impact on bus superstructure due to rollover md. liakat ali universiti

IMPACT ON BUS SUPERSTRUCTURE DUE

TO ROLLOVER

MD. LIAKAT ALI

UNIVERSITI TEKNOLOGI MALAYSIA

IMPACT ON BUS SUPERSTRUCTURE DUE TO ROLLOVER

MD. LIAKAT ALI

A thesis submitted in fulfilment of the

requirements for the award of the degree of

Master of Engineering (Mechanical Engineering)

Faculty of Mechanical Engineering

Universiti Teknologi Malaysia

NOVEMBER 2008

iii

To my beloved father, mother, brother, sister and all of my teachers who have

inspired and guided me to continue higher education.

iv

ACKNOWLEDGEMENT

The successful completion of a project mostly requires help and cooperation

from other people. Here, I would like to express my heartiest gratitude to my

supervisors Assoc. Prof. Mustafa Bin Yusof and Prof. Dr. Roslan Bin Abdul

Rahman, the members of the panel of evaluation Prof. Dr. Mohd Nasir Bin Tamin,

Dr. Amran Bin Ayob, the research students of CSM Laboratory Farizana bt Jaswadi,

Lai Zheng Bo, Fethma M. Nor, Hassan Othman and all other laboratory technicians

of the Faculty of Mechanical Engineering, Universiti Teknologi Malaysia. I am

grateful to them for their contribution to complete the project successfully.

v

ABSTRACT

Bus is a popular and common transport in the world. The safety of bus

journey is a fundamental concern. The risk of injuries and fatalities is severe when

the bus structure fails during a rollover accident. Adequate design and sufficient

strength of the bus superstructure can reduce the number of injuries and fatalities.

This study examines the deformation response of a typical bus structure during a

rollover test simulation. A simplified box structure was modeled using finite

element analysis software and simulated in a rollover condition according to the

requirements of UNECE Regulation 66. The same box model was fabricated to

validate the results obtained from finite element analysis simulation. After

successful validation of the box model simulation, a complete bus structure with

forty four passengers’ capability was developed using finite element analysis

software. The simulation of the bus was conducted using the same inputs used in

box model simulation. Four simulations have been conducted to get the dimensions

of different members of the superstructure of bus which is capable to protect rollover

crash. The analysis suggested that, the failure of bus frame during rollover situation

is basically dependent on the total mass of bus and on the strength of bus

superstructure.

VI

ABSTRAK

Diantara jenis-jenis pengangkutan awam , penggunaan bas awam telah menjadi

pilihan dan penting di mata masyarakat dunia. Oleh kerana itu faktor keselamatan dari

segi struktur bas berkenaan menjadi keperluan utama di dalam proses mereka bentuk

sesebuah bas. Kebanyakkan kecederaan dan kemalangan maut berpunca daripada

kegagalan struktur bas apabila kemalangan yang melibatkan bas berkenaan terbalik.

Kajian ini adalah bertujuan meyelidik kekuatan rangka bas dalam meyediakan

melindungi penumpang apabila kemalangan berlaku. Satu model keberkesanan telah

diterbitkan menggunakan kaedah unsur terhingga dan simulasi model ini dilakukan

mengikut piawai yang telah ditentukan oleh peraturan 66 UNECE. Model bas berkenaan

telah dihasilkan di dalam makmal bagi menentu-sahkan analisis yang menggunakan

kaedah unsur terhingga. Setelah berjaya proses menentu-sahkan analisis berkenaan,

model simulasi bas dengan 44 penumpang telah dijalankan.Sebanyak 4 proses simulasi

telah dijalankan untuk mendapatkan perihal atau kelakuan rangka bas yang pelbagai

mengikut keadaan. Berdasarkan kajian ini, mendapati bahawa kegagalan sesuatu rangka

bas apabila kemalangan melibatkan bas terbalik, adalah bergantung kepada jumlah berat

tanggungan dan kekuatan rangka bas berkenaan.

vii

TABLE OF CONTENTS

CHAPTER TITLE PAGE

DECLARATION ii

DEDICATION iii

ACKNOWLEDGEMENT iv

ABSTRACT v

ABSTRAK vi

TABLE OF CONTENTS vii

LIST OF TABLES x

LIST OF FIGURES xi

LIST OF ABBREVIATIONS xiv

LIST OF SYMBOLS xv

LIST OF APPENDICES

1 INTRODUCTION

1.1 Background 1

1.2 Problem Statement 4

1.3 Objective of Study 6

1.4 Scope of Project 6

2 LITERATURE REVIEW

2.1 Introduction 7

2.2 Previous Studies 7

3 RESEARCH METHODOLOGY

3.1 Research Methodology 12

3.1.1 The Steps of Analyses 14

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3.2 Finite Element Analysis 15

3.3 A Simple Example of Finite Element

Analysis 15

3.3.1 Potential Energy Approach 20

3.4 Theory of Vibration 23

3.4.1 Natural Frequency of Free

Transverse Vibration 23

3.4.2 Natural Frequency of Free

Longitudinal Vibration 25

3.5 Modal Analysis 27

3.7 Residual Space in Bus 28

4 RESULTS 4.1 Introduction 31

4.2 Simulation of Box Model 32

4.2.1 Inputs Used in Simulation 33

4.2.2 Results of Simulation 40

4.3 Simulation of Box Model to Extract

Natural Frequency and Mode Shape 43

4.3.1 Inputs Used in Simulation 43

4.3.2 Results of Simulation 45

4.4 Validation of Box Model Simulation 47

4.4.1 Results of Rollover Experiment 47

4.5 Numerical Analysis of Box Model 49

4.6 Simulation of Bus Prototype 52

4.7 Results of Bus Simulation 55

4.7.1 Simulation of Bus with More

Passenger Load 55

4.7.2 Simulation with More Structural

Strength 58

4.7.3 Simulation of Bus with less

Total Mass 60

ix

4.7.4 Simulation of Bus with Less

Passenger Load 63

5 DISCUSSION

5.1 Introduction 67

5.2 Analysis of the Results 67

6 CONCLUSION

6.1 Conclusion on Bus Structure 71

6.2 Recommendation for Future Study 71

REFERENCES 72

Appendix 76

Bibliography 83

x

LIST OF TABLES

TABLE NO. TITLE PAGE

3.1 The values of shape functions 30

4.1 Dimensions of box model 32

4.2 Dimensions of box profile 34

4.3 Properties of mesh 36

4.4 The comparison between two element libraries of Abaqus 37

4.5 Dimensions of bus prototype 53

4.6 Different masses of bus prototype 53







5.1 Variation of maximum stress with total mass of bus 69

1 The plastic properties of mild steel 76

2 Values of stain obtained from TML Portable Data Logger 76

3 Values of stain obtained from numerical analysis 79

4 Values of stain obtained from UPC 601- G Data Logger 80

5 New values of offsets of the strain gauges 81

6 The values of strains after changing offsets 81

7 The new values of scaling factor for UPC 601- G

Data Logger 82

8 Values of strain after calibration from UPC 601- G

Data Logger 82

xi

LIST OF FIGURES

FIGURE NO. TITLE PAGE

1.1 Trip over of a vehicle on road surface 2

1.2 Fall over of vehicle out of road 2

1.3 Flip over of vehicle on road surface 2

1.4 Bounce over of vehicle after facing impact sidewise 3

1.5 Turn over motion of vehicle 3

1.6 Climb over situation of vehicle 4

1.7 End-over-end motion of vehicle 4

1.8 A bus has faced rollover 5

1.9 The damage of a bus frame after rollover crash 5

3.1 Flowchart of the steps of analyses 14

3.2 A simply supported beam with two types of loads 15

3.3 Deformation of beam neutral axis 16

3.4 The stress distribution in the beam transverse plane 16

3.5 Finite element discretization in global coordinate 17

3.6 Finite element discretization in local coordinate 17

3.7 Interpretation of Hermit shape function 18

3.8 Natural frequency of free transverse vibration of a

cantilever beam 24

3.9 Natural frequency of free longitudinal vibration of a

spring-mass system 25

3.10 Lateral arrangements of residual space inside the bus 29

3.11 Longitudinal arrangements of residual space inside a bus 29

4.1 Three dimensional view of the box model used in simulation 32

4.2 Two dimensional view of the box model used in simulation 33

4.3 The stress-strain plot of mild steel 34

xii


4.4 The box profile used in all members of box model and in

some members bus model 35

4.5 The deformation of cross section of Timoshenko beam 38

4.6 Linear brick, quadratic brick, and modified tetrahedral

elements 40

4.7 Maximum deformation of box model during rollover motion 40

4.8 Maximum stress and its location in the box model 41

4.9 Plot of total energy (TE) of the box model simulation 41

4.10 Plot of kinetic energy (KE) of the bus model simulation 42

4.11 Plot of internal energy (IE) of the bus model simulation 42

4.12 Plot of linear velocity of the bus model in rollover simulation 44

4.13 Plot of angular velocity of the bus model in rollover

Simulation 44

4.14 The first mode of the model during first impact 46

4.15 The second mode of the model during first impact 46

4.16 The third mode of the model during first impact 46

4.17 The box model used in the experiment of validation 47

4.18 The plot of strain obtained from dynamic strain

measuring system 48

4.19 The position of critical deformation in the box model

during rollover test 48

4.20 (a) position of box model before first impact, (b) position

of box model during first impact (c) position of box model

just after first impact and (d) the model is in rest after rollover

process 49

4.21 The centre of gravity of the box model 50

4.22 The position of box model before rolling over 51

4.23 The position of box model during rolling over 52

4.24 The left side view of bus frame used in simulation 53

4.25 The isometric view of bus prototype used in simulation 54

4.26 The isometric view of bus prototype placed on the ditch by

an angle of 53 degree with vertical plane before simulation 54

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4.27 The deformation of superstructure of bus during first

impact of rollover 56

4.28 Plot of kinetic energy (KE) of the bus simulation 56

4.29 Plot of Internal energy (IE) of the bus simulation 57

4.30 Plot of total energy (TE) of the bus simulation 57




4.33 Plot of internal energy (IE) of the bus simulation 60







4.39 The deformation of superstructure of bus during first impact

of rollover 65




5.1 The plot of total mass vs. maximum stress 69

xiv

LIST OF ABBREVIATIONS

NHTSA - National Highway Traffic Safety Administration

CG - Center of Gravity

ADR - Australian Design Rule

UN-ECE - United Nations Economic Commission for Europe

ELR - Emergency Locking Retractors

MDOF - Multi-Degrees of Freedom

TE - Total Energy

KE - Kinetic Energy

IE - Internal Energy

SG - Strain Gauge

xv

LIST OF SYMBOLS

L, l - Length

E - Modulus of Elasticity

A - Area

F - Force

D, d - Diameter

K - Stiffness

δ - Static Deflection

m - Mass

g - Constant due to Gravity

t - Time

fn - Natural Frequency (Hz)

tp - Time Period

W - Weight

ω - Natural Frequency (rad/s)

SR - Residual Space

H - Height

xvi

LIST OF APPENDICES

APPENDIX TITLE PAGE

A The plastic properties of mild steel 76

B Calibration of UPC 601- G (Dynamic Strain

Measuring Instrument) 77

CHAPTER 1

INTRODUCTION

1.1 Background Nowadays, highway traffic safety is a very important issue over the world.

Everyday a noticeable number of vehicles are facing different types of accidents.

Rollover is one of the severe types of accidents. Accidents due to rollover are very

frequent over the world. Rollover fatalities have become a major safety issue. Most

rollover crashes occur when a vehicle runs off the road or rotate sidewise on the road

by a ditch, curb, soft soil, or other objects. Besides, the forward speed as well as the

sideways speed of a vehicle causes rollover that greatly increases the extent of

damage to the vehicle and its occupants during rollover.

Rollover accidents are also very common and frequent in Malaysia. In most

of the rollover accidents of buses, its roof faces strong impact with the surface of

road. However, this impact leads to collapse of bus roof causing severe injury to the

occupants and extreme damage to the frame of bus. National Highway Traffic

Safety Administration (NHTSA, 2002 b), USA, reported that only about 3% of all

crashes are rollovers that caused 33% of total crash related deaths. This example

clearly showed the severity of rollover crashes compared to other types of crashes.

Rollover may be of different types depending on the reasons that commence

it. The definitions include the following factors:

(i) Trip-over: If the lateral motion of the vehicle is suddenly slowed or

stopped, it increases the tendency to rollover of bus. The opposing

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force may be produced by a curb, pot-hole or pavement in which the bus

wheels dig into.

Figure 1.1: Trip over of a vehicle on road surface.

(ii) Fall-over: This type of rollover occurs when the road surface, on which

the bus is traveling, slopes downward in the direction of movement of

the vehicle such that the center of gravity (c. g.) becomes outboard of its

wheels (the distinction between this code and turn-over is a negative

slope).

Figure 1.2: Fall over of vehicle out of road.

(iii) Flip-over: When a vehicle is rotated along its longitudinal axis by a

ramp-like object such as a turned down guardrail or the back slope of a

ditch. The vehicle may be in yaw when it comes in contact with a

ramp-like object.

Figure 1.3: Flip over of vehicle on road surface.

3

(iv) Bounce-over: When a vehicle rebounds off a fixed object and overturns

as a consequence. The rollover must occur in close proximity to the

object from which it is deflected.

Figure 1.4: Bounce over of vehicle after facing impact sidewise.

(v) Turn-over: When centrifugal forces from a sharp turn or vehicle rotation

is resisted by normal surface friction (most common for vehicle with

higher distance between road surface and c. g.). The surface includes

pavement surface and gravel, grass, dirt, etc. There is no furrowing and

gouging at the point of impact. If rotation and/or surface friction causes

a trip, the rollover is classified as a turn-over.

Figure 1.5: Turn over motion of vehicle.

(vi) Collision with another vehicle: when a vehicle impacts sidewise with

another vehicle, it causes rollover. Mostly, rollover is the immediate

result of an impact between two vehicles.

(vii) Climb-over: when vehicle climbs over a fixed object (e.g. guard rail,

barrier) that is high enough to lift the vehicle completely off the ground,

the vehicle must roll on the opposite side from which it approached the

object.

4

Figure 1.6: Climb over situation of vehicle.

(viii) End-over-end: when a vehicle rolls primarily about its lateral axis, i.e.

the pitch motion of a vehicle is called end-over-end.

Figure 1.7: End-over-end motion of vehicle.

1.2 Problem Statement

Rollover crashes cause extreme damage to both of the occupants and to the

bus frame in several ways. Firstly, when a bus faces rollover, its roof impacts with

the surface of road. If the roof of bus is not enough strong to withstand that impact, it

collapses and presses the occupants on the seats (Figure 1.8 and Figure 1.9).

Secondly, if the roof of bus is too rigid to resist the force of impact, it does not

collapse. However, the inertia of occupants produces high speed to them and presses

them with the roof. In the second case, the extent and the number of injuries can be

decreased by using seat belt with sufficient strength. In contrast, in the first case

there is no way to protect occupants from serious injuries. Because if the roof of bus

fails, then the occupants must be pressed on the seats.

5

Figure 1.8: The severe damage of bus after rollover accident (Courtesy of

www.thestar.com.my).

Figure 1.9: The damage of a bus frame after rollover crash (Courtesy of

www.thestar.com.my).

From the above discussion, it is clear that, the effect of rollover on the

superstructure of bus and the detailed analysis of that is very important to decrease

the extremity of damages on both of the occupants and the bus frame.

http://www.thestar.com.my/

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1.3 Objective of Study

The objective of the project includes the investigation of the effects of initial

impact due to rollover of a bus on its frame according to UN-ECE Regulation 66.

Initial impact indicates the first impact of the bus frame with the surface of ground.

Main focus is given on the impact of a bus with road surface only. The impacts of

bus frame due to rollover with other materials are not included.

1.4 Scope of Project

The scope of the project includes the following analyses.

(i) Simulation of bus frame: It includes the simulation of bus frame using

appropriate finite element analysis software to observe the effects of

initial impact due to rollover.

(ii) Numerical analysis: It includes to analyze the box model for potential

energy, kinetic energy and centre of gravity during rollover motion.

(iii) Dynamic analysis: This part is related to investigate the natural

frequencies and mode shapes of box frame during first impact of

rollover.

(iv) Rollover test: Experiment is to carry out on a simple box model to check

the reliability and acceptability of the results obtained from the

simulation of same model.

(v) To suggest the possible and relevant improvements in the design of bus

frame to prevent the damage of rollover crash.

CHAPTER 2

LITERATURE REVIEW

2.1 Introduction

In past years, many researches have been carried out on rollover of bus. In

most of researches, importance was given on the extent of damage of rollover instead

of the reasons of damage. However, it must be more important to draw more

attention on the reasons of fatalities and injuries due to rollover, i.e. what are the

drawbacks in the design of bus frame as well as in the superstructure of bus.

2.2 Previous Studies

So many researches have been carried out on rollover of different vehicles.

Some of those researches are briefly cited in this section. Kecman, D., and Tidbury,

G. H. [1] presented a pioneer research on how to calculate different parameters for

the certification of rollover related issues which was accepted as a base of ECE

Regulation 66. The authors concluded that, finite element analysis is a cost effective

way of describing bus structures to comply with the new bus structure strength in

rollover requirements. White, D. M. [2] worked on the rollover accident simulation

program (RASP) developed to study design factors which affect rollover stability.

The main parameter investigated were spring stiffness, height of CG and roll

movement of inertia. The height of CG was the most critical factor affecting rollover

harms.

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Kumagai et al., [3] simulated a bus using full FEA program. The result of full

scale dynamic rollover test of a complete bus to ADR 59 or ECE 66 were used to

verify the predictions of a model based on the dynamic testing of some critical

structural components. A good agreement was shown between the test and the

analysis technique. The same work was done by Niii, N., and Nakagawa, K [4] later

on in 1996. Kecman, D., and Dutton, A.J. [5] described the development of a seat to

meet both the ECE 80 Regualtion (for unbelted occupants) and the ADR 68 (for

belted occupants), which is still commercially feasible in terms of weight and cost.

Initial components were tested and combined with an analytical study using

MADYMO and CRASH-D to optimize the design of a new seat.

Kecman, D., and Randell, N. [6] studied on the methods of structural design

by ECE Regulation 66. Both Quasi-static and full dynamic analysis of the rollover

test can be used for the development of the structure. Quasi-static analysis still

appears to be more reliable for type approval process. Botto et al. [7] described an

analysis of eleven rollover accidents from a sample of seventy eight bus collisions

occurred in France. A total of 2925 occupants were involved. Frontal impact were

found as most severe one accounting 44.9 % bus collisions and there were 41 %

rollovers described as either trip over, flip over or rollover depending on the extent

of the roll of bus.

Rasenack et al. [8] presented a survey of bus collision between 1985-1993 in

Germany. Eight of the collisions were rollovers accounting for 50.2 % of all severe

injuries and 90 % of all fatalities. Vincze-Pap, S. [9] reviewed the experience of

IKARUS Company, a Hungarian bus manufacturer, in the development of test

specifications for coach rollover safety. The paper continued with a comparison of

the four different test methods in the ECE 66 Regulation accepted for type approval

of buses and coaches. Full-scale rollover test on a complete vehicle, rollover test on

body segment or segments, pendulum test on body segment or segments, verification

of superstructure strength by calculation.

Characteristics of on-road rollovers regarding driver input data steering wheel

angle amplitude and steering wheel rate and vehicle response data lateral

9

acceleration, yaw rate, body roll angle and roll rate were presented by Marine, Micky

C., Thomas, Terry M. and Wirth, Jeffrey L. [10]. In order to reduce fatalities and

serious injuries in rollover accidents Wallner, Ed. and Schiffmann, Jan K. [11]

developed an automotive rollover sensor to accurately estimate vehicle roll and pitch

angles to predict timely the initiation of rollover, to eliminate false activation of

safety devices and to function the safety devices properly during airborne conditions

as autonomous as possible. It does not require information from other vehicle

subsystems.

Parenteau, Chantal, Gopal, Madana and Viano, David [12] studied the U.S.

accidents data to determine the impact of occupants with interior and the severity of

injuries for front-seated occupants in rollover. The effects of occupant’s impact with

roof, windshield, interior and pillars were analyzed in their study. Roper, L. David

[13] studied the effect of lateral speed, height of the center of gravity and different

types of road surfaces numerically in his detailed work to investigate the reasons of

rollover that helps to initiate rollover. Ferrer, I., and Miguel, J. L., A [14] presented

a repot on the reasons of fatalities during rollover accidents of high speed buses.

Research concluded that, most of the fatalities were caused due to ejection of

passengers from bus and impact with bus interior.

Parenteau, Chantal S. et al. [15] analyzed different types of rollover accidents

occurred in USA in 1999. According to their conclusion, rollovers were most

commonly induced when the lateral motion of the vehicle was suddenly slowed or

stopped. The performance of ELR's (emergency-locking retractors) in rollover

accidents with an emphasis on vehicle dynamics and occupant kinematics were

studied by Thomas, Terry M. et al. [16]. More emphasis was given on the design of

belt and belt locking system to prevent occupants from impact with interior to reduce

injuries in rollover. Because, occupants without belting are more likely to be injured

than that of belted. The effects of roof crash during rollover accidents were

investigated by Meyer, Steven E. et al. [17]. The result of their investigation was,

reinforced roofs can reduce the severity and number of injuries.

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The behaviors of vehicles under severe maneuvering conditions that may

initiate rollover were studied by Kazemi, Reza and Soltani, K. [18] by using

computer simulation. Design of chassis and the effect of road surface were their

main focus. Meaningful improvements of some design parameters were suggested in

their work. Carlson, Christopher R. and Gerdes, J. Christian [19] developed a

framework for automobile stability control. The framework was then demonstrated

with a roll mode controller which seeks to actively limit the peak roll angle of the

vehicle while simultaneously tracking the driver's yaw rate command.

The mitigation of rollover injuries by increasing roof strength using A-pillar,

roof rail and header intersection was assessed by Bish, Jack et al. [20]. Their

conclusion was to increase the strength of roof sufficiently to prevent roof crash

during rollover that might decrease the degree of fatalities. Etherton, J. R.,

McKenzie, E. A. and Powers, J. R. [21] presented the importance of automatically

deployable rollover protective structure (AutoROPS) for the protection of rollover

accidents and to increase the capability of operating a mower in low clearance

conditions. Viano, David C. and Parenteau, Chantal [22] studied the rollover safety

and statistics of injuries. The main focus of their study was rollover sensing

equipments to activate belt pre-tensioners, roof-rail airbags and convertible pop-up

rollbars that must decrease the number of injuries.

Herbst, Brian et al. [23] studied the effect of roof intrusion and roof contact

injury in rollover. Their suggestion was to use composite sheet metal and epoxy

system as the fabrication material of bus roof. Kasturi, Srinivasan (kash) et al. [24]

investigated the effects of two-point seat belt, three-point seat belt and airbags to

mitigate the injuries of rollover accidents. They found that, seat belts having

stronger and reliable design decrease the number of fatalities and the number of

injuries in rollover. Because, occupant of a particular seat may be escaped from seat

belt if the design is simple and weak. Chang, Wen-Hsian et al. [25] studied the data

obtained from the passengers of an automobile rollover accident to assess the major

injuries of the passengers and the associated risk factors for each type of injury.

They revealed that major injuries were occurred when the passengers of one side

were fallen on the passengers of other side due to rollover of a bus. They suggested

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that, the use of seat belts can decrease the severity of injuries by protecting the

impacts among passengers of a bus.

The necessity of belts to decrease fatalities in rollover crashes was analyzed

by Albertsson, Pontus et al. [26]. The impact with the interior materials was a vital

factor to increase injury in rollover accidents. The reduction of rollover fatalities

regarding ejection of occupants from automobile and providing sufficient restraint to

the kinematics of occupant to restrict impact with interior were investigated by

Meyer, Steven E., Forrest, Steven and Brian, Herbst [27]. The ejection of passengers

from bus causes serious harm to them. They suggested that, using proper restraint

with the frame of bus can protect occupants’ ejection completely.

The rollover phenomenon of car-to-truck involved in front, rear and side

collisions were investigated by Hashemi, S.M.R., Walton, A.C. and Anderson, J. C.

[28]. They gave more focus on structural analysis of truck with respect to the

structural geometry and dimensions of car and under-run protection. The effects of

mass and height of center of gravity on rollover scenario were numerically analyzed

by Castejon, Luis et al. [29]. They found some necessary suggestions to improve the

design of vehicles that might reduce the tendency to rollover. Camera-matching

video analysis techniques were used to quantify the vehicle dynamics and

deformation for a dolly rollover test run in accordance with the SAE recommended

practice J2114 by Rose, Nathan A. et al. [30]. They tried to observe the dynamic

behavior of vehicle during rollover by optical means.

From the above discussion, it is clear that, very few researches have been

carried out on the effects of rollover on the bus frame. Most of the works were

related to the surveying of the number of fatalities. Some of the researches have

been conducted to analyze the reasons of rollover. On the other hand, the

importance of different types of seat belts to prevent occupants from crushing with

interior has been discussed from different points of views. Whereas, the effects of

initial impact on bus frame regarding static and dynamic analysis of bus

superstructure to prevent roof crash during rollover is the main focus of this project.

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CHAPTER 3

RESEARCH METHODOLOGY

3.1 Introduction

The effects of initial impact of rollover on bus frame can be investigated

considering various factors. This project includes static analysis, dynamic analysis,

simulation of bus frame and comparison of numerical results with experimental

results obtained by other people. Static analysis is associated with stress and strain

analysis of bus frame using any suitable finite element analysis software under the

impact load during rollover. Dynamic analysis incorporates natural frequencies and

mode shapes of bus frame using the same software during rollover phenomenon.

Along with these analyses, the simulation of bus frame is to be carried out to

visualize the effects of initial impact of rollover on it by using finite element analysis

software.

Before analyzing the bus frame using finite element analysis software, a

simple structure was designed having almost same material and structural

characteristics with a bus frame. The impact of rollover on the simplified structure

was studied using the same software fulfilling the requirements of UN-ECE

Regulation 66. The same structure was fabricated in laboratory and was taken under

practical experiment to investigate the accuracy of results obtained from numerical

simulation. The validation of bus model simulation was successful regarding two

parameters. An important parameter of validation process was the pattern of rollover

motion. The patterns of rollover motion and its different stages obtained from finite

element analysis software and experiment were very similar. The second parameter

13

of validation was the magnitude of maximum strain and its location associated with

bus model during first impact of rollover. The results obtained from these two

processes were also very similar. Upon successful validation of rollover simulation

of the bus model, the complete bus frame was studied in the same finite element

analysis software using exactly same inputs used in the bus model simulation.

Again, to investigate the accuracy of results obtained from the numerical

analysis of bus frame, a simple analysis of potential energy and kinetic energy were

performed on the same bus frame. Malaysia followed a standard to conduct rollover

experiment and simulation on bus frame to study the effects of rollover impact

related to the strength and safety of bus frame. The name of the standard is UN-ECE

Regulation 66 composed by UN.

Then the results of experimental and numerical analyses were compared to

study and observe the similarities, dissimilarities and the impact of rollover on bus

frame.

14

3.1.1 The Steps of Analyses

Figure 3.1: Flowchart of the steps of analyses.

Box Model

FE Rollover Test

Rollover Test

Stress, Strain Results

Stress, Strain Results

Successful Validation

No

Yes

FE bus structure rollover simulation

Vibration Analysis

Structural Analysis according to UNECE

Regulation 66

15

3.2 Finite Element Analysis

Finite element analysis is a simple, robust and efficient method of obtaining

numerical approximate solution from the mathematical model of a structure. The

essence of the finite element method is to analyze complex mathematical problem

whose solution is difficult to get using other methods. The basic principle of this

method is to decompose a simple or complicated structure into small pieces which is

called ‘element’. The elements are connected by nodes with each other. Numerical

calculations are performed on each of these elements to get an approximate solution

of those elements. Then the solutions of each elements are combined together to

obtain the global approximate solution of the whole structure. The analysis of a

structure using finite element method is carried out in sequential steps as described in

section 3.3.

3.3 A Simple Example of Finite Element Analysis

A simply supported beam subjected to two types of loads is shown in Figure

3.2. The loads are distributed load P over the length L and concentrated load Pm.

Figure 3.2: A simply supported beam with two types of loads.

PmP

L

y

x

16

Due to applied loads shown in Figure 3.2, the beam experiences an in-plane

deformation. The deformation shape of its neutral axis is illustrated in Figure 3.3.

Figure 3.3: Deformation of beam neutral axis.

Deformation at any point is measured by two parameters. The vertical

deflection v and rotational slope v'. The beam cross section is considered symmetric

with respect to the plane of loading. For small deformation elementary beam theory

gives,

Stress, yI

M=σ

Strain, EIMy

E==

σε

Curvature, EIM

dxvd=2

2

Figure 3.4: The stress distribution in the beam transverse plane.

x

y

y

Shear force

Bending moment

Neutral axis

σ

x

vv′

17

The finite element model of the beam is discretized into a number of

elements. Each node has two degrees of freedom. At any node i they are Q2i-1

(vertical deflection) and Q2i (slope or rotation).

Figure 3.5: Finite element discretization in global coordinate.

Figure 3.6: Finite element discretization in local coordinate.

We define Hermite shape functions for interpolating the transverse

+++= [ i = 1, 2, 3, 4]

displacement v along a single beam element. Here a, b, c and d are arbitrary

constants.

32 ξξξ iiiii dcbaH

18

1

Slop=0

Slop=0 H1

ζ=0 ζ= +1 ζ=-1

H2

1

Sl

The four shape functions are given by,

H

Figure 3.7: Interpretation of Hermit shape function.

op= -1 0 2

Slop= 0

-1 +1 0

H3Slop= 0

Slop= 0

1 Slop= 1 Slop= 0 0

H4+1 -1

1 ( ) ( ξξ +−= 2141 2 )

Or, ( )31 =H 32

41 ξξ +−

H

2 ( ) ( 1141 2 +−= ξξ )

Or ( )32H 21

41 ξξξ +−−=

H

3 ( ) ( ξξ −+= 2141 2

)

Or, ( )33H 32

41 ξξ −+=

H

4 ( ) ( 1141 2 −+= ξξ )

Or, ( )34 ξH 21

41 ξξ ++−−=

19

Values of the H at local nodes ξ = -1) and 2' (ξ = +1) are given in Table 3.1.

Table 3.1: The values of shape functions

Vertical deflection can be expressed at any point on a beam element in

i

'1 (

v

terms of Hermite shape functions is as given below,

24231211 )()()(ξξ

ξddvHvH

ddvHvHv +++=

he local-global coordinate relationship can be expressed as,

T

ξ = ( )12

2xx −

( )1xx − 1−

Or, ξ⎟⎠⎞

⎜⎝⎛ −

+⎟⎠⎞

⎜⎝⎛ +

=22

2121 xxxxx

The differentiation of x with respect toξ is obtained as,

( )22

12 elxxddx

=−

=ξ

(3.1)

Equation (3.1) can be converted as,

dxdvl

ddx

dxdv

ddv e .

2. ==ξξ

(3.2)

here, W dxdv at local node 1 is and at 2 is

1'v 2

'v .

1H 1'H 2H 2'H 3H 3'H 4H 3'H X= -1 1 0 0 1 0 0 0 0 X= 1 0 0 0 0 1 0 0 1

20

Therefore, v ( )ξ can now be expressed as,

44332211 22)( qHlqHqHlqHv ee +++=ξ (3.3)

a matrix form equation (3.3) can be expressed as,

(3.4)

Where,

In

[ ]{ }qHv =

[ ] ⎥⎦⎤

⎢⎣⎡= 4321 22

HlHHlHH ee

3.3.1 Potential Energy Approach

Finite element formulation can be obtained for a beam element using the

p

{ }

⎪⎪⎭

⎪⎪⎬

⎫

⎪⎪⎩

⎪⎪⎨

⎧

=

4

3

2

1

vvvv

q

potential energy approach. The total potential energy π of the continuum beam is

given by,

∫ ∑∫ −−⎟⎟⎠

⎞⎜⎜⎝

⎛=

L

mm

m

L

p vPpvdxdxdx

vdEI0 0

2

2

2

21π (3.5)

Where,

∫ ⎟⎟⎠

⎞⎜⎜⎝

⎛Ldx

dxvdEI

0

2

2

2

21 = Internal strain energy

= Potential Energy due to distributed force

∫

Lpvdx

0

21

mm

mvP∑ = Potential energy due to concentrated force

Where, p is the distributed load, is point load, is deflection at point

and ' is slope at point .

expression of stiffness matrix

mp mv m

kv k

The [ ]ek can be obtained for a single beam

element using the potential energy method. The internal strain energy for a beam

element is given by,

∫ ⎟⎟⎠

⎞⎜⎜⎝

⎛=

L

e dxdx

vdEIU0

2

2

2

21 (3.6)

here, W ξdI

dx e

2=

he expression of T 22 dxvd in terms of H, ξ and is given below, el

ξddv

ldxdv

e

2=

2

2

2

22

2 4⎟⎟⎠

⎞⎜⎜⎝

⎛=

ξdvd

ldxvd

e

(3.7)

Substitution of in equation 3.7 and simplification yields, [ ]{ }qHv =

[ ] { }qd

Hdd

Hdl

qdx

vdT

e

T⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛2

2

2

2

4

2

2

2 16ξξ

(3.8)

And,

⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ +

−⎟⎠⎞

⎜⎝⎛ +−

=⎟⎟⎠

⎞⎜⎜⎝

⎛22

3123

2231

23

2

2ee ll

dHd ξξξξξ

(3.9)

22

Substitution of equations (3.8) and (3.9) into equation (3.7) and substitution of

( ) ξdldx e 2= results,

[ ] { }qd

lSymmetric

l

lll

ll

lEIqU

e

e

eee

ee

e

Te ξ

ξ

ξξξ

ξξξξ

ξξξξξξ

∫−

⎥⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

⎟⎠⎞

⎜⎝⎛ +

+−

⎟⎠⎞

⎜⎝⎛ +−

+−−⎟⎠⎞

⎜⎝⎛ +−

+−+−

=1

1

22

2

22

22

22

3

431

)31(83

49

1691)31(

83

431

)31(83

49)31(

83

49

821

tegrating each term in the matrix and considering that, In +

=1 2 2ξξ d ∫−1 3

=1

0ξ

=1

2ξ

ence, the simplified expression of the internal strain energy can be expressed as,

∫−1ξ d

+

∫−1d

+

H

{ } [ ] { }qkqU eTe 2

1= (3.10)

is the element stiffness matrix and is given by, Where [ ]ek

[ ]⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−−−−

−−

=

22

22

3

4626612612

2646612612

eeee

ee

eeee

ee

e

llllll

llllll

lEIk

23

3.4 Theory of Vibration

Every structure has its own natural frequency. The natural frequency of free

Since, this project is related to calculate the natural frequency of free vibration

3.4.1 Natural Frequency of Free Transverse Vibration

A simple cantilever bean under transverse load W is shown in figure 3.6.

= Stiffness of shaft.

e to the weight of the body and load.

vibration of a structure is very important for the stability of it in any assembly.

Natural frequency of any structure should be well known before using it in an

assembly. But the natural frequency of any structure greatly depends on its

boundary conditions. Moreover, the presence of external force again changes the

vibration characteristics of structures. This type of vibration is known as forced

vibration.

of bus frame, the theories of natural frequency of free longitudinal vibration and free

transverse vibration are explained here.

Different symbols are used to represent the following meanings,

s

δ = Static deflection du

x = Displacement of body from mean position at any time t.

m = Mass of body, where m = W/g.

g = Gravitational constant.

24

sx

W

Figure 3.8: Natural frequency of free transverse vibration of a cantilever beam.

Acceleration on the beam = 2

2

dtxdm (3.11)

Restoring force on the beam = -s.x (3.12)

Equating equations 3.11 and 3.12, it can be written that,

xsdt

xdm .2

2

−=

or, 0.2

2

=+ xsdt

xdm

or, 0.2

2

=+ xms

dtxd (3.13)

Hence, the time period and natural frequency of transverse vibrations can be

obtained as,

Time period, smt p π2= (3.14)

And natural frequency, ms

tf

pn π2

11==

or, δπgfn 2

1= (3.15)

Position after time t

δ

x

Mean Position m.d2x/dt2

25

Thus the natural frequency of free transverse vibration of the structure shown

in figure 3.8 can be calculated.

3.4.2 Natural Frequency of Free Longitudinal Vibration

A simple spring-mass system is shown in figure 3.9. One end of the spring is

fixed at a rigid support and another end is carrying a load of W. Different symbols

are used to represent the following meanings,

s = Stiffness of spring.

δ = Static deflection due to the weight of the load.

x = Displacement of body from mean position at any time t.

m = Mass of body, where m = W/g.

g = Gravitational constant.

Figure 3.9: Natural frequency of free longitudinal vibration of a spring-mass system.

At the equilibrium position of the load, the gravitational force W= m.g is

balanced by spring force s.δ. At any time t, if the displacement of the mass is x from

its equilibrium position then the following calculations can be written,

w

Unstrained position

δ

x

s(δ+x)

Equilibrium position

2

2

dtxdm W

26

Restoring force = W-s(δ+x)

= s. δ – s. δ – s.x ; since, W= s. δ.

= -s.x (3.16)

And, accelerating force = mass ×acceleration

= 2

2

dtxdm (3.17)

The following equation can be obtained by equating equations 3.16 and 3.17,

xsdt

xdm .2

2

−=

or, 0.2

2

=+ xsdt

xdm

or, 0.2

2

=+ xms

dtxd (3.18)

Where, angular frequency of the load is,

ms

=ω

Time period is given by,

smt p π2= (3.19)

Natural frequency is expressed as,

ms

tf

pn π2

11==

δπgfn 2

1= (3.20)

Thus the natural frequency of free longitudinal vibration of the structure

shown in figure 3.9 can be calculated.

27

3.5 Modal Analysis

Modal analysis is the process of determining the modes of vibration. It is the

study of the natural characteristic of structure. Modal analysis can be carried out

experimentally and analytically. For experimental type, a modal testing is first

required. Modal testing is a construction of a mathematical model of the vibration

properties and behavior of a structure by experimental means. The vibration

properties are defined by the dynamic parameters natural frequencies, modal

damping at resonance and the vibration pattern or mode shapes for the resonance.

There are three parameters (eigenvalue, percent damping and eigenvector) of

modal analysis in theoretical calculation. These parameters can be obtained by the

following method for multi-degrees of freedom (MDOF) systems. An independent

MDOF system can be considered with N degrees of freedom. The governing

equation of motion of the system can be expressed in matrix form as,

[ ]{ } [ ]{ } { })()()( tftxktxM =+&& (3.21)

Where,

[M] = N×N mass matrix.

[k] = N×N stiffness matrix.

f(t) = N×1 transient applied force matrix.

x(t) = N×1 time dependent displacement matrix.

To determine the natural modal parameters, it is necessary to consider the free

vibration condition. i.e. {f(t)} = 0. Then equation 3.21 is reduced to,

[ ]{ } [ ]{ } 0)()( =+ txktxM && (3.22)

It can be assumed that, a solution of equation 3.22 exists of the form,

{x(t)} = {X}.eiωt (3.23)

28

Where, {X} is an N×1 vector of time independent amplitudes. Thus,

{ } tieXtx ωω }{)( 2−=&& (3.24)

Substitution of equations 3.24 and 3.23 into equation 3.22 yields, [ ] [ ]{ }{ } 02 =− tieXMk ωω (3.25)

For a nontrivial solution and since eiωt ≠ 0, for any instant of time t equation

3.25 can be expressed as,

[ ] [ ]{ }{ } 02 =− XMk ω (3.26)

Since, {X} ≠ 0, then equation 3.26 can be written as,

[ ] [ ]{ } 02 =− Mk ω (3.27)

Equation 3.27 is known as the characteristic equation for the system which

yields N possible positive real solutions ω12, ω2

2, ….. ωN

2 also known as eigenvalues

of equation 3.25. The values of ω1, ω2, ….. ωN are the undamped natural frequencies

of the system. Substituting the values of ω into equation 3.25 and solving for {X}, N

possible vector solutions can be found. These values are known as eigenvectors. In

addition, the eigenvectors represents the mode shapes of the system.

3.6 Residual Space in Bus

According to UN-ECE Regulation 66, a bus design can be approved for

fabrication if the superstructure of the bus is strong enough to maintain a safe

residual space inside the bus for occupants during rollover. The envelope of the

vehicle’s residual space is defined by creating a vertical transverse plane within the

29

vehicle which has the periphery described in Figure 3.10 and moving this plane

through the length of the vehicle as shown in Figure 3.11.

(i) The SR (Residual Space) point located on the seat-back of each outer

forward or rearward facing seat (or assumed seat position) is 500 mm

above the floor under the seat and 150 mm from the inside surface of the

side wall. These dimensions are also be applied in the case of inward facing

seats in their centre planes.

(ii) If the two sides of the vehicle are not symmetrical in respect of floor

arrangement and, therefore, the height of the SR points, the step between the

two floor lines of the residual space shall be taken as the longitudinal

vertical centre plane of the vehicle.

Figure 3.10: Lateral arrangements of residual space inside the bus (Courtesy of UNECE Regulation 66).

Figure 3.11: Longitudinal arrangements of residual space inside a bus (Courtesy of UNECE Regulation 66).

30

(iii) The rearmost position of the residual space is a vertical plane 200 mm

behind the SR point of the rearmost outer seat, or the inner face of the rear

wall of the vehicle if this is less than 200 mm behind that SR point. The

foremost position of the residual space is a vertical plane 600 mm in front

of the SR point of the foremost seat (whether passenger, crew, or driver) in

the vehicle set at its fully forward adjustment. If the rearmost and foremost

seats on the two sides of the vehicle are not in the same transverse planes,

the length of the residual space on each side is to be different.

(iv) The residual space is continuous in the passenger, crew and driver

compartments between its rearmost and foremost plane and is defined by

moving the defined vertical transverse plane through the length of the

vehicle along straight lines through the SR points on both sides of the

vehicle. Behind the rearmost and in front of the foremost seat’s SR point

the straight lines are horizontal.

CHAPTER 4

RESULTS

4.1 Introduction

Simulation is a very important and useful mean to study and examine the

behaviour of a body under some precise conditions. Nowadays, simulation of a bus

has become very popular. Malaysian government has imposed the UN-ECE

regulation 66 for approval of bus regarding rollover safety. Because, the industry

which wants to manufacture and sale bus of any category needs to get approval from

some authorities. Therefore, it has become the easiest way to present a complete

document to the authority collecting results of that test of bus in terms of simulation.

It does not require to manufacture a bus before applying approval to the authority.

Thus, simulation of a bus can save a lot of money of industries. The five basic

methods of UN-ECE Regulation 66 are given below.

(i) Rollover test on full-scale vehicle (basic approval method)

(ii) Rollover test using body sections (equivalent approval method)

(iii) Quasi-static loading test of body sections (equivalent approval method)

(iv) Quasi-static calculation based on testing of components (equivalent

approval method).

(v) Computer simulation of rollover test on complete vehicle (equivalent

approval method).

In this research, computer simulation of complete bus has been carried out as

an equivalent approval method.

32

4.2 Simulation of Box Model

A simplified model of a practical bus was modeled using finite element

analysis software to conduct rollover simulation. The model was designed in such a

way that, it consists of the same type of structural characteristics of a practical bus

frame. The simplified model was designed with the intension to perform practical

rollover test on the same model fabricated by the researcher. The dimensions, three

dimensional view and two dimensional view of the box model are given in Table 4.1,

Figure 4.1 and Figure 4.2.

Table 4.1: Dimensions of box model

Length of model 1 m

Width of model 0.5 m

Height of model 0.75 m

Height of ditch 0.8 m

Figure 4.1: Three-dimensional view of the box model used in simulation.

33

Figure 4.2: Two dimensional view of the box model used in simulation.

4.2.1 Inputs Used in Simulation

The inputs of any simulation play the main role of realistic simulation to get

the results that are very close to the practical results. The following inputs were used

in the simulation of bus model to get acceptable and reliable results.

Material properties of model: material used for box model is mild steel with

Young’s modulus 200 GPa and density 7860 Kg/m3. The stress-strain plot of mild

steel is given in Figure 4.3 and the plastic property of the same material is given in

appendix A.

34

0

125

250

375

500

0 0.05 0.1 0.15 0.2Strain

Von

Mis

es S

tress

(MPa

)

Figure 4.3: The stress-strain plot of mild steel.

Material properties of surface: The material of surface was required to be

very hard to get the behaviour of concrete. To get this property, the Young’s

modulus was used as 200×1012 Pa and the density was used as 7860 Kg/m3.

Cross section profile of the frame: The cross section profile of all members of

the frame was box profile. The values of different dimensions are given in Table 4.2.

Table 4.2: Dimensions of box profile

Dimension Value (m)

a 0.019

b 0.019

Uniform thickness, t 0.0019

35

b t

a

Figure 4.4: The box profile used in all members of box model and in some members

bus model.

Initial Inputs: There were no linear velocity and angular velocity inputs in the

initial step. ‘All with surf’ interaction and ‘ENCASTRE’ boundary conditions were

used as initial inputs.

Interaction Properties: There were two types of contact properties inputs. In

case of tangential behaviour, ‘Penalty’ friction formulation method with 0.4 friction

coefficient and for normal behaviour, ‘hard contact’ pressure overclosure method

allowing separation after contact were used.

Steps: There were two steps used in the simulation. Besides the compulsory

‘initial’ step, ‘Dynamic, Explicit’ step was used with linear bulk viscosity parameter

as 0.06 and quadratic bulk viscosity parameter as 1.2. The values of both of these

two bulk viscosities were set as default by ABAQUS.

Applied load on the model: The gravity load with the value of 9.81 m/s2 was

used on the whole model.

36

Meshing: The properties of mesh are given in Table 4.3.

Table 4.3: Properties of mesh

Element library Standard

Family Beam

Geometric Order Linear

Beam type Shear-flexible

Linear bulk viscosity scaling factor 1.0

Quadratic bulk viscosity scaling factor 1.0

B31 A 2-node linear beam in space

A brief description of the element properties mentioned in Table 4.3 is given

below. There are two built in element libraries in Abaqus. The comparison between

these two libraries are given in Table 4.4.

37

Table 4.4: The comparison between two element libraries of Abaqus

Quantity Abaqus/Standard Abaqus/Explicit

Element

library

Offers an extensive element

library.

Offers an extensive library of

elements well suited for explicit

analyses. The elements available are

a subset of those available in

Abaqus/Standard.

Analysis

procedures

General and linear

perturbation procedures are

available.

General procedures are available.

Material

models

Offers a wide range of

material models.

Similar to those available in

Abaqus/Standard, a notable

difference is that failure material

models are allowed.

Contact

formulation

Has a robust capability for

solving contact problems.

Has a robust contact functionality

that readily solves even the most

complex contact simulations.

Solution

technique

Uses a stiffness-based

solution technique that is

unconditionally stable.

Uses an explicit integration solution

technique that is conditionally

stable.

Disk space

and memory

Due to the large numbers of

iterations possible in an

increment, disk space and

memory usage can be large.

Disk space and memory usage is

typically much smaller than that for

Abaqus/Standard.

38

All beam elements in Abaqus are ‘beam-column’ elements. It means, they

allow axial, bending, and torsional deformation. The Timoshenko beam elements

also consider the effects of transverse shear deformation.

The linear elements (B21 and B31) and the quadratic elements (B22 and B32)

are shear deformable, Timoshenko beams. Thus, they are suitable for modeling both

stout members, in which shear deformation is important, and slender beams in which

shear deformation is not important. The cross-sections of these elements behave in

the same manner as the cross-sections of the thick shell elements, as illustrated in

Figure 4.5.

Figure 4.5: The deformation of cross section of Timoshenko beam.

Abaqus assumes the transverse shear stiffness of these beam elements to be

linear elastic and constant. In addition, these beams are formulated so that their

cross sectional area can change as a function of the axial deformation, an effect that

is considered only in geometrically nonlinear simulations in which the section

Poisson's ratio has a nonzero value. These elements can provide useful results as

long as the cross-section dimensions are less than 1/10 of the typical axial

dimensions of the structure, which is generally considered to be the limit of the

applicability of beam theory. If the beam cross-section does not remain plane under

bending deformation, beam theory is not adequate to model the deformation.

39

Bulk viscosity introduces damping associated with volumetric straining. Its

purpose is to improve the modeling of high-speed dynamic events. Abaqus/Explicit

contains two forms of bulk viscosity, linear and quadratic. Linear bulk viscosity is

included by default in an Abaqus/Explicit analysis. Linear bulk viscosity is found in

all elements and is introduced to damp “ringing” in the highest element frequency.

This damping is sometimes referred to as truncation frequency damping. It

generates a bulk viscosity pressure that is linear in the volumetric strain rate.

The second form of bulk viscosity pressure is found only in solid continuum

elements (except the plane stress element CPS4R). This form is quadratic in the

volumetric strain rate. Quadratic bulk viscosity is applied only if the volumetric

strain rate is compressive.

Displacements, rotations, temperatures and the other degrees of freedom are

calculated only at the nodes of the element. At any other point in the element, the

displacements are obtained by interpolating from the nodal displacements. Usually

the interpolation order is determined by the number of nodes used in the element.

(i) Elements that have nodes only at their corners, such as the 8-node brick

shown in Figure 4.6 (a), use linear interpolation in each direction and are

often called linear elements or first-order elements.

(ii) Elements with mid-side nodes, such as the 20-node brick shown in Figure

4.6 (b), use quadratic interpolation and are often called quadratic elements

or second-order elements.

(iii) Modified triangular or tetrahedral elements with midside nodes, such as the

10-node tetrahedron shown in Figure 4.6 (c), use a modified second-order

interpolation and are often called modified elements or modified second-

order elements.

40

Figure 4.6: Linear brick, quadratic brick, and modified tetrahedral elements.

Abaqus/Standard offers a wide selection of both linear and quadratic

elements. Abaqus/Explicit offers only linear elements, with the exception of the

quadratic beam and modified tetrahedron and triangle elements.

4.2.2 Results of Simulation

A dynamic simulation was performed on the box model using the inputs

described in section 4.2.1 for the duration of 1.5 seconds. The effect of first impact

on the box model due to rollover on the surface was observed. The magnitude and

location of maximum stress and strain obtained from the result of simulation are

given in Figure 4.7 and Figure 4.8.

The magnitude of maximum deformation was obtained as 1.947×10-3 m and

its location is at the superstructure of bus model as shown in Figure 4.7.

Figure 4.7: Maximum deformation of box model during rollover motion.

41

The magnitude of maximum stress was obtained as 280 MPa which is more

than the yield strength of mild steel as shown in Figure 4.8.

Figure 4.8: Maximum stress and its location in the box model.

The plots of total energy (TE), kinetic energy (KE) and internal energy (IE)

found from the result of simulation of bus model extracted at 150 points during the

simulation are shown in Figure 4.9, Figure 4.10 and Figure 4.11.

-4000

0

4000

8000

12000

16000

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Time (Sec)

Tota

l Ene

rgy

(J)

Figure 4.9: Plot of total energy (TE) of the box model simulation.

The plot of total energy shows that, initially the value of total energy is zero.

At time zero of the simulation, the body was in rest with zero kinetic energy and a

maximum of potential energy. When the simulation started, kinetic energy increases

due to increase in velocity. Hence, the total energy increases until the body face

impact with the surface. After facing impact, the kinetic energy was absorbed by the

42

deformation of the box model. The linear and rotational velocities decrease showing

a constant level of total energy.

0

40

80

120

160

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1

Time (Sec)

Kine

tic E

nerg

y (J

)

.6

Figure 4.10: Plot of kinetic energy (KE) of the bus model simulation.

The plot of kinetic energy shows that, initially the value of kinetic energy is

zero. Because, initially there was no velocity with the body. When the simulation

started, the velocity of the body started to increase due to gravity. This in turn,

increases kinetic energy. It becomes maximum when just at the time when the body

faced impact with the surface. After first impact the velocity of the body decreases

dramatically resulting a sharp decrease in kinetic energy. After first impact, the

body started to drop on the surface showing fluctuation in kinetic energy.

-400

0

400

800

1200

1600

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Time (Sec)

Inte

rnal

Ene

rgy

(J)

Figure 4.11: Plot of internal energy (IE) of the bus model simulation.

Figure 4.11 shows that, the value of internal energy remains constant until the

body faced first impact. Before first impact there was no change in the structure

except kinetic energy and potential energy. Kinetic energy and potential energy are

43

not included in internal energy. But, after first impact the kinetic energy of the body

was absorbed by the deformed members resulting sharp increase in internal energy.

After first impact, the body got some permanent deformation and stopped moving

yielding constant value of internal energy.

4.3 Simulation of Box Model to Extract Natural Frequency and Mode Shape

Since the analysis steps in Abaqus to extract natural frequency and mode

shape are different than the steps to extract stress and strain, different simulation was

performed to do that using the same design of box model. To get natural frequencies

and mode shapes where the body is subjected to impact, it is recommended by

Abaqus to do the simulation placing the body on the surface with which it is going to

face impact giving the proper inputs of different parameters.

4.3.1 Inputs Used in Simulation

The following inputs were used in the simulation to get accurate and reliable

results of natural frequencies and mode shapes.

Material properties of model and surface, loading, cross sectional properties

of model elements, boundary condition, interaction property, mesh properties and

dimensions used in the simulation were exactly same that are described in section

4.2.1. The only change in inputs was in initial inputs.

Initial Inputs: The initial inputs are very important in the simulation where

the initial step is assumed at an intermediate state of a dynamic simulation. There

are two very important initial inputs in the simulation of bus model to get practical

result. First one is the linear velocity and second one is the angular velocity of the

body while it is facing impact with the surface. The magnitudes and directions of

44

linear velocity and angular velocity were extracted from the simulation intended to

get stress, strain and energies. The plots of the velocities are shown in Figure 4.12

and Figure 4.13.

-2

0

2

4

0 0.4 0.8 1.2 1.6Time (Sec)

Velo

city

(m/s

)

3.08

Figure 4.12: Plot of linear velocity of the bus model in rollover simulation.

The plot of linear velocity shows a constant velocity (3.08 m/s) after a certain

period. During rollover process, when the body was disengaged from its support and

only the gravitational force was activated the body achieved a constant velocity.

This constant velocity was maintained until the body faced impact with the surface.

Because of the same reason, the plot of angular velocity (Figure 4.13) shows a

constant angular velocity for the same time interval of linear velocity plot.

0

5

10

15

20

25

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Time (Sec)

Ang

ular

Vel

ocity

(Rad

/s)

4.33

Figure 4.13: Plot of angular velocity of the bus model in rollover simulation.

From the plot of linear velocity, it is found that the bus model faced first

impact with ground surface at 0.61 sec after starting the simulation. The linear

velocity along vertically downward direction at 0.61 sec was found as 3.08 m/s. The

45

angular velocity of the bus model at the same time of first impact during the

simulation was found as 4.33 rad/sec. Therefore, the inputs of linear velocity and

angular velocity in the simulation of frequency and mode shape extraction were set

as 3.08 m/s and 4.33 rad / sec respectively.

Steps: There were three steps used in the simulation of frequency and mode

shape extraction. The first step was the inherent ‘initial’ step. Load and interaction

property were applied in this step. The second step was the ‘frequency’ step with

Lanczos eigensolver. The third step was the ‘modal dynamics’ step to extract mode

shapes of the model. The simulation was conducted for 0.02 second. There were 15

modes extracted during this small fraction of time with natural frequency of each

mode.

4.3.2 Results of Simulation

There were two types of results extracted from this simulation. First one is the

natural frequency and the second one is the mode shape. The first three mode shapes

and their natural frequencies are given below.

The first mode, second mode and third mode of the model during first impact

are shown in Figure 4.14, Figure 4.15 and Figure 4.16. The natural frequencies of the

modes were found as 43.36 Hz, 46.45 Hz and 58.57 Hz respectively.

46

Figure 4.14: The first mode of the model during first impact.

Figure 4.15: The second mode of the model during first impact.

Figure 4.16: The third mode of the model during first impact.

47

4.4 Validation of Box Model Simulation

To validate the results of box model simulation obtained from finite element

analysis software, a box model was fabricated with the same dimensions and

material properties (Figure 4.17) of the model used in the simulation. Then rollover

test was carried out on the model meeting all of the necessary requirements of UN-

ECE regulation 66. The strain, natural frequency and the motion of rolling over of

the model were observed during the experiment. A sophisticated instrumentation

system ‘UPC 601-G’ was used to measure dynamic strain at different four positions

on the box model. To measure natural frequency, a dynamic data logger, computer

and accelerometer setup was used during the rollover process. Although it is

recommended by UNECE Regulation 66 that, the rollover motion should be

recorded by two video cameras, one video camera had been used to do that.

Figure 4.17: The box model used in the experiment of validation.

4.4.1 Results of Rollover Experiment

To get accurate result of dynamic strain, a sophisticated calibration of

dynamic strain measuring system was done with static strain measuring data logger.

The process of calibration is described in Appendix B. The plot of the data obtained

from four strain gauges of dynamic strain measuring system are given in Figure 4.18.

48

Strain Vs. Time Plot

0

500

1000

1500

2000

0 20 40 60 80 100 120

Duration of Rollover Motion

Stra

in (m

icon

/mic

ron)

SG-1SG-2SG-3SG-4

Figure 4.18: The plot of strain obtained from dynamic strain measuring system.

From figure 4.18 it is found that, the bus model was subjected to a maximum

strain of 1801 µm at the position of it shown in figure 4.19.

Figure 4.1

test.

The

validation

found from

The zones of critical deformation

9: The position of critical deformation in the box model during rollover

observation of rolling over motion was the most important parameter of

experiment. The four important stages of rollover motion of box model

the video camera are shown in Figure 4.20.

49

(a) (b)

(c) (d)

Figure 4.20: (a) position of box model before first impact, (b) position of box model

during first impact (c) position of box model just after first impact and (d) the model

is in rest after rollover process.

4.5 Numerical Analysis of Box Model

In Figure 4.21, ‘ABCDEF’ represents the left side view of the box model used

in the simulation as well as in the experiment. ‘BE’ represents a stainless steel sheet

metal to add some additional load to the structure. The structure was made of

stainless steel bars of hollow-square profile to represent the superstructure of box

frame. The different dimensions of the structure are given below.

Length of structure = 1.0 m

Width of structure, AF = 0.5 m

Height of structure, AC = 0.75 m

Height of plate, AB = 0.2 m

H and G represent the centre of gravities of the frame and steel plate respectively.

50

Figure 4.21: The centre of gravity of the box model.

Since the structure is uniform and symmetrical, ‘G’ must be the midpoint of

BE and ‘I’ must be the midpoint of ‘AC’.

According to Pythagoras’s theorem,

AH2 = AI 2 + HI 2

Or, AH2 = (0.75/2)2 + (0.5/2)2

Or, AH = 0.45 m

And,

AG2 = AB2 + BG2

Or, AG2 = (0.2)2 + (0.5/2)2

Or, AG = 0.32 m

Mass of the frame m1 = 12.82 Kg

Mass of the plate m2 = 13.36 Kg

Total mass of the model M = 26.18 Kg

The axis of rotation of the frame during rollover test is through the point A

and perpendicular to the surface of paper. If the radius of gyration of the total mass is

A

B

H

C D

I

E G

F

51

‘K’, the concept of radius of gyration can be obtained as,

M×K2 = m1 × AH2 + m2 × AG2

26.18 × K2 = 12.82 × (0.45)2 + 13.36 × 0.322

Or, K = 0.39 m

Hence, the distance K represents the distance of CG of the box model from

point A which is equal to h in Figure 4.22.

CG

Figure 4.22: The position of box model before rolling over.

Let, h = 0 at the surface of ditch and g be the constant of gravity. Then the

total potential energy (PE1) of the model at the time when it was about to start

rollover can be expressed as,

PE1 = M * g* (h + 0.8) J

PE1 = 26.18 × 9.81 × (0.39 + 0.8)

PE1 = 305.62 J

Since the body is in static state, the kinetic energy (KE1) of the model at the

position shown in Figure 4.22 can be found as:

KE1 = 0.0 J

h=0

h

0.8 m

α

52

Figure 4.23: The position of box model during rolling over.

When the body faced impact with the surface, the potential energy must be

convert to kinetic energy, frictional energy loss, sound energy and some other form

of energies. The value of maximum velocity obtained from the results of bus model

simulation was 3.08 m/s. Hence, the value of kinetic energy of the body before

facing impact with the surface can be found as follows:

KE = 2

21 MV

KE = 0.5 × 26.18 × (3.08)2

KE = 124.17 J

4.6 Simulation of Bus Prototype

Validation of box model simulation was conducted to observe the accuracy of

different results obtained from the analysis of finite element analysis software. Upon

satisfactory validation of box model simulation, a bus prototype was modeled

(Figure 4.24, Figure 4.25 and Figure 4.26) to analyze it to meet the requirements of

UN-ECE Regulation 66 with the specifications given in Table 4.5 and Table 4.6.

The passenger capacity of the bus is forty-four in all simulations.

h=0h1θ

53

Table 4.5: Dimensions of bus prototype

Dimension Magnitude (m)

Length 11.14

Width 2.2

Height 2.86

Dimensions of different profiles

used in superstructure

50 mm × 50 mm × 5 mm L-profile

50 mm × 50 mm × 5 mm box profile


Types of beams and columns Fixed-fixed end conditions

Table 4.6: Different masses of bus prototype

Name of Load Mass (Kg.)

Air conditioner unit 210

Fuel tank 253

Engine 500

Passengers, seats and floor 3660

Others 977

Total mass 5600

Figure 4.24: The left side view of bus frame used in simulation.

The bus frame was designed neglecting the masses due to steel sheet to cover

the bus frame, glass of all applications. The distributed loads of engines, different

54

electromechanical fittings, instrument box, air-conditioner etc. were assumed as

dead loads of rectangular solids. The air-conditioner load was assumed only on top

of the roof. All of the beams and columns were used as beam element instead of

truss element. Since, dead loads are of no interest of analysis, the dead loads were

defined as rigid bodies to reduce computational time.

Figure 4.25: The isometric view of bus prototype used in simulation.

Figure 4.26: The isometric view of bus prototype placed on the ditch by an angle of

53 degree with vertical plane before simulation.

To reduce the duration of simulation, small mesh size of about 10 cm was

used in superstructure and comparatively bigger mesh sizes were used in other parts

of the bus prototype. Since the superstructure faced impact with the ground and the

effect of impact on the bus frame was the observation of simulation, small mesh size

55

was used in the superstructure. In contrast, bigger mesh sizes were used in the parts

having no impact with ground surface had less effect on the result of simulation.

All other inputs were same with the inputs of box model simulation described in

section 4.2.1.

4.7 Results of Bus Simulation

The main objective of the simulation of bus prototype is to find a design and

corresponding all dimensions satisfying UN-ECE Regulation 66 of rollover test.

Many simulations were performed using the same bus design changing the strength

of the superstructure and loads of floor and passengers’ seats. Some of the

simulations of bus frame with different strength and passenger load were found that

were capable to preserve residual space inside bus during rollover simulation.

4.7.1 Simulation of Bus with More Passenger Load

The different specifications of the bus prototype used in this simulation are

given in Table 4.5 and Table 4.6. The simulation shows significant deformation of

superstructure as in Figure 4.27. The deformation was such that the bus

superstructure could not preserve safe residual space for passengers. The bus frame

was subjected to a very high Mises stress of 335 MPa which is more than the yield

strength of mild steel. This excessive stress caused some permanent deformation in

the bus frame. Hence, the strength of the superstructure was not sufficient to fulfill

the requirements of residual space of UN-ECE Regulation 66.

56

Critical beams

Figure 4.27: The deformation of superstructure of bus during first impact of rollover.

The plot of kinetic energy (KE), internal energy (IE) and total energy (TE) of

this simulation are given in Figure 4.28, Figure 4.29 and Figure 4.30 respectively.

0.E+00

3.E+07

6.E+07

9.E+07

1.E+08

0 0.5 1 1.5 2 2.5 3

Duration of Simulation (S)

Kin

etic

Ene

rgy

(J)

Figure 4.28: Plot of kinetic energy (KE) of the bus simulation.

57

0.E+00

2.E+07

4.E+07

6.E+07

8.E+07

0 0.5 1 1.5 2 2.5 3


Inte

rnal

Ene

rgy

(J)

Figure 4.29: Plot of Internal energy (IE) of the bus simulation.

0.E+00

4.E+06

8.E+06

1.E+07

0 0.5 1 1.5 2 2.5 3


Tota

l Ene

rgy

(J)

Figure 4.30: Plot of total energy (TE) of the bus simulation.

The physical interpretations of the plot of kinetic energy (Figure 4.28) and

internal energy (Figure 4.29) are same with the explanations of kinetic energy and

internal energy as in section 4.2.2. The only difference is in the plot of total energy

(Figure 4.30). The plot of total energy of box model simulation shows a constant

value after the impacts with the surface. In contrast, the plot of total energy of bus

simulation shows an increasing trend of total energy after impacts. The reason is, in

box model simulation the results are considered for a short period of time after the

body comes to rest and in bus simulation the results are taken before the bus comes

to rest after the rollover process. Since, the bus simulation takes so long time, the

total time of all steps were set to a value which calculates the effect of first impact.

The results of rollover process of bus until the body comes to rest was not

considered. If the data were collected for sufficient long time to record the process

until the bus comes to rest, the plot of total energy must show a constant value after

the impacts with the surface.

58

4.7.2 Simulation with More Structural Strength

Since the strength of superstructure of the bus used in simulation of section

4.7.1 is not sufficiently strong to preserve residual space for passengers, another

simulation was performed with increased dimensions of the superstructure members

that gives increased strength of superstructure. The different specifications of the

bus prototype used in this simulation are given in Table 4.7 and Table 4.8.



Length 11.14

Width 2.2

Height 2.86



65 mm × 65 mm × 5.2 mm L-profile


49.4 mm × 49.4 mm ×3 mm box profile





Fuel tank 253

Engine 500

Passengers, seats and floor 3660

Others 1007

Total mass 5630

The dimensions of different members of superstructure were increased by

twenty percent that increased the total mass of bus prototype by thirty kilograms.

The simulation showed comparatively less deformation of superstructure compared

to the deformation of the simulation of section 4.7.1 as shown in Figure 4.31. The

59

bus frame was subjected to a very high Mises stress of 314 MPa which is more than

the yield strength of mild steel. This excessive stress caused some permanent

deformation in the bus frame. The deformation was such that the bus superstructure

could not preserve safe residual space for passengers as shown in Figure 4.31. So,

the strength of the superstructure was not sufficient to fulfill the requirements of

residual space of UN-ECE Regulation 66.




0.E+00

4.E+07

8.E+07

1.E+08

0 0.5 1 1.5 2 2.5 3


Kin

etic

Ene

rgy

(J)


60

0.E+00

3.E+07

6.E+07

0 0.5 1 1.5 2 2.5

Duration of Simulation

3

(J)

Inte

rnal

Ene

rgy(

J)

Figure 4.33: Plot of internal energy (IE) of the bus simulation.

0.E+00

4.E+06

8.E+06

1.E+07

0 0.5 1 1.5 2 2.5


3

Tota

l Ene

rgy

(J)


The physical interpretations of the plot of kinetic energy (Figure 4.32),

internal energy (Figure 4.33) and total energy (Figure 4.34) are same with the

explanations of kinetic energy, internal energy and total energy as in section 4.7.1.

4.7.3 Simulation of Bus with less Total Mass

Since the strength of the bus prototypes used in the simulations of section

4.7.1 and section 4.7.2 were not sufficiently strong to preserve residual space for

passengers, another simulation was performed with no passenger load and with the

same superstructure strength as in section 4.7.1. Hence, the total mass of the bus

61

was decreased. The different specifications of the bus prototype used in this

simulation are given in Table 4.9 and Table 4.10.



Length 11.14

Width 2.2

Height 2.86










Fuel tank 139

Engine 257

Floor 667

Passenger and seat 0.0

Others 1576

Total mass 2740

The dimensions of different members of superstructure were kept same as in

section 4.7.1. The loads due to passengers and seats were removed to get a light

model. The masses of air-condition unit, engine and fuel tank were also decreased.

Thus the total mass of bus prototype was reduced to 2740 kilograms. The simulation

showed comparatively less deformation of superstructure compared to the

deformation of the simulation of section 4.7.1 and section 4.7.2 as shown in Figure

4.35. The bus frame was subjected to a less Mises stress of 273 MPa compared to

62

preceding simulations, which is more than the yield strength of mild steel. This

stress caused a negligible permanent deformation in the bus frame. The deformation

was such that the bus superstructure was capable to preserve safe residual space for

passengers as shown in Figure 4.35. So, the strength of the superstructure was

enough sufficient to fulfill the requirements of residual space of UN-ECE Regulation

66.




0.E+00

2.E+07

4.E+07

6.E+07

0 0.5 1 1.5 2 2.5 3


Kin

etic

Ene

rgy

(J)


63

-5.E+06

1.E+07

3.E+07

4.E+07

0 0.5 1 1.5 2 2.5 3


Inte

rnal

Ene

rgy

(J)


0.00E+00

1.50E+06

3.00E+06

4.50E+06

0 0.5 1 1.5 2 2.5 3


Tota

l Ene

rgy

(J)




explanations of kinetic energy and internal energy as in section 4.7.1.

4.7.4 Simulation of Bus with Less Passenger Load

Since the strength of the bus prototype used in the simulation of section 4.7.3

was sufficiently strong to preserve residual space for passengers, another simulation

was performed with some passenger load and with the same superstructure strength

as in section 4.7.3. The different specifications of the bus prototype used in this

simulation are given in Table 4.11 and Table 4.12.

64



Length 11.14

Width 2.2

Height 2.86










Fuel tank 139

Engine 257

Floor and seats 2022

Others 1602

Total mass 4100

The dimensions of different members of superstructure were kept same as in

section 4.7.3. The loads due to passenger-seats were given from practical point of

view to get a realistic bus design. The masses of air-condition unit, engine and fuel

tank were kept unchanged with the simulation of section 4.7.3. Thus the total mass

of bus prototype was reduced to 4100 kilograms. The simulation shown a little bit

more deformation of superstructure compared to the deformation of the simulation of

section 4.7.3 as shown in Figure 4.39. The bus frame was subjected to a Mises stress

of 294 MPa, which is more than the yield strength of mild steel. This stress caused a

little bit permanent deformation in the bus frame. The deformation was such that the

bus superstructure was capable to preserve safe residual space for passengers as

shown in Figure 4.38. Hence, the strength of the superstructure was enough

sufficient to fulfill the requirements of residual space of UN-ECE Regulation 66.

65




0.E+00

3.E+07

6.E+07

9.E+07

0 0.5 1 1.5 2 2.5 3


Kin

etic

Ene

rgy

(J)


0.E+00

2.E+07

4.E+07

6.E+07

0 0.5 1 1.5 2 2.5 3


Inte

rnal

Ene

rgy

(J)


66

0.E+00

2.E+06

4.E+06

6.E+06

0 0.5 1 1.5 2 2.5 3


Tota

l Ene

rgy

(J)




explanations of kinetic energy and internal energy as in section 4.7.1.

CHAPTER 5

DISCUSSION

5.1 Introduction

The analysis was conducted to observe the effects of impact due to rollover on

the bus frame by using finite element analysis software. Simulation performed by

finite element analysis software depends on various inputs. Thus, the inputs are the

most important parameters in any simulation. To validate the results of simulations

obtained from finite element analysis software, a validation experiment was

performed on a simplified bus model. The results of validation experiment were

very similar to the results of simulation of the same bus model. Then, the simulation

of a complete bus was carried out to scrutinize the effect of impact due to rollover as

well as the factors that contribute more to the failure of bus frame in rollover

situation.

5.2 Analysis of the Results

The simulation of simple bus model was accomplished for the purpose of

validation of various inputs used in the simulation. The different parameters were

observed in the validation process are deformation of the superstructure and the

pattern of rollover motion of bus model in both of the simulation and experiment.

The maximum deformation of bus frame obtained from finite element analysis

simulation is 1947 µm and that obtained from validation experiment is 1801 µm.

Another important parameter of validation was the type of rollover motion, which

68

was obtained as completely same. This proved that the inputs used in the simulation

of bus model were accurate from practical point of view.

Moreover, the finite element analysis simulation as well as the validation

experiment showed that the bus model was subjected to maximum deformation at its

superstructure. Hence, it can be concluded that intensive care should be drawn on

the strength of superstructure during design process regarding the total mass of bus.

The first three natural frequencies of bus model were found to be as 43.36 Hz,

46.45 Hz and 58.57 Hz respectively. The mode shapes obtained from the simulation

of bus model expressed that, the superstructure of bus faced more deformation

during rollover impact. If the frequency of excitation force during impact due to

rollover coincides with any one of the natural frequencies, the bus frame starts to

vibrate with very high amplitude, which is the severe condition that leads the bus

frame to fail.

The plot of total energy showed that the magnitude of total energy increased

until the bus frame faced impact with ground surface. Initially the body was placed

at a height of 0.8 m and during rolling over motion when it faced impact with the

surface, potential energy was converted into kinetic energy. Hence, the plot of

kinetic energy showed the maximum value of kinetic energy just at the moment of

first impact with the surface. Then the kinetic energy was absorbed by the bus frame

which increased the value of total energy during first impact. The value of kinetic

energy found by numerical analysis of bus model just before the body faced first

impact with surface was 124.17 J and that obtained from finite element analysis

software was 133.751 J. Undoubtedly, it proved the perfect accuracy of finite

element software simulation of bus model.

69

The simulation of the complete bus which is capable to accommodate forty

four passengers was carried out changing total mass of bus and the strength of

superstructure. The results obtained from four different simulations of the complete

bus are given in Table 5.1.

Table 5.1: Variation of maximum stress with total mass of bus

Total Mass (Kg.) Maximum Stress (MPa)

5600 335

5630 314

4100 294

2740 273

270

300

330

2500 4000 5500

Total Mass (Kg)

Max

imum

Str

ess

(MPa

)

Figure 5.1: The plot of total mass vs. maximum stress.

Table 5.1 showed that the magnitude of maximum stress obtained from the

simulation of complete bus decreased with decreasing total mass. The simulation of

bus with a total mass of 5630 Kg. showed that maximum stress obtained from this

simulation was less than that obtained from the simulation of bus with a total mass of

5600 Kg. These two simulations were conducted to observe the effect of the

strength of superstructure keeping the total mass almost same. In these two

simulations, the dimensions of the members of bus superstructure were different. In

case of the bus with total mass of 5630 Kg., the dimensions of different

superstructure members were 20 percent more than that of the bus with total mass

70

5600 Kg. which in turn increased the strength of superstructure. This increased the

total mass of bus by only 30 Kg. yielding a significant decrease in the maximum

stress as well as deformation.

The simulation of bus with a total mass of 4100 Kg. was the most realistic

simulation regarding total mass. In this simulation the loads due to passengers’ seats

and other loads like air-conditioner, engine, fuel tank, battery etc. were set from

practical point of view. The simulation showed that the maximum stress was 294

MPa which is much less than the ultimate strength of mild steel but more than the

yield strength. In contrast, the deformation of bus was in acceptable limit according

to the UN-ECE Regulation 66 preserving safe residual space for passengers.

CHAPTER 6

CONCLUSION

6.1 Conclusion on Bus Structure

The analysis of bus simulation regarding UN-ECE Regulation 66 gives very

useful and fruitful results. It can be concluded that the safe residual space for

passengers inside bus during rollover impact is strongly dependent on some

parameters. The strength of bus superstructure is the most important thing to be

considered in the design process. The total mass and the dimensions of the members

of superstructure should be optimized to get maximum ration of strength to total

mass. For the same superstructure strength, the simulation of bus with more total

mass is not capable to preserve safe residual space during rollover process.

Simulation with more total mass shows abnormal type of rollover motion resulting

more deformation with structural vibration. Hence, the total mass should be as less

as possible keeping sufficient strength of superstructure.

If the air conditioner unit is placed on the roof, it should be as light as

possible. The design should be such that, the CG is as low as possible. It produces

less KE during rollover situation which helps to conserve safe residual space in bus

during first impact even for comparatively weaker superstructure. The simulation of

bus should be performed with maximum expected length and width. The increase in

length of bus by 10 percent does not have significant effect on the deformation of

superstructure during rollover accident. The increase in total mass of bus by 10

percent also does not have significant effect on the deformation of superstructure

during rollover accident.

72

6.2 Recommendation for Future Study

The bus prototype used in the simulations was developed with the same

dimensions of a practical bus model. However, the dead loads of bus were not same

with a practical bus. Although the simulations were performed to observe the effect

of total load on residual space during rollover motion by changing different loads,

the positions of loads can be considered for future studies to make the bus prototype

more realistic.

73

REFERENCES

1. Kecman, D., and Tidbury, G.H., Optimisation of a Bus Superstructure from the

Rollover Safety Point of View. Tenth Intenational technical Conference on

Experimental Safety Vehicles, Oxford, England, 1985.

2. White, D.M., P.S.V. Rollover Stability. Tenth International Technical

Conference on Expemental Safety Vehicles, Oxford, England, 1985.

3. Kumagai, K., Kabeshita, Y., Enomoto, H., and Shimojima, S., An analysis

Method for Rollover Strength of Bus Structures, Fourteenth International

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APPENDIX A

Table 1: The plastic properties of mild steel

Yield Stress (MPa) Plastic Strain (m/m)

200 0.0

210 0.01

220 0.02

230 0.03

240 0.04

250 0.05

260 0.06

270 0.07

280 0.08

290 0.09

300 0.10

310 0.11

325 0.12

340 0.13

360 0.14

380 0.15

400 0.16

78

APPENDIX B

Calibration of UPC 601- G (Dynamic Strain Measuring Instrument)

The accuracy of the results obtained from UPC 601- G depends on the perfect

calibration of the system. The calibration of this instrument was accomplished by

comparing with TML Portable Data Logger (Model TDS - 302), a static data logger.

TML Portable Data Logger is an instrument that gives the value of static strain

directly measured by strain gauge. For the purpose of calibration, four strain gauges

were attached on both sides of a simply supported beam as shown in Figure 1. The

symbol SG in Figure 1 indicates strain gauge.

Figure 1: Positions of strain gauges with a simply supported beam.

The four strain gauges were connected to the data logger (TML Portable Data

Logger) to get static strain of the four positions on the beam. The unit was set as

micron (µm). The results of four stain gauges for four different loads are given in

Table 1.

Table 2: Values of stain obtained from TML Portable Data Logger

Load

(Kg.)

SG-1

(µm)

SG-2

(µm)

SG-3

(µm)

SG-4

(µm)

0.0 0.0 0.0 0.0 0.0

1.0 52 43 46 34

2.0 100 80 75 63

3.0 149 117 110 91

Load SG-4 SG-3

SG-1 SG-2

79

To validate the results obtained from the static data logger, numerical

analyses have been carried out on the strain gauges to obtain the strain readings of all

four strain gauges using the following method.

P

(a) (b)

Figure 2: (a) The loading of a simply supported beam, (b) The cross section of the

beam.

Figure 3: The moment diagram of a simply supported beam.

The formulas used to calculate the strains of all four strain gauges as shown in

Figure 1 are given below.

IMc

=σ (1)

Eσε = (2)

Inserting the value of σ in equation 2 results,

IEMc

=ε (3)

P/2 P/2

L

h

b

c

L

M

80

Where,

M = Moment of applied force

c = Distance between neutral axis and top surface along transverse plane

I = The mass moment of inertial ( m4)

E = The Young’s modulus of elasticity (200 GPa for steel)

σ = Stress (Pa)

ε = Strain

Using the formula of equation 3 the values of strains of all four strain gauges

for four different loadings are given in Table 2.

Table 3: Values of stain obtained from numerical analysis

Load

(Kg.)

SG-1

(µm)

SG-2

(µm)

SG-3

(µm)

SG-4

(µm)

0.0 0.0 0.0 0.0 0.0

1.0 47.53 38.1 48.53 36.75

2.0 95.06 76.2 97.06 73.5

3.0 142.59 114.3 145.6 110.25

81

0

40

80

120

160

0 0.5 1 1.5 2 2.5 3 3.5

Load (Kg)

Stra

in (m

icro

n)

CalculatedSG-1

0

20

40

60

80

100

120

140

0 0.5 1 1.5 2 2.5 3 3.

Load (Kg)

Stra

in

5

(mic

ron)

CalculatedSG-2

(a) (b)

0

20

40

60

80

100

120

140

160

0 0.5 1 1.5 2 2.5 3 3.5

Load (Kg)

Stra

in (m

icro

n)

Calculated

SG-3

0

20

40

60

80

100

120

0 0.5 1 1.5 2 2.5 3 3.5

Load (Kg)

Stra

in (m

icro

n)

Calculated

SG-4

(c) (d)

Figure 4: Comparison between theoretical and experimental results of strain (a)

strain gauge-1, (b) strain gauge-2, (c) strain gauge-3 and (d) strain gauge-4.

Then the static stain measuring instrument was disconnected from the strain

gauges and dynamic strain measuring instrument (UPC 601- G) was connected.

Initially the offsets of all items were set to 1000. The results obtained from the

instrument for four strain gauges keeping the same loading conditions are given in

Table 3.

Table 4: Values of stain obtained from UPC 601- G Data Logger

Load (Kg.) SG-1 SG-2 SG-3 SG-4

0.0 753.2 532.11 -376.5 -621.53 1.0 780.42 552.84 -397.3 -636.78 2.0 804.21 571.45 -413.24 -649.89 3.0 827.7 589.44 -430.92 -663.92

82

The expected value of strains for all strain gauges at 0.0 Kg. load are 0.0.

Since the found strains are not of zero magnitudes at zero load, the offsets were set

to the new values shown in Table 4.7 for each strain gauge.

Table 5: New values of offsets of the strain gauges

SG-1 SG-2 SG-3 SG-4

265 468 1376 1621

After setting these offsets the new results of strain for the same load

conditions obtained were as in Table 5.

Table 6: The values of strains after changing offsets

Load (Kg.) SG-1 SG-2 SG-3 SG-4

0.0 0.2 0.11 -0.5 0.47 1.0 27.42 20.84 -21.3 -14.78 2.0 51.21 39.45 -37.24 -27.89 3.0 74.7 57.44 -54.92 -41.92

The magnitude of strain obtained from TML Portable Data Logger SG-1 for 3

Kg. load was 149 µm. Hence, the value of strain from SG-1 of UPC 601- G Data

Logger for 3 Kg. load must be 149 µm. The following change in scaling factor was

used to do that.

The scaling factor used for SG-1, m = 1000

Value of strain of SG-1, y = 74.7

Value of offset for SG-1, c = 265

From the equation of straight line it can be written that,

y = m*x + c

or, 74.7 = 1000*x + 265

or, x = -0.191

83

To get the value of strain from SG-1 for 3 Kg. load as y = 149, the new value

of scaling factor to be set as:

y = m1* x +c

or, 149 = m1 * (-0.191) + 265

or, m1 = 607.3

In the same process, the new scaling factors of all strain gauges were found as

in Table 6. After setting the values of new scaling factors results of strain obtained

from the UPC 601- G Data Logger are given in Table 7. Thus, the results obtained

from the UPC 601- G Data Logger were in the unit of micrometer (µm). The values

were found with a negligible error from static and dynamic strain measuring

instruments.

Table 7: The new values of scaling factor for UPC 601- G Data Logger

Scaling Factor SG-1 SG-2 SG-3 SG-4

Previous 1000 900 1100 600

New 607.3 770 1143 718

Table 8: Values of strain after calibration from UPC 601- G Data Logger

Load

(Kg.)

SG-1

(µm)

SG-2

(µm)

SG-3

(µm)

SG-4

(µm)

0.0 0.6 -0.9 -0.2 0.67

1.0 51.3 42.4 -43.1 -33.7

2.1 98.1 80.6 -76.7 -64.3

3.0 150.7 116.4 -112.4 -92.5

The streaming mode of the UPC 601- G Data Logger was set in such a way

that it can record 100 data points in around five seconds of time.

84

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1. Norrie, D. H., and Devries, G., An Introduction to Finite Element Analysis, New

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Publishing House (Pvt.) Ltd., 2000.

3. Ross, C.F.T., Finite Element Methods in Structural Mechanics, New York, Ellis

HOrwood Limited, 1985.

4. Reddy, J. N., Finite Element Method, Hightstown, McGraw-Hill Inc., 1984.

5. Nazri, Kamsah, Finite Element Method, 2007, Universiti Teknologi Malaysia.

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impact on bus superstructure due to rollover md. liakat ali universiti