Tài liệu Cable stayed bridges non linear effects

Cable Stayed Bridges Non – Linear Effects Tony Dempsey ROUGHAN & O’DONOVAN Consulting Engineers Presentation Layout 1. Introduction 2. Cable-Stayed Bridges - Steel Theory & Examples 3. Cable-Stayed Bridges - Concrete Theory & Examples 4. Cable-Stayed Bridges - Composite Examples 2 1. Introduction • Cable Stayed Bridges – Non Linearity Geometric Non Linear (GNL) – Large Displacement Material Non Linear (MNL) – Moment Curvature Non Linear Time Dependent Effects (TDE) Non Linear Cable Elements (NLE) Non – Linear Combinations (GNL / MNL / TDE / NLE) Cable – Rupture & Plastic Analysis • Cable Stayed Bridges – Static Linear Analysis 3 2. Cable-Stayed Bridges - Steel Steel Pylon Design – Second Order Effects • BS 5400 Part 3: Clause 10 • First Principle Approach • Perry Robertson Failure Criteria d4y P d2y + =0 4 2 EI dx dx σ= σ y + (1 + η )σ E 2 σ y + (1 + η )σ E  −   2 2  − σ yσ E  4 2. Cable-Stayed Bridges - Steel Steel Pylon Design – Second Order Effects 1.20 Euler Failure Curve Mean Axial Stress Perry Robertson Failure Curve 1.00 BS 5400 Part 3 Curve A Ratio σc / σy BS 5400 Part 3 Curve B BS 5400 Part 3 Curve C BS 5400 Part 3 Curve D 0.80 BS 449 BS5950 Curve A BS5950 Curve B 0.60 BS5950 Curve C 0.40 0.20 0.00 0 50 100 150 200 Slenderness Ratio 5 2. Cable-Stayed Bridges - Steel Samuel Beckett Bridge, Dublin, Ireland Courtesy Santiago Calatrava 6 2. Cable-Stayed Bridges - Steel Samuel Beckett Bridge, Dublin, Ireland 7 2. Cable-Stayed Bridges - Steel Strabane Footbridges, Northern Ireland 8 2. Cable-Stayed Bridges - Steel Steel Pylon Design – Second Order Effects 1.20 Euler Failure Curve Mean Axial Stress Perry Robertson Failure Curve 1.00 BS 5400 Part 3 Curve A Ratio σc / σy BS 5400 Part 3 Curve B BS 5400 Part 3 Curve C BS 5400 Part 3 Curve D 0.80 BS 449 BS5950 Curve A BS5950 Curve B 0.60 BS5950 Curve C 0.40 0.20 0.00 0 50 100 150 200 Slenderness Ratio 9 2. Cable-Stayed Bridges - Steel Steel Pylon Design – Second Order Effects 1.20 Euler Failure Curve Mean Axial Stress Perry Robertson Failure Curve 1.00 Ratio σc / σy BS 5400 Part 3 Curve A BS 5400 Part 3 Curve B 0.80 BS 5400 Part 3 Curve C BS 5400 Part 3 Curve D BS 449 0.60 BS5950 Curve A BS5950 Curve B BS5950 Curve C 0.40 0.20 0.00 0 50 100 150 200 Slenderness Ratio 10 2. Cable-Stayed Bridges - Steel Samuel Beckett Bridge, Dublin, Ireland Analysis A = ULS DL + SDL + Wind Analysis B = ULS DL + SDL + Wind + Back-Stay Imbalance Analysis C = ULS DL + SDL Wind + Construction Tolerance Analysis D = ULS DL + SDL Wind + Back-Stay Imbalance + Constr. Tol. 2.5 Load Factor 2.0 Pylon Tip - Analysis D Pylon M12 - Analysis D Pylon Tip - Analysis A Pylon M12 - Analysis A Pylon Tip - Analysis B Pylon M12 - Analysis B Pylon Tip - Analysis C Pylon M12 - Analysis C 1.5 1.0 0.5 -2.00 -1.00 0.0 0.00 1.00 2.00 3.00 4.00 Transverse Displacement (m) 11 5.00 6.00 2. Cable-Stayed Bridges - Steel Samuel Beckett Bridge, Dublin, Ireland Analysis A = ULS DL + SDL + Wind Analysis B = ULS DL + SDL + Wind + Back-Stay Imbalance Analysis C = ULS DL + SDL Wind + Construction Tolerance Analysis D = ULS DL + SDL Wind + Back-Stay Imbalance + Constr. Tol. 2.5 Load Factor 2.0 1.5 Pylon Tip - Analysis D Pylon M12 - Analysis D Pylon Tip - Analysis A Pylon M12 - Analysis A Pylon Tip - Analysis B Pylon M12 - Analysis B Pylon Tip - Analysis C Pylon M12 - Analysis C -0.20 -0.15 -0.10 1.0 0.5 -0.05 0.0 0.00 0.05 0.10 0.15 Transverse Displacement (m) 12 0.20 2. Cable-Stayed Bridges - Steel Samuel Beckett Bridge, Dublin, Ireland 13 2. Cable-Stayed Bridges - Steel Samuel Beckett Bridge, Dublin, Ireland 14 2. Cable-Stayed Bridges - Steel Samuel Beckett Bridge, Dublin, Ireland 15 3. Cable-Stayed Bridges - Concrete Boyne Bridge, Meath / Louth, Ireland 16 3. Cable-Stayed Bridges - Concrete Dublin Eastern Bypass, Ireland 17 3. Cable-Stayed Bridges - Concrete Dublin Eastern Bypass, Ireland 18 3. Cable-Stayed Bridges - Concrete Taney Bridge, Ireland 19 3. Cable-Stayed Bridges - Concrete Taney Bridge, Ireland Tower Design 20