Bridging Your Innovations to Realities

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2 Overview Seismic Design Process as per Eurocode8-2 Basic Requirement No-collapse Minimization of damage Compliance Criteria Seismic Action Resistance Verification Capacity Design Ductility Verification Effective Stiffness Elastic Response Spectrum Time-History Representation Design Response Spectrum Regularity of Ductile Bridges Methods of Analysis Verification Equivalent Static Seismic Force Method Response Spectrum Method Time History Analysis Pushover Analysis

3 Overview Basic Requirements Basic requirements No collapse requirement (ULS) Bridge should retain its structural integrity and adequate residual resistance, although at some parts of the bridge considerable damage may occur. Sustain the actions from emergency traffic, and inspections and repair can be performed easily. Minimisation of damage (SLS) Only secondary components and those parts of the bridge should incur minor damage during earthquakes with a high probability of occurrence.

4 Overview Compliance Criteria Resistance Verifications Ductile Behavior Limited Ductile Behavior Ductility Verifications Conformance to special detailing values is deemed to ensure adequate local and global ductility. Control of Displacements Global Level Design Ultimate Deformation Target Displacement ( d E ) Member Level θ p,e θ p,d θ p,e : Plastic hinge rotation demands θ p,d : Design rotation capacities, θ p,d = θ p,u / γ R,p

5 Overview Seismic Action Soil classes Ground Acceleration Seismic Actions Response Spectrum Elastic response spectrum Design response spectrum Spatial Variability of Seismic Action Time history representation

6 Overview Regularity of Ductile Bridges Regularity of the Bridge (1) Perform response spectrum analysis. (2) Calculate design member force and resistance due to the load combination which contains seismic load at the pier top or bottom. (3) Calculate the value r by the equation below. (4) If the ratio between the largest r and smallest r exceeds 2, the bridge is classified as Irregular shape. Nonlinear Analysis of Irregular Bridge Dynamic nonlinear time history analysis Nonlinear static analysis (Pushover analysis)

7 Overview Type of Seismic Analysis Method Equivalent Static Seismic Force method Response Spectrum Analysis Pushover Analysis Inelastic Time History Analysis Linear Analysis Non-linear Analysis Static Dynamic Static Dynamic

8 Overview Type of Seismic Analysis Method Objective of Seismic Analysis Assess displacement demands of a bridge and its individual components Equivalent Static Analysis, Linear elastic dynamic analysis: Appropriate analytical tools for estimating the displacement demands for normal bridges Pushover Analysis: Appropriate analysis tool used to establish the displacement capacities for bridges. Nonlinear Time History Analysis: Used for critical or essential bridges and in some cases for normal bridges using devices for isolation or energy dissipation

9 Seismic Demand Cracked Section Properties Effective Moment of Inertia Estimate Jcr based on M-Phi analysis in midas GSD. Reduction Factor = Jeff / Jg = 0.4

10 Seismic Demand Response Spectrum Function & Cases Implemented RS functions Eurocode8, AASHTO-LRFD 6 th, NBC, China, Taiwan, India..etc. Excitation Angle for considering the major axis of the structure Various Damping Method (Model, Mass & Stiffness Proportional, Strain Energy Proportional)

11 Seismic Demand Response Spectrum Load Case Modal Combination Type SRSS (Square Root of Sum of the Squares) CQC (Complete Quadratic Combination) ABS (Absolute Sum) Linear (Linear Sum)

12 Seismic Demand Response Spectrum Load Case Add Signs (+,-) to the results Along the Major Mode Direction: Restore the signs according to the signs (+, -) of the principal mode for every loading direction. Along the Absolute Maximum Value: Restore the signs according to the signs of the absolute maximum values among all the modal results. Select Mode Shapes Select modes for modal combination. Using the Select Mode Shapes option, linearly combine the modes while entering the Mode Shape Factors directly.

13 Damping Damping Modal User defines the damping ratio for each mode, and the modal response will be calculated based on the user defined damping ratios. Mass & Stiffness Proportional Damping coefficients are computed for mass proportional damping and stiffness proportional damping. Strain Energy Proportional Damping ratios for each mode are automatically calculated using the damping ratios specified for element groups and boundary groups in Group Damping, which are used to formulate the damping matrix.

14 Modal Analysis Modal Analysis Eigen Vectors Subspace Iteration This method is effectively used when performing eigenvalue analysis for a finite element system of a large scale (large matrix system) and commonly used among engineers. Lanczos Tri-diagonal Matrix is used to perform eigenvalue analysis. This method is effectively used when performing eigenvalue analysis for lower modes. Ritz Vectors Unlike the natural eigenvalue modes, load dependent Ritz vectors produce more reliable results in dynamic analyses with relatively fewer modes. The Ritz Vectors are generated reflecting the spatial distribution or the characteristics of the dynamic loading.

15 Modal Analysis Modal Analysis Results Natural Period & Frequency Modal Participation Masses Eigen Vectors

16 Seismic Demand Calculation of Displacement Demand Node Load DX (m) DY (m) DZ (m) RX ([rad]) RY ([rad]) RZ ([rad]) 636 RS_X(RS) RS_Y(RS)

17 Seismic Demand Displacement Magnification Design Seismic Displacement η: Damping correction factor μ d : Displacement ductility factor d Ee : Displacement derived from a linear elastic analysis based on the elastic spectrum q: Behavior factor

18 Seismic Demand Combination of Orthogonal Displacement Demands Either the SRSS or the complete CQC modal combination rules are applicable. The design seismic action effects A Ed should be derived from the most adverse of the following combinations: D RS_Y = 0.3 * D EX * D EY = m D EX = D EeX * M u_dx D EY = D EeY * M u_dy Node Load DX (m) DY (m) DZ (m) RX ([rad]) RY ([rad]) RZ ([rad]) 636 RS_Y(RS)

19 Pushover Analysis Pushover Analysis Overview Why Pushover Analysis? 1) The estimation of the sequence and the final pattern of plastic hinge formation 2) The estimation of the redistribution of forces following the formation of plastic hinges 3) The assessment of the capacity curve of the structure and of the deformation demands of the plastic hinges up to the target displacement alpha_u alpha_1 Process in midas Civil Pushover Global Control Define Lateral Loads Define Hinge Properties Assign Hinges Check Hinge Status Check Pushover Curve and Target Disp. Perform Analysis

20 Pushover Analysis Pushover Global Control Initial Load: Enter the initial load (in general, the gravity loads) for pushover analysis. Convergence Criteria: Specify the maximum number of (iterations) sub-iterations and a tolerance limit for convergence criterion. Stiffness Reduction Ratio: Specify stiffness reduction ratios after the 1st and 2nd yielding points (1st yielding for bilinear curve, 1st and 2nd yielding for trilinear curve) relative to the elastic stiffness. Reference location for distributed hinges: Specify the reference location for calculating yield strength of beam elements which distributed hinge is assigned.

21 Pushover Analysis Pushover Load Cases Horizontal Load Increment Load Distribution Method Constant along the deck Proportional to the first mode shape

22 Pushover Analysis Pushover Load Cases FEMA 273, Eurocode 8, Multi-linear, Masonry & User-defined hinge type Displacement control & Force control Truss, Beam, Wall element & Spring Performance point & Target displacement Checking for acceptable performance (Drift limits & deformation/strength capacity) Load Pattern (1) Static Load (2) Mode Shape (3) Uniform Acceleration (4) Mode Shape * Mass

23 Pushover Analysis Pushover Analysis Element Type Beam, Column Truss General Link (Isolators) Definition Moment-Rotation Moment-Curvature Hinge Properties FEMA Bi-linear type Tri-linear type Eurocode8 Axial force-moment interaction

24 Pushover Analysis Pushover Hinge Property from Moment Curvature Curve

25 Pushover Analysis Hinge Length L: Distance from the plastic hinge section to the section of zero moment, under the seismic action f yk : Characteristic yield stress (in MPa) d bl : Bar diameter

26 Pushover Analysis Pushover Hinge Properties

27 Pushover Analysis Pushover Curve Capacity Curve (MDOF) Base Share vs Displacement Shear Coefficient vs Displacement Shear Coefficient vs Draft Load Factor vs Displacement

28 Pushover Analysis Global Deformation Verification Design Ultimate Deformation Target Displacement ( d E ) Load Direction Demand (m) Capacity (m) Ratio Remark RS_Y(RS) DY OK

29 Pushover Analysis Local Deformation Verification Θ p,e : Plastic Rotation demand, theta_pd in Chord Rotation Check Table Θ p,u : Plastic rotation capacity γ R,p : Factor to reflect local defects of the structure, uncertainties of model, and the dispersion of the relevant test results (recommended value = 1.40)

30 Time History Analysis Types of Time History Analysis Boundary Nonlinear Time History Analysis The nonlinearity of the structure is modeled through General Link of Force Type, and the remainder of the structure is modeled linear elastically. Boundary nonlinear time history analysis is analyzed by converting the member forces of the nonlinear system into loads acting in the linear system. Because a linear system is analyzed through modal superposition, this approach has an advantage of fast analysis speed compared to the method of direct integration, which solves equilibrium equations for the entire structure at every time step. Inelastic Time History Analysis Inelastic time history analysis is dynamic analysis, which considers material nonlinearity of a structure. Considering the efficiency of the analysis, nonlinear elements are used to represent important parts of the structure, and the remainder is assumed to behave elastically. Linear Time History Analysis Soil-Structure Interaction Fiber Analysis

31 Time History Analysis Time History Analysis Overview Process in midas Civil Inelastic Hinges or Isolators Time Forcing Function Time History Load Cases Ground Acceleration Perform Analysis

32 Time History Analysis Applicable Base Isolators in midas Civil Base Isolators Lead Rubber Bearing Isolator Friction Pendulum System Isolator

33 Time History Analysis Dampers Applicable Dampers in midas Civil Viscoelastic Damper Hysteretic System Damper [Visco Elastic Damper] [Viscoelastic Damper] [Hysteretic System Damper] [Hysteretic System Damper]

34 Time History Analysis Inelastic Time History Analysis Inelastic Hinge Model Kinematic Hardening Takeda Slip Model Multi-linear Model Inelastic Time History Analysis of Extradosed Bridge Ground Acceleration Inelastic Hinge [Status of Yielding] [Ductility Factor] Hysteresis Curve (Rz-Mz)

35 Time History Analysis Time Forcing Function [Time Function] [Database of Earthquake Record] [Sinusoidal Function]

36 Time History Analysis Analysis Results (Graph & Text output) [Hysteretic Graph of Visco elastic Damper] [Text Output of Displacement, Velocity, Acceleration] [Time History Text Output] [Time History Graph at pier top (Time Domain & Frequent Domain]

37 Time History Analysis Vibration Analysis due to Walking Load [Dynamic Nodal Load] [Acceleration Graph by Walking Load] [Train Load Data Generator]

38 Time History Analysis Multiple Support Excitation Ground Acceleration Arrival time : t = 3.48 seconds Arrival time : t = 1.56 sec

39 Time History Analysis Condensed Spring Support with 6x6 Coupled Matrix for Damping and Mass [General Spring Support]

40 Time History Analysis Soil Structure Interaction with Kinematic Hinge Model Displacement Push -displacement p Deformed Shape y

41 Time History Analysis Fiber Analysis Section division for Fiber Model definition Fiber Cell Result Plotting Inelastic Material Properties (Stress-strain curve) Kent & Park Model Menegotto-Pinto Model