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Bridging Your Innovations to Realities Midas Civil

• Lateral Force method of Analysis

• Modal Response Spectrum Analysis

• Pushover Analysis

• Inelastic Time History Analysis

Overview

Type of Seismic Analysis Method

Linear Analysis Non-linear Analysis

Static Dynamic Static Dynamic


Mass

• Nodal Masses

• Floor Diaphragm Masses

• Loads to Masses

• Consistent Mass

• Self-weight to Mass

[Lumped Mass and Consistent Mass]

Lumped Mass

Consistent Mass

Mass of Structure

210 0 0 0 0 0 1

0 210 0 0 0 0 1

0 0 210 0 0 0 1

0 0 0 210 0 0 2420

0 0 0 0 210 0 2

0 0 0 0 0 210 2

L

u

ALI

u

2 2

2 2

140 0 0 70 0 0 1

0 156 22 0 54 13 1

0 22 4 0 13 3 1

70 0 0 140 0 0 2420

0 54 13 0 156 22 2

20 13 3 0 22 4

c

u

L L

L L L LALI

u

L L

L L L L

ν1 ν2

u1 u2

θ1 θ2

1 2


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.

Damping


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.

Bridging Your Innovations to Realities Midas Civil Modal Analysis

Construction Stage Analysis Control for Structural Stiffness in Post CS

The member forces of the last step of the last construction stage in a construction stage analysis

are converted into Initial Force for Geometric Stiffness to reflect the forces into the geometric stiffness of the structure at the post construction (Post CS) stage.

Load > Initial Forces > Small Displacement

> Initial Element Forces(CS)


Modal Analysis Results

Modal Analysis

• Natural Period & Frequency

• Modal Participation Masses

• Eigen Vectors


Modal Analysis Results

Modal Analysis

Display the Mode Shape normalized to unity (maximum eigenvector = 1)

Where, φ: Mode shape vector, M: Mass in input unit


Implemented RS functions

such as IBC 2000, Eurocode8, NBC, Canada, China, Taiwan, India..etc.

IBC 2012 & 2009 will be available in the new version (2012 June).

Excitation Angle for considering the major axis of the structure

Various Damping Method

(Model, Mass & Stiffness Proportional, Strain Energy Proportional)

Response Spectrum Function & Cases

Response Spectrum Analysis


SRSS (Square Root of Sum of the Squares)

CQC (Complete Quadratic Combination)

ABS (Absolute Sum)

Linear (Linear Sum)

Modal Combination Type

Response Spectrum Load Case



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.

Response Spectrum Load Case


Add Signs (+,-) to the 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.

Bridging Your Innovations to Realities Midas Civil Response Spectrum Analysis

Calculation of Displacement Demand.

The Displacements Central node of Pier due to Seismic Loads.

Node Load DX (in) DY (in) DZ (in) RX ([rad]) RY ([rad]) RZ ([rad])

636 RS_X(RS) 14.0144 0.000388 0.000847 0 0.051874 0.000001

636 RS_Y(RS) 0.001109 1.37547 0.015209 0.000051 0.00002 0.000105

DX and DY values in blue are obtained as Demands


Why Pushover Analysis?

a) To verify or revise the over strength ratio values (alpha_u/alpha_1)

b) To estimate the expected plastic mechanisms and the distribution of damage

c) To assess the structural performance of existing or retrofitted buildings

d) As an alternative to the design based on linear-elastic analysis which uses the

behavior factor, q

Pushover Global Control

Define Lateral Loads

Define Hinge Properties

Assign Hinges

Perform Analysis

Check Pushover Curve and

Target Disp.

Check Hinge Status

Process in midas Civil

alpha_u

alpha_1

Pushover Analysis Overview

Pushover Analysis


Acceptance Criteria

Immediate Occupancy(IO)

Life Safety(LS)

Collapse Prevention (CP)

Pushover Analysis as per FEMA

Pushover Analysis


Pushover Global Control

Pushover Analysis

• 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.


Load

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

Member Assignment


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


Pushover Curve

Pushover Analysis

Capacity Curve (MDOF)

Base Share vs Displacement

Shear Coefficient vs Displacement

Shear Coefficient vs Draft

Load Factor vs Displacement

Capacity Curve (SDOF)

Performance Point (FEMA)


Load Direction Demand (in) Capacity (in) Ratio

RS_X(RS) DX 14.014 3.2 4.38

RS_Y(RS) DY 1.375 1.2 1.15

Demand/Capacity Ratio

Result from Response Spectrum Analysis and Pushover Analysis

Capacity

Pushover Analysis


Time History Analysis Overview

Time History Analysis

Enter Mass Data Define Eigen value

Analysis Control Enter Inelastic Hinges

or General Links

Time Forcing Function Time History Load

Cases (optional)Time

Varying Static Load

-Dynamic Nodal Load -Ground Acceleration

-Multiple Support Excitation

Perform Analysis Verify Analysis Results

Process in midas Civil


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.

Types of Time History Analysis



Transient Time history analysis is carried out on the basis of loading a time load function only once. This is a common type for time history analysis of earthquake loads. Periodic Time history analysis on the basis of repeatedly loading a time load function, which has a period identical to End Time. This type is applicable for machine vibration loads.

Select a time history analysis condition previously defined, which precedes the time history analysis condition currently being defined. The Analysis Type and Analysis Method for the current time history analysis condition must be consistent with those for the preceding load condition

Time History Type

Order in Sequence Loading

Time History Load Case



Time Function

Time Forcing Function


Sinusoidal Function


Ground Acceleration & Dynamic Nodal Load


Assign time forcing function to specific nodes.

Dynamic Nodal Load

Enter the time forcing function by means of ground acceleration.

Ground Acceleration


Define a dynamic load case by multiplying static load cases already entered by time functions, which should be defined as a Normal type in the "Time Forcing Functions". This function is used to reflect the effect of the self-weight in the time history analysis due to seismic loads.

Time Varying Static Load


Define self weight as a static load

Define time forcing function for self weigh

Make a link between the static load case, time history load case, and time forcing function in Time Varying Static Load

Select the pre-defined time history load case as an “Sequential Loading” in Time History Load Case


Base Isolators and Dampers

Objectives of Seismic Isolation Systems

Enhance performance of structures at all hazard levels by:

Minimizing interruption of use of facility

Reducing damaging deformations in structural and nonstructural components

Reducing acceleration response to minimize contents related damage

Characteristics of Well-Designed Seismic Isolation Systems

Flexibility to increase period of vibration and thus reduce force response

Energy dissipation to control the isolation system displacement

Rigidity under low load levels such as wind and minor earthquakes


Bridging Your Innovations to Realities Midas Civil Time History Analysis

Base Isolators:

Lead Rubber Bearing Isolator

Friction Pendulum System Isolator

Applicable Base Isolators in midas Civil


[Viscoelastic Damper] [Hysteretic System Damper]

Applicable Dampers in midas Civil

Visco Elastic Damper

Hysteretic System Damper



Analysis Results (Graph & Text output)

[Hysteretic Graph of Visco elastic Damper]

[Time History Graph at pier top (Time Domain & Frequent Domain]

[Time History Text Output]

[Text Output of Displacement, Velocity, Acceleration]



Inelastic Time History Analysis


Hysteresis Curve (Rz-Mz) [Ductility Factor] [Status of Yielding]

Inelastic Hinge

Ground Acceleration

Inelastic Time History Analysis of Extradosed Bridge


Arrival time : t = 0 sec

Arrival time, : t = 2 seconds

Ground Acceleration

Multiple Support Excitation



General Spring Support with 6x6 Coupled Matrix for Damping and Mass


Bridging Your Innovations to Realities Midas Civil Time History Analysis

Multi-Linear Kinematic and Takeda Hinge Model

Takeda Hinge Model

Kinematic Hinge Model

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