Cable Stayed Bridges Non – Linear Effects Tony Dempsey ROUGHAN & O’DONOVAN Consulting Engineers Presentation Layout Introduction Cable-Stayed Bridges - Steel Theory & Examples Cable-Stayed Bridges - Concrete Theory & Examples Cable-Stayed Bridges - Composite Examples 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 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 EI dx dx σ= σ y + (1 + η )σ E σ y + (1 + η )σ E − 2 − σ yσ E 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 Curve A Ratio σc / σy BS 5400 Part Curve B BS 5400 Part Curve C BS 5400 Part Curve D 0.80 BS 449 BS5950 Curve A BS5950 Curve B 0.60 BS5950 Curve C 0.40 0.20 0.00 50 100 150 200 Slenderness Ratio Cable-Stayed Bridges - Steel Samuel Beckett Bridge, Dublin, Ireland Courtesy Santiago Calatrava Cable-Stayed Bridges - Steel Samuel Beckett Bridge, Dublin, Ireland Cable-Stayed Bridges - Steel Strabane Footbridges, Northern Ireland 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 Curve A Ratio σc / σy BS 5400 Part Curve B BS 5400 Part Curve C BS 5400 Part Curve D 0.80 BS 449 BS5950 Curve A BS5950 Curve B 0.60 BS5950 Curve C 0.40 0.20 0.00 50 100 150 200 Slenderness Ratio 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 Curve A BS 5400 Part Curve B 0.80 BS 5400 Part Curve C BS 5400 Part Curve D BS 449 0.60 BS5950 Curve A BS5950 Curve B BS5950 Curve C 0.40 0.20 0.00 50 100 150 200 Slenderness Ratio 10 Cable-Stayed Bridges - Concrete Taney Bridge Buckling Factor Flexural Stiffness (EI) Deck Pylon E I E I Gross properties EST IG IG FIP (pylon) Deck Creep (φ = 2) EST IG 0.5EST IG Comment φ = 2) FIP (deck)+Creep (φ 0.06ESTIG EST Buckling Magnification Factor Factor λ λ / λ −1 13.5 1.08 0.22ESTIG 5.5 1.22 0.22ESTIG 5.2 1.24 0.22ESTIG 3.3 1.44 EST = Youngs modulus – short term IG = Uncracked second moment of area 55 Cable-Stayed Bridges - Concrete Taney Bridge Buckling Factor Flexural Stiffness (EI) Deck Pylon E I E I Gross properties EST IG IG FIP (pylon) Deck Creep (φ = 2) EST IG 0.5EST IG Comment EST Buckling Magnification Factor Factor λ λ / λ−1 13.5 1.08 0.22ESTIG 5.5 1.22 0.22ESTIG 5.2 1.24 FIP (deck)+Creep (φ = 2) 0.06ESTIG 0.22ESTIG 3.3 1.44 φ = 1.72) EIS (deck)+Creep (φ 0.48ESTIG 0.22ESTIG 5.0 1.25 EST = Youngs modulus – short term IG = Uncracked second moment of area EIS = Secant Flexural Stiffness 56 Cable-Stayed Bridges - Concrete Taney Bridge Buckling Factor LU SAS Modeller 13.3 January 15, 2003 Buckling Mode Shape Cable-Stayed Span Anchor Span T IT LE: 57 Cable-Stayed Bridges - Concrete Taney Bridge First & Second Order Moments 45 40 35 Pylon Height (m) 30 25 20 15 First Order Moment BS5400 10 FIP Eurocode Numerical NL Analysis Section Capacity 58 00 80 00 60 00 40 00 20 00 00 -2 00 00 -4 00 00 -6 00 00 -8 Bending Moment (kN-m) Cable-Stayed Bridges - Concrete First & Second Order Moments FIP / Elastic Theory / Numerical NL Analysis EC2 Curvature Method BS5400 FIP (Taney) Numerical NL Analysis (Taney) EC2 (Taney) BS5400 (Taney) Ratio Second Order Moment / First Order Moment 3.0 2.5 2.0 1.5 1.0 0.5 0.0 Buckling Factor 59 Cable-Stayed Bridges - Concrete First & Second Order Moments • Low first order moment & buckling factor λ > Recommendation: Use EC2 or FIP • High first order moment & buckling factor λ > Recommendation: Use EC2 / FIP / BS 5400 • Buckling factor λ < Recommendation: Curvature Methods / Geometric & Material NonNon-Linear Analysis 60 Cable-Stayed Bridges - Concrete Second Order Effects – Extradosed Bridges 61 Cable-Stayed Bridges- Composite Monastery Road Bridge, Dublin, Ireland 62 Cable-Stayed Bridges- Composite Waterford Footbridge, Ireland 63 Cable-Stayed Bridges- Composite Waterford Footbridge, Ireland 64 Cable-Stayed Bridges- Composite Narrow Water Bridge, Ireland / Northern Ireland 65 Cable-Stayed Bridges- Composite Narrow Water Bridge, Ireland / Northern Ireland 66 Cable-Stayed Bridges- Composite Narrow Water Bridge, Ireland / Northern Ireland 67 Cable-Stayed Bridges- Composite New Wear Bridge, Sunderland Courtesy TECHNIKER / SPENCE 68 Thank You 69 ... Introduction Cable- Stayed Bridges - Steel Theory & Examples Cable- Stayed Bridges - Concrete Theory & Examples Cable- Stayed Bridges - Composite Examples Introduction • Cable Stayed Bridges – Non Linearity... 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 Cable- Stayed Bridges - Steel Steel Pylon Design – Second Order Effects • BS 5400 Part