Cable Stayed BridgesModeling and AnalysisVidish A. Iyer Structural Engineer and CAE consultant at Midas IT

Cable Stayed Bridges Modeling and Analysis Vidish A Iyer Structural Engineer and CAE consultant at Midas IT Bridging Your Innovations to Realities midas Civil Click to edit Master title style Bridging Your Innovations to Realities Click to edit Master subtitle style CONTENTS CONTENTS • • • • • About Midas IT About Midas Civil Modeling Philosophy Analysis Philosophy 2nd order and 3rd order Effects midas Civil Click to edit Master title style Click to editMIDAS Master IT subtitle style ABOUT CONTENTS MIDAS Programs were being developed since 1989 and have been used commercially since 1996 With our headquarters in South Korea , we currently have corporate offices in Beijing, Singapore, Shanghai, Detroit, Dallas, Europe, India and Japan and are ever expanding One of the Largest civil analysis software developers Proven Reliability with over 5,000 project applications Intensive quality control system Analyses verified by various institutions Bridging Your Innovations to Realities midas Civil midas Civil Why midas Civil title style Click to edit Master Bridging Your Innovations to Realities Integrated Solution System for Bridge and Civil Engineering Click edit Master subtitle CONTENTS WHAT IS MIDAS CIVIL style ? What istomidas Civil? FEM FBM BEM 2-D 3-D Structural Engineer General Purpose Geotechnical Engineer Special Purpose Bridge Underground Structure Plant Tunnel Building Dam midas Civil midas Civil Why midas Civil title style Click to edit Master Bridging Your Innovations to Realities Integrated Solution System for Bridge and Civil Engineering Click to edit CONTENTS WHAT TYPES OFsubtitle BRIDGES IT HANDLE ? What kind ofMaster bridge typestyle canCAN midas Civil handle? Conventional Bridge Staged Segmental Bridge Cable-stayed Bridge & Suspension Bridge midas Civil midas Civil Click to edit Master title style Bridging Your Innovations to Realities Integrated Solution System for Bridge and Civil Engineering Click to edit Master subtitle style CONTENTS MODELING PHILOSOPHY midas Civil Click to edit Master title style Bridging Your Innovations to Realities INITIAL SIZING • Aside from loadings , Pylon and Deck Geometry and orientation are usually driven by cost and aesthetics • Backstay forces are maximum when live load is on main span and lowest when it is on side spans • Backstays usually get largest stress variations among all cables midas Civil Click to edit Master title style Bridging Your Innovations to Realities INITIAL MODELING Three main modeling methods • Spine Beam Model • Multi-Scale Model • Meshed Finite Element model midas Civil Click to edit Master title style Bridging Your Innovations to Realities SPINE BEAM MODELING • Most common modeling method • Bridge is modeled using beam , truss elements and links • Deck Sections can be modeled using equivalent section properties 10 midas Civil Click to edit Master title style Bridging Your Innovations to Realities CABLE MODELING Cables can be modeled as tension trusses with sag effect considered through the Earnst Formula : 11 midas Civil Click to edit Master title style Bridging Your Innovations to Realities NONLINEAR EFFECTS Major Nonlinear Effects : • Sag Effect of cables • P-Delta effects ( 2nd order ) • Large deformation ( 3rd order ) 28 midas Civil Click to edit Master title style Bridging Your Innovations to Realities SAG EFFECTS Linear Analysis Non-Linear Analysis Cable element treated as equivalent truss with effective stiffness given by the formula shown below Cable element is transformed into elastic catenary element 29 midas Civil Click to edit Master title style Bridging Your Innovations to Realities 2nd ORDER EFFECTS • For short to medium span bridges deflections are quite small so the 2nd order effects can be limited to live load effects • For long span bridges , these should be considered for both construction and final stage calculations 30 midas Civil Click to edit Master title style Bridging Your Innovations to Realities 3rd ORDER EFFECTS • For very long span bridges , large deformation analysis may be needed • Usually analyzed as Geometric non-linear Analysis 31 midas Civil Click to edit Master title style Bridging Your Innovations to Realities LINEAR VS P-DELTA VS NONLINEAR • In general , no hard and fast rule to decide when 3rd order theory should be used • For short span bridges, Virlogeux et al (1994 ) suggest that dead load distribution be analyzed as first order and second order checks be done for live load computation • Wang et al (2003) suggest that for main spans beyond 600 m , 3rd order theory is recommended 32 midas Civil Click to edit Master title style Bridging Your Innovations to Realities PROJECT APPLICATIONS 33 Project Applications Bridging Your Innovations to Realities Ironton-Russell Bridge midas Civil Overall bridge length 1,900 ft Main span 950 ft Tower height 519 ft Location Crossing the Ohio River between Ironton and Russell Function/usage Roadway Bridge Designer Michael Baker, Jr., Inc Cost of construction $110 Million Number of elements and element types used Truss (Cable): 70 Beam: 2088 Shell: 2730 Type of analysis Construction Stage Analysis with Time-Dependent Effects Unknown Load Factor Analysis Eigenvalue Analysis Thermal Analysis Vehicle Load Optimization 34/138 Project Applications Bridging Your Innovations to Realities Weirton-Steubenville Bridge midas Civil Overall bridge length 1,965 ft Main span 820 ft Tower height 365 ft Location Crossing the Ohio River between Weirton (West Virginia) and Steubenville (Ohio) Function/usage Roadway Bridge Contractor S.J Groves & Sons Co Designer Michael Baker, Jr., Inc Consultant T.Y Lin International Year of completion 1989 (Health Monitoring, 2005) Cost of construction $30 Million Number of elements and element types used Truss (Cable): 52 Beam: 484 Shell: 13312 Type of analysis Construction Stage Analysis Cable Tension Optimization 35/138 Project Applications Bridging Your Innovations to Realities TU Delft / Movares Research Project on Train-Structure Interaction midas Civil Overall bridge length 400 m Main span 200 m Tower height 75 m (60 m above the deck) Function/usage Railway Bridge Consultant Movares Nederland BV Number of elements and element types used Truss: 56 (Stay cables) Beam: 582 (Deck and Tower) type of analysis Static Analysis Vehicle Load Optimization Time History Analysis FE model by A Steenbrink 36/138 Project Applications Bridging Your Innovations to Realities Korabelny Farvater Bridge midas Civil Overall bridge length 620 m Main span 310 m Tower height 128 m Location Saint-Petersburg Function/usage Roadway Bridge Designer Institute Strojproject Consultant Freyssinet International Year of completion Under design Cost of construction $ 20 Million Number of elements and element types used Truss (Cable): 104 Beam: 4063 Shell: 2288 Type of analysis Static Analysis Vehicle Load Optimization Eigenvalue Analysis 37/138 Project Applications Bridging Your Innovations to Realities Lazarevsky Bridge midas Civil Overall bridge length 120 m Main span 120 m Tower height 26 m Location Saint-Petersburg Function/usage Roadway Bridge Contractor Mostostroj Designer Institute Strojproject Year of completion 2009 Cost of construction $ 30 Million Number of elements and element types used Truss: 10 Beam: 903 Shell: 637 Type of analysis Static Analysis Vehicle Load Optimization Eigenvalue Analysis Construction Stage Analysis 38/138 Project Applications Bridging Your Innovations to Realities Incheon 2nd Bridge – 5th Longest Cable Stayed Bridge midas Civil Overall bridge length 1480 m Main span 800 m Tower height 230 m Location Incheon Function/usage Roadway Bridge Designer Seoyeong Engineering and Chodai Co., Ltd Year of completion 2009 Cost of construction $ 2.4 Billion Number of elements and element types used Truss (Cable): 176 Beam: 1653 Type of analysis Construction Stage Analysis with Time-Dependent Effects Cable Tension Optimization Geometric Nonlinear Analysis Vehicle Load Optimization 39/138 Project Applications Bridging Your Innovations to Realities Stonecutters Bridge – 3rd Longest Cable Stayed Bridge midas Civil Overall bridge length 1600 m Main span 1018 m Tower height 295 m Location Between Tsing Yi and Kowloon City, Hong Kong, China Function/usage Roadway Bridge Designer Ove Arup & Partners Cost of construction $355 Million Number of elements and element types used Truss (Cable): 224 Beam: 1638 Type of analysis Construction Stage Analysis with Time-Dependent Effects Cable Tension Optimization Geometric Nonlinear Analysis Eigenvalue Analysis Thermal Analysis Buckling Analysis 40/138 Project Applications Bridging Your Innovations to Realities Sutong Bridge – 2nd Longest Cable Stayed Bridge midas Civil Overall bridge length 8206 m Main span 1088 m Tower height 306 m Location Crossing Yangtze River in China between Nantong and Changshu Function/usage Roadway Bridge Designer Jiangsu Province Communications Planning and Design Institute Cost of construction $750 Million Number of elements and element types used Truss (Cable): 272 Beam: 760 Type of analysis Construction Stage Analysis with Time-Dependent Effects Cable Tension Optimization Geometric Nonlinear Analysis Eigenvalue Analysis Thermal Analysis Buckling Analysis 41/138 midas Civil Click to edit Master title style Bridging Your Innovations to Realities THANK YOU ! 42