Vehicle-Bridge Interaction Dynamics

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Vehicle-Bridge Interaction Dynamics"

Transcription

1 Vehicle-Bridge Interaction Dynamics With Applications to High-Speed Railways Y. B. Yang National Taiwan University, Taiwan J. D. Yau Tamkang University, Taiwan Y. S. Wu Sinotech Engineering Consultants, Ltd., Taiwan World Scientific NEW JERSEY LONDON SINGAPORE BEIJING' SHANGHAI HONGKONG TAIPEI CHENNAI

2 Contents Preface Acknowledgments List of Symbols xv xxi xxiii 1. Introduction Major Considerations Vehicle Models Bridge Models Railway Bridges and Vehicles Methods of Solution Impact Factor and Speed Parameter Concluding Remarks 22 Part I Moving Load Problems Impact Response of Simply-Supported Beams Introduction Simple Beam Subjected to a Single Moving Load Impact Factor for Midpoint Displacement Impact Factor for Midpoint Bending Moment Impact Factor for End Shear Force Simple Beam Subjected to a Series of Moving Loads 45

3 vi Vehicle-Bridge Interaction Dynamics Modeling of Wheel Loads of a Train Method of Solution Phenomenon of Resonance Phenomenon of Cancellation Optimal Design Criteria Illustrative Examples Comparison with Finite Element Solutions Effects of Moving Masses and Damping Effect of Span to Car Length Ratio Concluding Remarks Impact Response of Railway Bridges with Elastic Bearings Introduction Equation of Motion Fundamental Frequency of the Beam Dynamic Response Analysis Phenomena of Resonance and Cancellation Effect of Structural Damping Envelope Formula for Resonance Response Impact Factor and Envelope Impact Formulas Numerical Examples Phenomenon of Resonance Effect of Structural Damping Envelope Impact Formula Concluding Remarks Mechanism of Resonance and Cancellation for Elastically-Supported Beams Introduction Formulation of the Theory Assumed Modal Shape of Vibration Single Moving Load A Series of Moving Loads Conditions of Resonance and Cancellation Mechanism of Resonance and Cancellation 112

4 Contents vii 4.5 Field Measurement of Vibration of Railway Bridges Concluding Remarks Curved Beams Subjected to Vertical and Horizontal Moving Loads Introduction Governing Differential Equations Curved Beam Subjected to a Single Moving Load Vertical Moving Load Horizontal Moving Load Unified Expressions for Vertical and Radial Vibrations Solutions for Multi Moving Loads Conditions of Resonance and Cancellation Numerical Examples Comparison of Analytic with Finite Element Solutions Phenomenon of Cancellation Under Single or Multi Moving Masses Phenomenon of Resonance Under Multi Moving Masses IS Plot Impact Effect Caused by Moving Loads Concluding Remarks 152 Part II Interaction Dynamics Problems Vehicle Bridge Interaction Element Based on Dynamic Condensation Introduction Equations of Motion for the Vehicle and Bridge Element Equations in Incremental Form Equivalent Stiffness Equation for Vehicles Vehicle-Bridge Interaction Element 165

5 viii Vehicle-Bridge Interaction Dynamics 6.6 Incremental Dynamic Analysis with Iterations Equivalent Stiffness Equations for VBI System Procedure of Iterations Numerical Verification Simple Beam Subjected to Moving Sprung Mass Simple Beam Subjected to Moving Train Free-Fixed Beam with Various Models for Moving Vehicles Parametric Studies Models for Bridge, Train and Rail Irregularities Moving Load versus Sprung Mass Model Effect of Rail Irregularities Effect of Ballast Stiffness Effect of Vehicle Suspension Stiffness Effect of Vehicle Suspension Damping Concluding Remarks Vehicle-Bridge Interaction Element Considering Pitching Effect Introduction Equations of Motion for the Vehicle and Bridge Rigid Vehicle-Bridge Interaction Element Equations of Motion for the VBI System Numerical Studies Simple Beam Traveled by a Two-Axle System Simple Beam Traveled by a Train Consisting of Five Identical Cars Riding Comfort in the Presence of Track Irregularities 223

6 Contents ix Effect of Elasticity of the Suspension System Effect of Damping of the Suspension System Effect of Track Irregularity Concluding Remarks 229 Modeling of Vehicle Bridge Interactions by the Concept of Contact Forces Introduction Vehicle Equations and Contact Forces Solution of Contact Forces from Vehicle Equations VBI Element Considering Vertical Contact Forces Only VBI Element Considering General Contact Forces System Equations and Structural Damping Procedure of Time-History Analysis for VBI Systems Numerical Examples and Verification Cantilever Beam Subjected to a Moving Load Cantilever Beam Subjected to a Moving Mass Simple Beam Subjected to a Moving Sprung Mass Simple Beam Subjected to a Moving Rigid Bar Supported by Spring-Dashpot Units Bridge Subjected to a Vehicle in Deceleration Bridges Subjected to a Train Consisting of 10 Identical Cars Concluding Remarks 268

7 x Vehicle-Bridge Interaction Dynamics 9. Vehicle-Rails-Bridge Interaction Two-Dimensional Modeling Introduction Train and Bridge Models and Minimal Bridge Segment Vehicle's Equations of Motion and Contact Forces Rails and Bridge Element Equations Central Finite Rail (CFR) Element and Bridge Element Left Semi-Infinite Rail (LSR) Element Right Semi-Infinite Rail (RSR) Element VRI Element Considering Vertical Contact Forces Only VRI Element Considering General Contact Forces System Equations and Structural Damping Shift of Bridge Segment and Renumbering of Nodal Degrees of Freedom Verification of Proposed Procedure Numerical Studies Steady-State Responses of the Train, Rails and Bridge Impact Response of Rails and Bridge Under Various Train Speeds Response of Train to Track Irregularity and Riding Comfort of Train Effect of the Track System Concluding Remarks Vehicle-Rails-Bridge Interaction Three-Dimensional Modeling Introduction Three-Dimensional Models for Train, Track and Bridge 313

8 Contents xi 10.3 Vehicle Equations and Contact Forces Equations for the Rail and Bridge Elements Central Finite Rail (CFR) Element for Track A Central Finite Rail (CFR) Element for Track B The Bridge Element Left Semi-Infinite Rail (LSR) Element for Track A Right Semi-Infinite Rail (RSR) Element for Track A Left Semi-Infinite Rail (LSR) Element for Track B Right Semi-Infinite Rail (RSR) Element for Track B VRI Element Considering Vertical and Lateral Contact Forces VRI Element Considering General Contact Forces System Equations and Structural Damping Simulation of Track Irregularities Verification of the Proposed Theory and Procedure Dynamic Characteristics of Train-Rails-Bridge Systems Properties of the Railway Vehicles and Bridge Natural Frequencies of the Railway Vehicles and Bridge Dynamic Interactions Between the Train and Bridge Train-Rails-Bridge Interaction Considering Track Irregularities Dynamic Effects Induced by Trains at Different Speeds Response Induced by Two Trains in Crossing

9 xii Vehicle-Bridge Interaction Dynamics Criteria for Derailment and Safety Assessment of Trains Concluding Remarks Stability of Trains Moving over Bridges Shaken by Earthquakes Introduction Analysis Model for Train-Rails-Bridge System Railway-Bridge System with Ground Motions Central Finite Rail (CFR) Element for Track A Central Finite Rail (CFR) Element for Track B Bridge Element Left Semi-Infinite Rail (LSR) Element for Tracks A and B Right Semi-Infinite Rail (RSR) Element for Tracks A and B Method of Analysis Description of Input Earthquake Records Train Resting on Railway Bridge under Earthquake Responses of Bridge and Train Car Contact Forces between Wheels and Rails Maximum YQ Ratio for Wheelsets in Earthquake Stability of an Idle Train under Earthquakes of Various Intensities Trains Moving over Railway Bridges under Earthquakes Responses of Bridge and Train Car Maximum YQ Ratio for Moving Trains in Earthquake Stability Assessment of Moving Trains in Earthquake Concluding Remarks 470

10 Contents xiii Appendix A Derivation of Response Function P\ in Eq. (2.55) 473 Appendix B Newmark's (3 Method 477 Appendix C Appendix D Appendix E Appendix F Appendix G Appendix H Appendix I Appendix J Vertical Frequency of Vibration of Curved Beam 481 Horizontal Frequency of Vibration of Curved Beam 483 Derivation of Residual Vibration for Curved Beam in Eq. (5.53) 485 Beam Element and Structural Damping Matrix 489 F.I Equation of Motion for Beam Element F.2 Structural Damping Matrix 493 Partitioned Matrices and Vector for Vehicle, Eq. (9.4) 497 Related Matrices and Vectors for CFR Element 501 Related Matrices and Vectors for 3D Vehicle Model 503 Mass and Stiffness Matrices for Rail and Bridge Elements 507 J.I Mass and Stiffness Matrices of the CFR Element for Both Tracks 507 J.2 Mass and Stiffness Matrices of the Bridge Element 508

11 xiv Vehicle-Bridge Interaction Dynamics J.3 Mass and Stiffness Matrices for the LSR Element 509 J.4 Mass and Stiffness Matrices of the RSR Element 510 J.5 Related Matrices and Vectors for the Rail Elements 510 References 513 Subject Index 527

DYNAMIC RESPONSE OF VEHICLE-TRACK COUPLING SYSTEM WITH AN INSULATED RAIL JOINT

DYNAMIC RESPONSE OF VEHICLE-TRACK COUPLING SYSTEM WITH AN INSULATED RAIL JOINT 11 th International Conference on Vibration Problems Z. Dimitrovová et al. (eds.) Lisbon, Portugal, 9-12 September 2013 DYNAMIC RESPONSE OF VEHICLE-TRACK COUPLING SYSTEM WITH AN INSULATED RAIL JOINT Ilaria

More information

INTERACTION BETWEEN MOVING VEHICLES AND RAILWAY TRACK AT HIGH SPEED

INTERACTION BETWEEN MOVING VEHICLES AND RAILWAY TRACK AT HIGH SPEED INTERACTION BETWEEN MOVING VEHICLES AND RAILWAY TRACK AT HIGH SPEED Prof.Dr.Ir. C. Esveld Professor of Railway Engineering TU Delft, The Netherlands Dr.Ir. A.W.M. Kok Associate Professor of Railway Engineering

More information

Programming the Finite Element Method

Programming the Finite Element Method Programming the Finite Element Method FOURTH EDITION I. M. Smith University of Manchester, UK D. V. Griffiths Colorado School of Mines, USA John Wiley & Sons, Ltd Contents Preface Acknowledgement xv xvii

More information

EFFECTS ON NUMBER OF CABLES FOR MODAL ANALYSIS OF CABLE-STAYED BRIDGES

EFFECTS ON NUMBER OF CABLES FOR MODAL ANALYSIS OF CABLE-STAYED BRIDGES EFFECTS ON NUMBER OF CABLES FOR MODAL ANALYSIS OF CABLE-STAYED BRIDGES Yang-Cheng Wang Associate Professor & Chairman Department of Civil Engineering Chinese Military Academy Feng-Shan 83000,Taiwan Republic

More information

Dynamic Analysis of the Dortmund University Campus Sky Train

Dynamic Analysis of the Dortmund University Campus Sky Train Dynamic Analysis of the Dortmund University Campus Sky Train Reinhold Meisinger Mechanical Engineering Department Nuremberg University of Applied Sciences Kesslerplatz 12, 90121 Nuremberg, Germany Abstract

More information

FUNDAMENTAL FINITE ELEMENT ANALYSIS AND APPLICATIONS

FUNDAMENTAL FINITE ELEMENT ANALYSIS AND APPLICATIONS FUNDAMENTAL FINITE ELEMENT ANALYSIS AND APPLICATIONS With Mathematica and MATLAB Computations M. ASGHAR BHATTI WILEY JOHN WILEY & SONS, INC. CONTENTS OF THE BOOK WEB SITE PREFACE xi xiii 1 FINITE ELEMENT

More information

DYNAMIC ANALYSIS OF THICK PLATES SUBJECTED TO EARTQUAKE

DYNAMIC ANALYSIS OF THICK PLATES SUBJECTED TO EARTQUAKE DYNAMIC ANALYSIS OF THICK PLATES SUBJECTED TO EARTQUAKE ÖZDEMİR Y. I, AYVAZ Y. Posta Adresi: Department of Civil Engineering, Karadeniz Technical University, 68 Trabzon, TURKEY E-posta: yaprakozdemir@hotmail.com

More information

DEVELOPMENT AND APPLICATIONS OF TUNED/HYBRID MASS DAMPERS USING MULTI-STAGE RUBBER BEARINGS FOR VIBRATION CONTROL OF STRUCTURES

DEVELOPMENT AND APPLICATIONS OF TUNED/HYBRID MASS DAMPERS USING MULTI-STAGE RUBBER BEARINGS FOR VIBRATION CONTROL OF STRUCTURES 13 th World Conference on Earthquake Engineering Vancouver, B.C., Canada August 1-6, 2004 Paper No. 2243 DEVELOPMENT AND APPLICATIONS OF TUNED/HYBRID MASS DAMPERS USING MULTI-STAGE RUBBER BEARINGS FOR

More information

Worked Examples of mathematics used in Civil Engineering

Worked Examples of mathematics used in Civil Engineering Worked Examples of mathematics used in Civil Engineering Worked Example 1: Stage 1 Engineering Surveying (CIV_1010) Tutorial - Transition curves and vertical curves. Worked Example 1 draws from CCEA Advanced

More information

STUDY OF DAM-RESERVOIR DYNAMIC INTERACTION USING VIBRATION TESTS ON A PHYSICAL MODEL

STUDY OF DAM-RESERVOIR DYNAMIC INTERACTION USING VIBRATION TESTS ON A PHYSICAL MODEL STUDY OF DAM-RESERVOIR DYNAMIC INTERACTION USING VIBRATION TESTS ON A PHYSICAL MODEL Paulo Mendes, Instituto Superior de Engenharia de Lisboa, Portugal Sérgio Oliveira, Laboratório Nacional de Engenharia

More information

HAROLD CAMPING i ii iii iv v vi vii viii ix x xi xii 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52

More information

Dispersion diagrams of a water-loaded cylindrical shell obtained from the structural and acoustic responses of the sensor array along the shell

Dispersion diagrams of a water-loaded cylindrical shell obtained from the structural and acoustic responses of the sensor array along the shell Dispersion diagrams of a water-loaded cylindrical shell obtained from the structural and acoustic responses of the sensor array along the shell B.K. Jung ; J. Ryue ; C.S. Hong 3 ; W.B. Jeong ; K.K. Shin

More information

Numerical Methods for Engineers

Numerical Methods for Engineers Steven C. Chapra Berger Chair in Computing and Engineering Tufts University RaymondP. Canale Professor Emeritus of Civil Engineering University of Michigan Numerical Methods for Engineers With Software

More information

THE TIME-DISCRETE METHOD OF LINES FOR OPTIONS AND BONDS

THE TIME-DISCRETE METHOD OF LINES FOR OPTIONS AND BONDS THE TIME-DISCRETE METHOD OF LINES FOR OPTIONS AND BONDS APDEApproach % " 24 BSV ViSfVs^i + pbi

More information

PREDICTION OF MACHINE TOOL SPINDLE S DYNAMICS BASED ON A THERMO-MECHANICAL MODEL

PREDICTION OF MACHINE TOOL SPINDLE S DYNAMICS BASED ON A THERMO-MECHANICAL MODEL PREDICTION OF MACHINE TOOL SPINDLE S DYNAMICS BASED ON A THERMO-MECHANICAL MODEL P. Kolar, T. Holkup Research Center for Manufacturing Technology, Faculty of Mechanical Engineering, CTU in Prague, Czech

More information

Finite Element Method (ENGC 6321) Syllabus. Second Semester 2013-2014

Finite Element Method (ENGC 6321) Syllabus. Second Semester 2013-2014 Finite Element Method Finite Element Method (ENGC 6321) Syllabus Second Semester 2013-2014 Objectives Understand the basic theory of the FEM Know the behaviour and usage of each type of elements covered

More information

ESSENTIAL COMPUTATIONAL FLUID DYNAMICS

ESSENTIAL COMPUTATIONAL FLUID DYNAMICS ESSENTIAL COMPUTATIONAL FLUID DYNAMICS Oleg Zikanov WILEY JOHN WILEY & SONS, INC. CONTENTS PREFACE xv 1 What Is CFD? 1 1.1. Introduction / 1 1.2. Brief History of CFD / 4 1.3. Outline of the Book / 6 References

More information

INTER-NOISE 2007 28-31 AUGUST 2007 ISTANBUL, TURKEY

INTER-NOISE 2007 28-31 AUGUST 2007 ISTANBUL, TURKEY INTER-NOISE 2007 28-31 AUGUST 2007 ISTANBU, TURKEY Force estimation using vibration data Ahmet Ali Uslu a, Kenan Y. Sanliturk b, etin Gül Istanbul Technical University Faculty of echanical Engineering

More information

DYNAMIC ANALYSIS ON STEEL FIBRE

DYNAMIC ANALYSIS ON STEEL FIBRE International Journal of Civil Engineering and Technology (IJCIET) Volume 7, Issue 2, March-April 2016, pp. 179 184, Article ID: IJCIET_07_02_015 Available online at http://www.iaeme.com/ijciet/issues.asp?jtype=ijciet&vtype=7&itype=2

More information

Schneps, Leila; Colmez, Coralie. Math on Trial : How Numbers Get Used and Abused in the Courtroom. New York, NY, USA: Basic Books, 2013. p i.

Schneps, Leila; Colmez, Coralie. Math on Trial : How Numbers Get Used and Abused in the Courtroom. New York, NY, USA: Basic Books, 2013. p i. New York, NY, USA: Basic Books, 2013. p i. http://site.ebrary.com/lib/mcgill/doc?id=10665296&ppg=2 New York, NY, USA: Basic Books, 2013. p ii. http://site.ebrary.com/lib/mcgill/doc?id=10665296&ppg=3 New

More information

! n. Problems and Solutions Section 1.5 (1.66 through 1.74)

! n. Problems and Solutions Section 1.5 (1.66 through 1.74) Problems and Solutions Section.5 (.66 through.74).66 A helicopter landing gear consists of a metal framework rather than the coil spring based suspension system used in a fixed-wing aircraft. The vibration

More information

Addis Ababa University Addis Ababa Institute of Technology (AAiT)

Addis Ababa University Addis Ababa Institute of Technology (AAiT) Addis Ababa University Addis Ababa Institute of Technology (AAiT) School of Mechanical & Industrial Engineering Railway Engineering Stream Effect of Track Stiffness Variation on the Dynamic Response of

More information

Finite Element Formulation for Beams - Handout 2 -

Finite Element Formulation for Beams - Handout 2 - Finite Element Formulation for Beams - Handout 2 - Dr Fehmi Cirak (fc286@) Completed Version Review of Euler-Bernoulli Beam Physical beam model midline Beam domain in three-dimensions Midline, also called

More information

ENTERPRISE. - David L. Olson University of Nebraska, USA. Desheng Dash Wu University of Toronto, Canada. World Scientific

ENTERPRISE. - David L. Olson University of Nebraska, USA. Desheng Dash Wu University of Toronto, Canada. World Scientific Financial Engineering and Risk Management Vol.1 ' ENTERPRISE T - David L. Olson University of Nebraska, USA Desheng Dash Wu University of Toronto, Canada World Scientific NEW JERSEY LONDON SINGAPORE BEIJING

More information

Seismic Response Analysis of the Underwater High-rise Independent Intake Tower. Zhang Liaojun Wu Zuoguo Ye Shangfang Zhang Huixing

Seismic Response Analysis of the Underwater High-rise Independent Intake Tower. Zhang Liaojun Wu Zuoguo Ye Shangfang Zhang Huixing Seismic Response Analysis of the Underwater High-rise Independent Intake Tower Zhang Liaojun Wu Zuoguo Ye Shangfang Zhang Huixing College of Water Conservancy and Hydropower Engineering, Hohai University,Nanjing,China,

More information

Non-hertzian contact model in wheel/rail or vehicle/track system

Non-hertzian contact model in wheel/rail or vehicle/track system XXV Symposium Vibrations in Physical Systems, Poznan Bedlewo, May 15-19, 212 Non-hertzian contact model in wheel/rail or vehicle/track system Bartłomiej DYNIEWICZ Institute of Fundamental Technological

More information

Numerical modeling of dam-reservoir interaction seismic response using the Hybrid Frequency Time Domain (HFTD) method

Numerical modeling of dam-reservoir interaction seismic response using the Hybrid Frequency Time Domain (HFTD) method Numerical modeling of dam-reservoir interaction seismic response using the Hybrid Frequency Time Domain (HFTD) method Graduation Committee: Prof. Dr. A.V. Metrikine Dr. Ir. M.A.N. Hriks Dr. Ir. E.M. Lourens

More information

Study of Analysis System for Bridge Test

Study of Analysis System for Bridge Test Study of Analysis System for Bridge Test Chen Ke, Lu Jian-Ming, Research Institute of Highway, 100088, Beijing, China (chenkezi@163.com, lujianming@263.net) Summary Analysis System for Bridge Test (Chinese

More information

Common Beam Formulas (http://structsource.com/analysis/types/beam.htm)

Common Beam Formulas (http://structsource.com/analysis/types/beam.htm) Common Beam Formulas (http://structsource.com/analysis/types/beam.htm) Beam formulas may be used to determine the deflection, shear and bending moment in a beam based on the applied loading and boundary

More information

Micro Mechanical Transducers

Micro Mechanical Transducers HANDBOOK OF SENSORS AND ACTUATORS 8 Micro Mechanical Transducers Pressure Sensors, Accelerometers and Gyroscopes Min-Hang Bao Department of Electronic Engineering Fudan University Shanghai, China ELSEVIER

More information

Equivalent Spring Stiffness

Equivalent Spring Stiffness Module 7 : Free Undamped Vibration of Single Degree of Freedom Systems; Determination of Natural Frequency ; Equivalent Inertia and Stiffness; Energy Method; Phase Plane Representation. Lecture 13 : Equivalent

More information

Unit 21 Influence Coefficients

Unit 21 Influence Coefficients Unit 21 Influence Coefficients Readings: Rivello 6.6, 6.13 (again), 10.5 Paul A. Lagace, Ph.D. Professor of Aeronautics & Astronautics and Engineering Systems Have considered the vibrational behavior of

More information

Mesh Moving Techniques for Fluid-Structure Interactions With Large Displacements

Mesh Moving Techniques for Fluid-Structure Interactions With Large Displacements K. Stein Department of Physics, Bethel College, St. Paul, MN 55112 T. Tezduyar Mechanical Engineering, Rice University, MS 321, Houston, TX 77005 R. Benney Natick Soldier Center, Natick, MA 01760 Mesh

More information

Glencoe. correlated to SOUTH CAROLINA MATH CURRICULUM STANDARDS GRADE 6 3-3, 5-8 8-4, 8-7 1-6, 4-9

Glencoe. correlated to SOUTH CAROLINA MATH CURRICULUM STANDARDS GRADE 6 3-3, 5-8 8-4, 8-7 1-6, 4-9 Glencoe correlated to SOUTH CAROLINA MATH CURRICULUM STANDARDS GRADE 6 STANDARDS 6-8 Number and Operations (NO) Standard I. Understand numbers, ways of representing numbers, relationships among numbers,

More information

A dynamic model for an asymmetrical vehicle/track system

A dynamic model for an asymmetrical vehicle/track system Journal of Sound and Vibration 267 (23) 591 64 JOURNAL OF SOUND AND VIBRATION www.elsevier.com/locate/jsvi A dynamic model for an asymmetrical vehicle/track system K. Hou*, J. Kalousek, R. Dong 1 Centre

More information

Response to Harmonic Excitation Part 2: Damped Systems

Response to Harmonic Excitation Part 2: Damped Systems Response to Harmonic Excitation Part 2: Damped Systems Part 1 covered the response of a single degree of freedom system to harmonic excitation without considering the effects of damping. However, almost

More information

Analysis of seismic response control for long-span cable-stayed. bridge under traveling wave input *

Analysis of seismic response control for long-span cable-stayed. bridge under traveling wave input * Analysis of seismic response control for long-span cable-stayed bridge under traveling wave input * QI ing-jun, LI iao-jun 2 ( Associate Professor, School of Civil Engineering, Shandong Jianzhu University,

More information

Research Article Dynamic Response Analysis of an Asymmetric Coupled Vehicle-Track System Generated by Voided Elastic Two-Block Sleeper

Research Article Dynamic Response Analysis of an Asymmetric Coupled Vehicle-Track System Generated by Voided Elastic Two-Block Sleeper Shock and Vibration Article ID 526360 Research Article Dynamic Response Analysis of an Asymmetric Coupled Vehicle-Track System Generated by Voided Elastic Two-Block Sleeper Zhenxing He 1 and Xinwen Yang

More information

Spon Press PRESTRESSED CONCRETE DESIGN EUROCODES. University of Glasgow. Department of Civil Engineering. Prabhakara Bhatt LONDON AND NEW YORK

Spon Press PRESTRESSED CONCRETE DESIGN EUROCODES. University of Glasgow. Department of Civil Engineering. Prabhakara Bhatt LONDON AND NEW YORK PRESTRESSED CONCRETE DESIGN TO EUROCODES Prabhakara Bhatt Department of Civil Engineering University of Glasgow Spon Press an imprint of Taytor & Francfe LONDON AND NEW YORK CONTENTS Preface xix Basic

More information

DESIGN AND ANALYSIS OF BRIDGE WITH TWO ENDS FIXED ON VERTICAL WALL USING FINITE ELEMENT ANALYSIS

DESIGN AND ANALYSIS OF BRIDGE WITH TWO ENDS FIXED ON VERTICAL WALL USING FINITE ELEMENT ANALYSIS International Journal of Civil Engineering and Technology (IJCIET) Volume 7, Issue 2, March-April 2016, pp. 34-44, Article ID: IJCIET_07_02_003 Available online at http://www.iaeme.com/ijciet/issues.asp?jtype=ijciet&vtype=7&itype=2

More information

Course in. Nonlinear FEM

Course in. Nonlinear FEM Course in Introduction Outline Lecture 1 Introduction Lecture 2 Geometric nonlinearity Lecture 3 Material nonlinearity Lecture 4 Material nonlinearity continued Lecture 5 Geometric nonlinearity revisited

More information

3-D WAVEGUIDE MODELING AND SIMULATION USING SBFEM

3-D WAVEGUIDE MODELING AND SIMULATION USING SBFEM 3-D WAVEGUIDE MODELING AND SIMULATION USING SBFEM Fabian Krome, Hauke Gravenkamp BAM Federal Institute for Materials Research and Testing, Unter den Eichen 87, 12205 Berlin, Germany email: Fabian.Krome@BAM.de

More information

DYNAMIC RESPONSE OF CONCRETE GRAVITY DAM ON RANDOM SOIL

DYNAMIC RESPONSE OF CONCRETE GRAVITY DAM ON RANDOM SOIL International Journal of Civil Engineering and Technology (IJCIET) Volume 6, Issue 11, Nov 2015, pp. 21-31, Article ID: IJCIET_06_11_003 Available online at http://www.iaeme.com/ijciet/issues.asp?jtype=ijciet&vtype=6&itype=11

More information

Finite Element Model Calibration of a Full Scale Bridge Using Measured Frequency Response Functions

Finite Element Model Calibration of a Full Scale Bridge Using Measured Frequency Response Functions Finite Element Model Calibration of a Full Scale Bridge Using Measured Frequency Response Functions Masoud Sanayei 1 and Jesse D. Sipple 2 1 Professor, Department of Civil and Environmental Engineering,

More information

Relevant parameters for a reference test track Deliverable D1.7

Relevant parameters for a reference test track Deliverable D1.7 RIVAS Railway Induced Vibration Abatement Solutions Collaborative project Relevant parameters for a reference test track Deliverable D1.7 Submission date: 20/08/2012 Project Coordinator: Bernd Asmussen

More information

FXA 2008. UNIT G484 Module 2 4.2.3 Simple Harmonic Oscillations 11. frequency of the applied = natural frequency of the

FXA 2008. UNIT G484 Module 2 4.2.3 Simple Harmonic Oscillations 11. frequency of the applied = natural frequency of the 11 FORCED OSCILLATIONS AND RESONANCE POINTER INSTRUMENTS Analogue ammeter and voltmeters, have CRITICAL DAMPING so as to allow the needle pointer to reach its correct position on the scale after a single

More information

Using Spring-Mass Models to Determine the Dynamic Response of Two-Story Buildings Subjected to Lateral Loads

Using Spring-Mass Models to Determine the Dynamic Response of Two-Story Buildings Subjected to Lateral Loads Using Spring-Mass Models to Determine the Dynamic Response of Two-Story Buildings Subjected to Lateral Loads S.T. De la Cruz, M.A. Rodríguez & V. Hernández Autonomous University of Ciudad Juárez, Ciudad

More information

Nonlinear analysis and form-finding in GSA Training Course

Nonlinear analysis and form-finding in GSA Training Course Nonlinear analysis and form-finding in GSA Training Course Non-linear analysis and form-finding in GSA 1 of 47 Oasys Ltd Non-linear analysis and form-finding in GSA 2 of 47 Using the GSA GsRelax Solver

More information

Concrete Pipe Design Manual INDEX OF CONTENTS. FOREWORD... iii. Chapter 1. INTRODUCTION... 1

Concrete Pipe Design Manual INDEX OF CONTENTS. FOREWORD... iii. Chapter 1. INTRODUCTION... 1 Concrete Pipe Design Manual INDEX OF CONTENTS FOREWORD...... iii Chapter 1. INTRODUCTION... 1 Chapter 2. HYDRAULICS OF SEWERS Sanitary Sewers... 3 Determination of Sewer System Type... 3 Determination

More information

Problem of the gyroscopic stabilizer damping

Problem of the gyroscopic stabilizer damping Applied and Computational Mechanics 3 (2009) 205 212 Problem of the gyroscopic stabilizer damping J. Šklíba a, a Faculty of Mechanical Engineering, Technical University in Liberec, Studentská 2, 461 17,

More information

EVALUATION OF DYNAMIC LOAD ON RAILTRACK SLEEPERS BASED ON VEHICLE-TRACK MODELING AND ANALYSIS

EVALUATION OF DYNAMIC LOAD ON RAILTRACK SLEEPERS BASED ON VEHICLE-TRACK MODELING AND ANALYSIS International Journal of Structural Stability and Dynamics Vol., No. 3 () 355 374 c World Scientific Publishing Company EVALUATION OF DYNAMIC LOAD ON RAILTRACK SLEEPERS BASED ON VEHICLE-TRACK MODELING

More information

Single Axle Running Gears FEBA - a New Concept of Radial Steering

Single Axle Running Gears FEBA - a New Concept of Radial Steering Single Axle Running Gears - a New Concept of Radial Steering Oldrich Polach DaimlerChrysler Rail Systems (Switzerland) Ltd, Winterthur OP BWED, 8-Mai- - Seite 1 - _Milan.ppt Contents Introduction of Adtranz

More information

Design of diaphragm and sheet pile walls. D-Sheet Piling. User Manual

Design of diaphragm and sheet pile walls. D-Sheet Piling. User Manual Design of diaphragm and sheet pile walls D-Sheet Piling User Manual D-SHEET PILING Design of diaphragm and sheet pile walls User Manual Version: 14.1.34974 31 July 2014 D-SHEET PILING, User Manual Published

More information

Gravity Field and Dynamics of the Earth

Gravity Field and Dynamics of the Earth Milan Bursa Karel Pec Gravity Field and Dynamics of the Earth With 89 Figures Springer-Verlag Berlin Heidelberg New York London Paris Tokyo HongKong Barcelona Budapest Preface v Introduction 1 1 Fundamentals

More information

Asymptotic Analysis of Fields in Multi-Structures

Asymptotic Analysis of Fields in Multi-Structures Asymptotic Analysis of Fields in Multi-Structures VLADIMIR KOZLOV Department of Mathematics, Linkoeping University, Sweden VLADIMIR MAZ'YA Department of Mathematics, Linkoeping University, Sweden ALEXANDER

More information

AN INTRODUCTION TO NUMERICAL METHODS AND ANALYSIS

AN INTRODUCTION TO NUMERICAL METHODS AND ANALYSIS AN INTRODUCTION TO NUMERICAL METHODS AND ANALYSIS Revised Edition James Epperson Mathematical Reviews BICENTENNIAL 0, 1 8 0 7 z ewiley wu 2007 r71 BICENTENNIAL WILEY-INTERSCIENCE A John Wiley & Sons, Inc.,

More information

Finite Element Formulation for Plates - Handout 3 -

Finite Element Formulation for Plates - Handout 3 - Finite Element Formulation for Plates - Handout 3 - Dr Fehmi Cirak (fc286@) Completed Version Definitions A plate is a three dimensional solid body with one of the plate dimensions much smaller than the

More information

Finite Elements for 2 D Problems

Finite Elements for 2 D Problems Finite Elements for 2 D Problems General Formula for the Stiffness Matrix Displacements (u, v) in a plane element are interpolated from nodal displacements (ui, vi) using shape functions Ni as follows,

More information

Statistical Characterization of Vehicle and Track Interaction Using Rail Vehicle Response and Track Geometry Measurements

Statistical Characterization of Vehicle and Track Interaction Using Rail Vehicle Response and Track Geometry Measurements Statistical Characterization of Vehicle and Track Interaction Using Rail Vehicle Response and Track Geometry Measurements by Darris L. White Thesis submitted to the Faculty of Virginia Polytechnic Institute

More information

Testing and Analysis to Optimize Transit System Maintenance:

Testing and Analysis to Optimize Transit System Maintenance: Transportation Technology Center, Inc., a subsidiary of the Association of American Railroads Testing and Analysis to Optimize Transit System Maintenance: Charity Ketchum Russell Walker Nicholas Wilson

More information

Calculus C/Multivariate Calculus Advanced Placement G/T Essential Curriculum

Calculus C/Multivariate Calculus Advanced Placement G/T Essential Curriculum Calculus C/Multivariate Calculus Advanced Placement G/T Essential Curriculum UNIT I: The Hyperbolic Functions basic calculus concepts, including techniques for curve sketching, exponential and logarithmic

More information

Back to Elements - Tetrahedra vs. Hexahedra

Back to Elements - Tetrahedra vs. Hexahedra Back to Elements - Tetrahedra vs. Hexahedra Erke Wang, Thomas Nelson, Rainer Rauch CAD-FEM GmbH, Munich, Germany Abstract This paper presents some analytical results and some test results for different

More information

SIMULATING THE DYNAMIC RESPONSE OF DIVINE BRIDGES

SIMULATING THE DYNAMIC RESPONSE OF DIVINE BRIDGES Pages 172-185 SIMULATING THE DYNAMIC RESPONSE OF DIVINE BRIDGES Mark F. Green and Haiyin Xie ABSTRACT This paper presents dynamic models of three bridges tested as part of the recently completed Dynamic

More information

MATHEMATICAL METHODS OF STATISTICS

MATHEMATICAL METHODS OF STATISTICS MATHEMATICAL METHODS OF STATISTICS By HARALD CRAMER TROFESSOK IN THE UNIVERSITY OF STOCKHOLM Princeton PRINCETON UNIVERSITY PRESS 1946 TABLE OF CONTENTS. First Part. MATHEMATICAL INTRODUCTION. CHAPTERS

More information

Chapter 5: Tool Dynamometers

Chapter 5: Tool Dynamometers Chapter 5: Tool Dynamometers LEARNING OBJECTIVES Different types of transducers used in Dynamometers Design Requirements Types of Dynamometers ---------------------------------------------------------------------------------------------------------------------

More information

ANALYSIS OF STRUCTURAL MEMBER SYSTEMS JEROME J. CONNOR NEW YORK : ':,:':,;:::::,,:

ANALYSIS OF STRUCTURAL MEMBER SYSTEMS JEROME J. CONNOR NEW YORK : ':,:':,;:::::,,: ANALYSIS OF JEROME J. CONNOR, Sc.D., Massachusetts Institute of Technology, is Professor of Civil Engineering at Massachusetts Institute of Technology. He has been active in STRUCTURAL MEMBER teaching

More information

DYNAMICAL ANALYSIS OF SILO SURFACE CLEANING ROBOT USING FINITE ELEMENT METHOD

DYNAMICAL ANALYSIS OF SILO SURFACE CLEANING ROBOT USING FINITE ELEMENT METHOD International Journal of Mechanical Engineering and Technology (IJMET) Volume 7, Issue 1, Jan-Feb 2016, pp. 190-202, Article ID: IJMET_07_01_020 Available online at http://www.iaeme.com/ijmet/issues.asp?jtype=ijmet&vtype=7&itype=1

More information

The Basics of FEA Procedure

The Basics of FEA Procedure CHAPTER 2 The Basics of FEA Procedure 2.1 Introduction This chapter discusses the spring element, especially for the purpose of introducing various concepts involved in use of the FEA technique. A spring

More information

ANSYS Tutorial. Modal Analysis

ANSYS Tutorial. Modal Analysis ANSYS Tutorial Slides to accompany lectures in Vibro-Acoustic Desin in Mechanical Systems 2012 by D. W. Herrin Department of Mechanical Enineerin Lexinton, KY 40506-0503 Tel: 859-218-0609 dherrin@enr.uky.edu

More information

SEISMIC ANALYSIS OF A VERTICAL WATER TANK

SEISMIC ANALYSIS OF A VERTICAL WATER TANK SISOM 20 and Session of the Commission of Acoustics, Bucharest 25-26 May SEISMIC ANALYSIS OF A VERTICAL WATER TANK Nicolae ZEMTEV * AMEC NUCLEAR RO e-mail: nicolae.zemtev@amecnuclear.ro The calculation

More information

The coupled vibration analysis for vertical pumps and the pump station

The coupled vibration analysis for vertical pumps and the pump station The coupled vibration analysis for vertical pumps and the pump station Michiko SUGIYAMA EBARA Corporation Shuji YAMASHITA NIPPON STEEL Corporation 24 th INTERNATIONAL PUMP USERS SYMPOSIUM Abstract At the

More information

SEISMIC ANALYSIS OF GROUND SUPPORTED WATER TANK WITH DIFFERENT ASPECT RATIOS

SEISMIC ANALYSIS OF GROUND SUPPORTED WATER TANK WITH DIFFERENT ASPECT RATIOS SEISMIC ANALYSIS OF GROUND SUPPORTED WATER TANK WITH DIFFERENT ASPECT RATIOS Kalyani Vanjari 1, Dr.Prof.R.S.Talikoti 2 1 PG Student, Department of Civil Engineering, Late G.N.Sapkal College of Engineering,

More information

PURCHASING & SUPPLY CHAIN MANAGEMENT

PURCHASING & SUPPLY CHAIN MANAGEMENT FIFTH EDITION PURCHASING & SUPPLY CHAIN MANAGEMENT Analysis, Strategy, Planning and Practice AHJAN J. VAN WEELE Eindhoven University of Technology, The Netherlands ;\ CENGAGE t% Learning" Australia Brazil

More information

SEISMIC DESIGN. Various building codes consider the following categories for the analysis and design for earthquake loading:

SEISMIC DESIGN. Various building codes consider the following categories for the analysis and design for earthquake loading: SEISMIC DESIGN Various building codes consider the following categories for the analysis and design for earthquake loading: 1. Seismic Performance Category (SPC), varies from A to E, depending on how the

More information

Knowledge Management

Knowledge Management Series on Innovation and Knowledge - Vol. 11 Knowledge An Interdisciplinary Perspective Sajjad M Jasimuddin Aberystwyth University, UK World Scientific NEW JERSEY LONDON SINGAPORE BEIJING SHANGHAI HONG

More information

SERVICE MANAGEMENT AN INTEGRATED APPROACH TO SUPPLY CHAIN MANAGEMENT AND OPERATIONS. Cengiz Haksever Barry Render

SERVICE MANAGEMENT AN INTEGRATED APPROACH TO SUPPLY CHAIN MANAGEMENT AND OPERATIONS. Cengiz Haksever Barry Render SERVICE MANAGEMENT AN INTEGRATED APPROACH TO SUPPLY CHAIN MANAGEMENT AND OPERATIONS Cengiz Haksever Barry Render Preface CONTENTS xxi Part I: Understanding Services 1 THE IMPORTANT ROLE SERVICES PLAY IN

More information

New approaches in Eurocode 3 efficient global structural design

New approaches in Eurocode 3 efficient global structural design New approaches in Eurocode 3 efficient global structural design Part 1: 3D model based analysis using general beam-column FEM Ferenc Papp* and József Szalai ** * Associate Professor, Department of Structural

More information

Fundamentals of Heat and Mass Transfer

Fundamentals of Heat and Mass Transfer 2008 AGI-Information Management Consultants May be used for personal purporses only or by libraries associated to dandelon.com network. SIXTH EDITION Fundamentals of Heat and Mass Transfer FRANK P. INCROPERA

More information

Introduction to Robotics Analysis, Systems, Applications

Introduction to Robotics Analysis, Systems, Applications Introduction to Robotics Analysis, Systems, Applications Saeed B. Niku Mechanical Engineering Department California Polytechnic State University San Luis Obispo Technische Urw/carsMt Darmstadt FACHBEREfCH

More information

Wheelset Structural Flexibility and Track Flexibility in Vehicle-Track Dynamic Interaction

Wheelset Structural Flexibility and Track Flexibility in Vehicle-Track Dynamic Interaction Wheelset Structural Flexibility and Track Flexibility in Vehicle-Track Dynamic Interaction by Nizar Chaar Doctoral Thesis TRITA AVE 2007:17 ISSN 1651-7660 ISBN 978-91-7178-636-4 Postal address Rail Vehicles

More information

APPLICATIONS OF TENSOR ANALYSIS

APPLICATIONS OF TENSOR ANALYSIS APPLICATIONS OF TENSOR ANALYSIS (formerly titled: Applications of the Absolute Differential Calculus) by A J McCONNELL Dover Publications, Inc, Neiv York CONTENTS PART I ALGEBRAIC PRELIMINARIES/ CHAPTER

More information

VERIFICATION OF THE METHOD FOR IMPROVING ACCURACY OF SIMPLIFIED SEISMIC RESPONSE ANALYSIS OF STEEL RIGID FRAME VIADUCTS

VERIFICATION OF THE METHOD FOR IMPROVING ACCURACY OF SIMPLIFIED SEISMIC RESPONSE ANALYSIS OF STEEL RIGID FRAME VIADUCTS International Journal of Civil Engineering and Technology (IJCIET) Volume 6, Issue 10, Oct 2015, pp. 46-61 Article ID: IJCIET_06_10_005 Available online at http://www.iaeme.com/ijciet/issues.asp?jtype=ijciet&vtype=6&itype=10

More information

A New Wheel/Rail Spatially Dynamic Coupling Model and its Verification

A New Wheel/Rail Spatially Dynamic Coupling Model and its Verification Vehicle System Dynamics 2004, Vol. 41, No. 4, pp. 301 322 A New Wheel/Rail Spatially Dynamic Coupling Model and its Verification G. CHEN 1 AND W.M. ZHAI 2 SUMMARY Based on the theory of vehicle-track coupling

More information

EVALUATION OF SEISMIC RESPONSE - FACULTY OF LAND RECLAMATION AND ENVIRONMENTAL ENGINEERING -BUCHAREST

EVALUATION OF SEISMIC RESPONSE - FACULTY OF LAND RECLAMATION AND ENVIRONMENTAL ENGINEERING -BUCHAREST EVALUATION OF SEISMIC RESPONSE - FACULTY OF LAND RECLAMATION AND ENVIRONMENTAL ENGINEERING -BUCHAREST Abstract Camelia SLAVE University of Agronomic Sciences and Veterinary Medicine of Bucharest, 59 Marasti

More information

Title: Zero-pad effects on conditional simulation and application of spatially-varying earthquake motions.

Title: Zero-pad effects on conditional simulation and application of spatially-varying earthquake motions. Cover page Title: Zero-pad effects on conditional simulation and application of spatially-varying earthquake motions. Authors: Nguyen Van Dinh 1 and Biswajit Basu 2 1, 2 School of Engineering, Trinity

More information

Software Factories: Assembling Applications with Patterns, Models, Frameworks, and Tools

Software Factories: Assembling Applications with Patterns, Models, Frameworks, and Tools Software Factories: Assembling Applications with Patterns, Models, Frameworks, and Tools Jack Greenfield Keith Short WILEY Wiley Publishing, Inc. Preface Acknowledgments Foreword Parti Introduction to

More information

CHAPTER 3. INTRODUCTION TO MATRIX METHODS FOR STRUCTURAL ANALYSIS

CHAPTER 3. INTRODUCTION TO MATRIX METHODS FOR STRUCTURAL ANALYSIS 1 CHAPTER 3. INTRODUCTION TO MATRIX METHODS FOR STRUCTURAL ANALYSIS Written by: Sophia Hassiotis, January, 2003 Last revision: February, 2015 Modern methods of structural analysis overcome some of the

More information

Institute of Actuaries of India Subject CT3 Probability and Mathematical Statistics

Institute of Actuaries of India Subject CT3 Probability and Mathematical Statistics Institute of Actuaries of India Subject CT3 Probability and Mathematical Statistics For 2015 Examinations Aim The aim of the Probability and Mathematical Statistics subject is to provide a grounding in

More information

Soil Dynamics Prof. Deepankar Choudhury Department of Civil Engineering Indian Institute of Technology, Bombay

Soil Dynamics Prof. Deepankar Choudhury Department of Civil Engineering Indian Institute of Technology, Bombay Soil Dynamics Prof. Deepankar Choudhury Department of Civil Engineering Indian Institute of Technology, Bombay Module - 2 Vibration Theory Lecture - 8 Forced Vibrations, Dynamic Magnification Factor Let

More information

CHAPTER 3 MODAL ANALYSIS OF A PRINTED CIRCUIT BOARD

CHAPTER 3 MODAL ANALYSIS OF A PRINTED CIRCUIT BOARD 45 CHAPTER 3 MODAL ANALYSIS OF A PRINTED CIRCUIT BOARD 3.1 INTRODUCTION This chapter describes the methodology for performing the modal analysis of a printed circuit board used in a hand held electronic

More information

COURSE SYLLABUS -----------------------------------------------------------------------------------

COURSE SYLLABUS ----------------------------------------------------------------------------------- Last Reviewed by: Leslie Wurst Date Approved: Date Revised: Fall 2012 COURSE SYLLABUS Syllabus for: MATH 1010 Math for General Studies Former Course and Title: Former Quarter Course(s): Mat 1260 Contemporary

More information

2D Geometric Transformations. COMP 770 Fall 2011

2D Geometric Transformations. COMP 770 Fall 2011 2D Geometric Transformations COMP 770 Fall 2011 1 A little quick math background Notation for sets, functions, mappings Linear transformations Matrices Matrix-vector multiplication Matrix-matrix multiplication

More information

The kinematic interaction of a single pile with heterogeneous soil

The kinematic interaction of a single pile with heterogeneous soil Earthquake Ground Motion: Input Definition for Aseismic Design 135 The kinematic interaction of a single pile with heterogeneous soil M. Maugeri, E. Motta, E. Raciti & D. Ardita Department of Civil and

More information

Vibrations of a Free-Free Beam

Vibrations of a Free-Free Beam Vibrations of a Free-Free Beam he bending vibrations of a beam are described by the following equation: y EI x y t 4 2 + ρ A 4 2 (1) y x L E, I, ρ, A are respectively the Young Modulus, second moment of

More information

FATIGUE ANALYSIS OF A BEAM SUBJECTED TO DYNAMIC LOADING. Cheng-Shun Chen * I-Chih Wang **

FATIGUE ANALYSIS OF A BEAM SUBJECTED TO DYNAMIC LOADING. Cheng-Shun Chen * I-Chih Wang ** FATIGUE ANALYSIS OF A BEAM SUBJECTED TO DYNAMIC LOADING ABSTRACT Cheng-Shun Chen * I-Chih Wang ** Department of Mechanical, Industrial, and Nuclear Engineering University of Cincinnati, Ohio, U.S.A. *

More information

SEISMIC CODE EVALUATION. MEXICO Evaluation conducted by Jorge Gutiérrez

SEISMIC CODE EVALUATION. MEXICO Evaluation conducted by Jorge Gutiérrez SEISMIC CODE EVALUATION MEXICO Evaluation conducted by Jorge Gutiérrez NAME OF DOCUMENT: Normas Técnicas Complementarias para Diseño por Sismo ( Complementary Technical Norms for Earthquake Resistant Design

More information

WAVES AND FIELDS IN INHOMOGENEOUS MEDIA

WAVES AND FIELDS IN INHOMOGENEOUS MEDIA WAVES AND FIELDS IN INHOMOGENEOUS MEDIA WENG CHO CHEW UNIVERSITY OF ILLINOIS URBANA-CHAMPAIGN IEEE PRESS Series on Electromagnetic Waves Donald G. Dudley, Series Editor IEEE Antennas and Propagation Society,

More information

Bearing position optimization for machine shaft

Bearing position optimization for machine shaft International Journal of Engineering and Technical Research (IJETR) ISSN: 2321-0869, Volume-2, Issue-4, April 2014 Bearing position optimization for machine shaft Mr. Patil Amit V., Prof. Meghna Pathak,

More information

Calculation and Analysis of Tunnel Longitudinal Structure under Effect of Uneven Settlement of Weak Layer

Calculation and Analysis of Tunnel Longitudinal Structure under Effect of Uneven Settlement of Weak Layer Calculation and Analysis of Tunnel Longitudinal Structure under Effect of Uneven Settlement of Weak Layer 1,2 Li Zhong, 2Chen Si-yang, 3Yan Pei-wu, 1Zhu Yan-peng School of Civil Engineering, Lanzhou University

More information

Determination of anti-pitch geometry acceleration [1/3]

Determination of anti-pitch geometry acceleration [1/3] Determination of anti-pitch geometry acceleration [1/3] 1 of 39 Similar to anti-squat Opposite direction of D Alembert s forces. Front wheel forces and effective pivot locations Determination of anti-pitch

More information