as modern emphasis on aesthetic consideration. As such the health and performance of such bridges is very important considering the strategic roles they play in our cities.
In advanced countries, Structural Health Monitoring (SHM) systems are Implemented more and more frequently with the aim to safeguarding the safety and service lives of structures especially bridges, because changes in the integrity of the material and / or structural properties of these structures are known to adversely affect their performance which can also be observed from the structures dynamic response such as the modal parameters (Netti et al., 2015).
It is well known that structures can resonate, which means that small forces can result in important deformations, and possibly, damages can be induced in the structure. The Tacoma Narrow suspension bridge disaster (1940) is a typical example of this, it collapsed due to wind-induced vibration (that is flutter). It was situated on the Tacoma Narrows in Puget Sound, near the city of Tacoma, Washington, and the bridge had only been open for traffic a few months after completion (Patrick, 2014).
Vibration is a mechanical phenomenon whereby oscillations occur about a point such as repetitive periodic change in displacement with respect to some reference point. The oscillations may be periodic such as the motion of a pendulum, or random such as the movement of a tyre on a gravel road. Vertical vibrations caused by vehicles are the major causes of significant motions for bridge decks with local vibrations in the neighbourhood of the expansion joints. Bridge vibrations can be stimulated in different ways as a result of pulsating loads that oscillate at the same natural frequency of the structures. This phenomenon can make the bridge to resonate thereby leading to permanent structural damages (Akiije and Omotoso, 2012).
According to David and Joanna (2014) Vibration generated by vehicles traveling at speeds can be a significant issue in considering the design life of highway bridges. Dynamic effects can potentially become more serious if the bridge is old and has been subjected to increases in both magnitude and frequency of loadings during its working life.
Bridges are therefore subjected to dynamic loads, in the form of vehicular traffic, which cause them to vibrate. A moving vehicle on a bridge generates deflections and stresses that are generally greater than those caused by the same vehicular loads applied statically. This is due to the dynamic interaction between the bridge and the vehicle. This interaction is a problem of considerable complexity and its solution is governed by both vehicle and bridge dynamic characteristics. Dynamic behaviours due to vehicles moving across rough surface decks have long been recognized as one of the primary concerns in designing and rating of bridges (Proenca and Fernando, 2005). In spite of its important role, the bridge-vehicle interaction dynamic analysis is hardly taken into consideration in bridge designs because of its considerable complexity. This complex dynamic phenomenon depends on so many parameters including types of bridge, dynamic properties of the bridge, vehicle characteristics, vehicle speeds, vehicle’s moving paths, number of vehicles, road surface roughness, etc., that prevent the interaction analysis (Senthilvasa et al., 2002).
Determination of the dynamic response of structures, especially bridges, has been the topic of numerous studies in recent years; however, the related question of user comfort on these vibrating bridges has received relatively little attention (Awall et al., 2012). A bridge vibration due to moving traffic is important for two reasons: (1) the stresses are increased above those due to static and dynamic load applications. This is normally accounted for by the “impact factor” or “dynamic amplification factor” in the design; (2) Excessive vibration may be noticeable to persons on the bridge. The human body, however, is primarily sensitive to dynamic effects such as acceleration and change of acceleration. Although not related to issues of safety, this may have the psychological effect of impairing public confidence in the structure and, therefore, demands consideration at the design stage (Awall et al., 2012). The basic idea behind modal analysis is that modal parameters (notably modal frequencies, modal shapes, and modal damping) are functions of the physical properties of the structure (mass, damping, and stiffness). Therefore, changes in the physical properties will cause detectable changes in the modal parameters (Zhang and Lynch, 2013).
1.2 Problem Statement and Justification
1.2.1 Problem Statement of Research
Mostly, profiles of Vertically Curved Concrete Flyover Bridges (VCCFB) are constructed using straight precast beams which in most cases provide less smooth profile for the bridges. That is, provide polygonal profile instead of the desired smooth parabolic profile. This type of bridges are mostly associated with problematic expansion joints especially at the cusp of the curve, with conspicuous gapping of the parapet at such locations. By observation at some of these type of bridges, the disparity in width of expansion gap at the cusp is due to the geometry of both the beam (straight) and the bridge as a whole (suppose parabolic). In some of such bridges vehicles moving at certain speed could bounce at each transition of the polygonal end formed by the straight beams. Also, vibrations or motion occurrences that often affects the comfort of bridge users are quite alarming. People without engineering training could easily spot pronounce gaping of parapet at varying elevations and ubiquitous expansion joints deterioration, resulting in unpleasant noise that lowers public confidence. A typical example of interest is the Kawo flyover bridge in Kaduna state, which based on verbal discussion with an Engineer in the design and implementation department of the Kaduna State Ministry of works and transport reveals that, many efforts have been made to provide a lasting solution to the continuous increase in the width of expansion joints which increasingly affects the comfort of users due to increasing vibration effect as a result of impact of tyres on the damage expansion joint, but all effort were not successful (Anonymous, 2015a). Hence, investigating the modal properties as well as dynamic response of different profiles of VCCFB with respect to human perceptibility to vehicular induced vibration is a step to finding best method of achieving profile for vertically curved bridges.
1.2.2 Justification of study
Understanding the dynamic properties of different profiles of VCCFB achieved using beams of different shape is timely. As such, models of VCCFB achieved using straight beams, slightly curved beam and combination of both (straight and curved beams) with the curved beams placed at the cusp of the curve will be studied with respect modal behaviour and human perceptibility to vibration threshold. The outcome of this study will serve as a guide to providing a suitable means of achieving the best profile for VCCFB.
1.3 Aim and Objectives
1.3.1 Aim
The aim of this work is to carryout modal analysis on the effect of vibrations induced by vehicular traffic on different profiles of vertically curved concrete flyover bridges.
1.3.2 Objectives
Objectives of the study are to:
- Conduct Modal analysis on Vertically Curved Concrete Flyover Bridge
- Compare modal parameters of the bridge model with the profile achieved using horizontal beams, and a model with the profile achieved using slightly curved beams.
(iii)Analyse bridge –vehicle response of the three models at varying vehicular velocities
- Identify human perceptibility to vibration for the models at varying vehicular speeds.
- Establish a suitable deck profile for such type of bridges
1.4 Scope and Limitations
1.4.1 Scope
The study will involve modal analysis of VCCFB models, one with the profile achieved using straight beams as it is commonly practiced, a model with the profile achieved with slightly curved beams and a model comprising straight and curved beam (). The analysis will be conducted using the finite element method as packaged in CSiBridge (2015) software. The bridge models will be simulated for all modal parameters at various damping ratios and vehicular velocities.
1.4.2 Limitation
The analysis is limited to models of Vertically Curved Concrete Flyover Bridges with profiles achieved using straight, curved and combination of both beams.
MODAL ANALYSIS OF VERTICALLY CURVED CONCRETE FLYOVER BRIDGES
