20121122 Civil Advanced Webinar Dynamic Analysis

7/29/2019 20121122 Civil Advanced Webinar Dynamic Analysis

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Bridging Your Innovations to Realities


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Bridging Your Innovations to RealitiesMidas Civil

LateralForcemethod ofAnalysis

ModalResponseSpectrumAnalysis

PushoverAnalysis

InelasticTimeHistoryAnalysis

Overview

Type of Seismic Analysis Method

Linear Analysis Non-linear Analysis

Static Dynamic Static Dynamic


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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

1 2

u1 u2

1 2

1 2


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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


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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 thecharacteristics of the dynamic loading.


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Bridging Your Innovations to RealitiesMidas 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 analysisare converted into Initial Force for Geometric Stiffness to reflect the forces into the geometric stiffnessof the structure at the post construction (Post CS) stage.

Load > Initial Forces > Small Displacement> Initial Element Forces(CS)


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Modal Analysis Results

Modal Analysis

Natural Period & Frequency

Modal Participation Masses

Eigen Vectors


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Modal Analysis Results

Modal Analysis

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

Where, : Mode shape vector,

M: Mass in input unit


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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 Anglefor considering the major axis of the structure

Various Damping Method

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

Response Spectrum Function & Cases

Response Spectrum Analysis


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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



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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.


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Bridging Your Innovations to RealitiesMidas 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


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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 GlobalControl

Define LateralLoads

Define HingeProperties

Assign Hinges

PerformAnalysis

Check PushoverCurve and

Target Disp.

Check HingeStatus

Process in midas Civil

alpha_u

alpha_1

Pushover Analysis Overview

Pushover Analysis


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Acceptance Criteria

Immediate Occupancy(IO)

Life Safety(LS)

Collapse Prevention (CP)

Pushover Analysis as per FEMA

Pushover Analysis


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Pushover Global Control

Pushover Analysis

Initial Load: Enter the initial load(in general, the gravity loads) forpushover analysis.

Convergence Criteria: Specify themaximum number of (iterations)sub-iterations and a tolerance

limit for convergence criterion.

Stiffness Reduction Ratio: Specifystiffness reduction ratios after the1st and 2nd yielding points (1styielding for bilinear curve, 1st and2nd yielding for trilinear curve)relative to the elastic stiffness.

Reference location for distributedhinges: Specify the referencelocation for calculating yieldstrength of beam elements whichdistributed hinge is assigned.


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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


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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


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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)


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Load Direction Demand (in) Capacity (in) RatioRS_X(RS) DX 14.014 3.2 4.38RS_Y(RS) DY 1.375 1.2 1.15

Demand/Capacity Ratio

Result from Response Spectrum Analysis and Pushover Analysis

Capacity

Pushover Analysis


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Time History Analysis Overview

Time History Analysis

Enter Mass DataDefine Eigen value

Analysis ControlEnter Inelastic Hinges

or General Links

Time Forcing FunctionTime History Load

Cases(optional)Time

Varying Static Load

-Dynamic Nodal Load-Ground Acceleration

-Multiple SupportExcitation

Perform Analysis Verify Analysis Results

Process in midas Civil


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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 anadvantage 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 ofthe 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



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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 ofearthquake 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



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Time Function

Time Forcing Function


Sinusoidal Function


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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


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Define a dynamic load case by multiplying static load cases already entered by timefunctions, 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 timeforcing function in Time Varying Static Load

Select the pre-defined time history load case as an Sequential Loading inTime History Load Case


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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



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Bridging Your Innovations to RealitiesMidas Civil Time History Analysis

Base Isolators:

Lead Rubber Bearing Isolator

Friction Pendulum System Isolator

Applicable Base Isolators in midas Civil


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[Viscoelastic Damper] [Hysteretic System Damper]

Applicable Dampers in midas Civil

Visco Elastic Damper

Hysteretic System Damper



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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]



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Inelastic Time History Analysis


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

Inelastic Hinge

Ground Acceleration

Inelastic Time History Analysis of Extradosed Bridge


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Arrival time : t = 0 sec

Arrival time, : t = 2 seconds

Ground Acceleration

Multiple Support Excitation



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



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Bridging Your Innovations to RealitiesMidas Civil Time History Analysis

Multi-Linear Kinematic and Takeda Hinge Model

Takeda Hinge Model

Kinematic Hinge Model


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20121122 Civil Advanced Webinar Dynamic Analysis