1997v05 Hangar Design

Pushover and Response Spectrum Analysis Demand & Capacity Evaluation

B r i d g i n g Y o u r I n n o v a t i o n s t o R e al al i t i es es

midas Civil

Bridging Your Innovations to Realities

Demand & Capacity Evaluation

Force Based Design : F D

FE

F Elastic Analysis

R FP

Inelastic Response

1 Design Load F P = FE / R D

Dy D

R = Response Modification Factor R = Du / Dy, represent the ductility capacity of the ERS

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Force Based Design : F D

FE

F Elastic Analysis

R FP

Inelastic Response

1 Design Load F P = FE / R D

Dy D

R = Response Modification Factor R = Du / Dy, represent the ductility capacity of the ERS

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Displacement-Based Design: F

Displacement-Based Design:

D

F

Elastic Analysis

FP

Equal Displacement Assumption: Displacements resulted from inelastic response is approximately equal to displacement obtained from linear elastic response spectrum analysis.

Inelastic Response

Design Load is simply FP. What to be checked: DD

Dy D

D

D≤

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Seismic Design Comparison of two Design Approaches: Force •

•

•

•

•

AASHTO LRFD Bridge Design Specification Complete design for STR, SERV limit state first Elastic demand forces divided by Response Modification Factor “R” Ductile response is assumed to be adequate without verification Capacity protection assumed

Capacity Protection: • • • •

Column Shear Capacity Pier Cap Foundation Joint

Displacement •

•

•

•

•

AASHTO Guide Specification for LRFD Seismic Bridge Design Complete design for STR, SERV limit state first Displacement demands checked against displacement capacity Ductile response is assured with limitations prescribed for each SDC Capacity protection assured

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3. Determination of Demand Elastic Dynamic Analysis: Step 3 : EDA Results RS X Maximum Deflection : 5.92 inches


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3. Determination of Demand Elastic Dynamic Analysis: Step 3 : EDA Results RS Y Maximum Deflection : 4.94 inches


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5. Determination of Capacity Displacement Capacity Set up of Pushover Model: Pushover Curve: (X Direction)


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5. Determination of Capacity Displacement Capacity Set up of Pushover Model: Pushover Curve: (Y Direction)


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1. Introduction Seismic Analysis: Seismic Analysis is a subset of structural analysis and is the calculation of the response of a building/bridge (or nonbuilding) structure to earthquakes. It is part of the process of structural design, earthquake engineering or structural assessment and retrofit (see structural engineering) in regions where earthquakes are prevalent.

Why is Seismic Analysis Important? Seismic Analysis would enable us to visualize the response of the bridge in the earthquake, which would enable us to obtain the additional forces or deformations that would be generated as a result of earthquake. Thus once the proper estimation of forces is done we can design the structure to withstand a particular level

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1. Introduction Consequences of Earthquake: > Lateral Forces applied by earthquake > Sudden force applied: vibration > Additional Forces due to P-Delta Effects > Non linear behavior of Steel and Concrete


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1. Introduction


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1. Introduction Methods of Earthquake Analysis: Certain methods are developed to estimate the earthquake forces.

Structure /Action

Static

Dynamic

Elastic

Equivalent Force Method

Response Spectrum

Non-linear

Pushover

Non Linear Time History

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1. Introduction Static Seismic Analysis : Pros: > Relatively Simple to understand and apply > Does not need rigorous calculations and hence quick Cons: > Does not take into account the dynamic response of the structure into account > The non linearity of the material is ignored > Does not lead to detailed response in earthquake


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1. Introduction Response Spectrum Analysis: Pros: > Applies the Dynamic Equation of Motion for earthquake force determination > Different modes of excitation are considered for obtaining the earthquake effect > Damping is considered while obtaining results Cons: > The non linearity of the material is ignored > Does not lead to detailed response in earthquake > Various combinations methods and results depend on them


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1. Introduction Pushover Analysis Pros: > Simple to understand and application > Non linear behavior of concrete and steel considered > Consideration of second order effects ( P delta ) Cons: > Dynamic Equation of motion is not considered > Structure is supposed to excite only in one direction or mode > Various methods of distribution of Forces, hence no specified scheme


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1. Introduction Time History Analysis Pros: > Consideration of Dynamic Equation of Motion > Non linear behavior of concrete and steel considered > Gives the displacement, velocity or acceleration of the structure with time in earthquake > Considers damping Cons: > Very difficult to understand and application > Requires computer software > Requires various additional parameters to do

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2. Code Specifications Highlight of SDC:  Adopt

a seven percent in 75 year design event for the development of a design spectrum

 Ensure

sufficient conservatism

 Categories:

SDC A,B,C,D

 Type of Design:  Type 1

 Type 2  Type 3

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2. Code Specifications Categories of SDC SDC A:  

 

No Displacement capacity check is needed No capacity design is needed SDC A minimum requirements No Liquefaction analysis

SDC B    

Implicit Displacement Capacity Check required Capacity Checks suggested SDC B level of Detailing Liquefaction Liquefaction assessment recommended for certain conditions


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2. Code Specifications Categories of SDC SDC C:  

 

Implicit Displacement capacity check is required Capacity design is required SDC C level of detailing Liquefaction Liquefaction assessment is necessary

SDC D:    

Pushover Analysis Required Capacity design required SDC D level of detailing Liquefaction Liquefaction assessment required


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2. Code Specifications Types of Design: Type 1: 

Design a ductile substructure with an essentially elastic superstructure

Type 2: Design an essentially elastic substructure with a ductile superstructure  Type 3:  Design an elastic superstructure and substructure with a fusing mechanism at the int erface between the superstructure and substructure

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2. Code Specifications

Demand Analysis: 1. 2.

SDC A doesn’t require the demand analysis. SDC B C D require the demand analysis so we will try to simulate the same in midas Civil.

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3. Performance Based Design Performance Based Design:

Performance-Based Building Design is an approach which focuses on the objective of a building asset, in order to prescribe desired results instead of the way and the method to get things done, as it’s concepted in a traditional practice. Performance concept is based on two key characteristics :

the use of two languages, one for the clients/users requirements and the other for the supply of the performance the need for validation and verification of results against performance targets.

•

•

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3. Performance Based Design Demand And Capacity: Demand: Demand is what is expected out of the structure based on the designed earthquake force. It can be in form of deformation, force etc. Capacity: Capacity is what the structure can deliver.

The assessment is OK when the capacity is greater than demand.

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3. Performance Based Design

Step 1: Demand Analysis


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4. Determination of Demand

In this tutorial we will deal with SDC D because once we understand all concepts of SDC 4 we can apply them in SDC B and C SDC D: Steps of SDC Design for SDC D: Step 1: Displacement Analysis Step 2: Displacement Capacity Step 3 : Satisfy Support Requirements Step 4: Capacity Design Step 5: Foundation Design Step 6: Detailing


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4. Determination of Demand SDC D: Step 1: Displacement Analysis


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4. Determination of Demand SDC D: Step 1: Displacement Analysis Analysis Procedure We would study procedure 2.


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4. Determination of Demand Elastic Dynamic Analysis or Response Spectrum Analysis can be done in midas civil. Guidelines of SDC: 1. A linear elastic multimodal spectral analysis using the appropriate response spectrum response spectrum must be Performed. 2. The damping must be selected as 5% 3. EDA results should be combined as Complete Quadratic combination


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5. Elastic Dynamic Analysis Response Spectrum Analysis:

Response Spectrum Analysis is a dynamic analysis which combines the response spectrum with the time period of the structure.

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5. Elastic Dynamic Analysis Response Spectrum Analysis:

Response Spectrum Analysis is a dynamic analysis which combines the response spectrum with the time period of the structure. From Combination of Response Spectrum and Eigen value period

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5. Elastic Dynamic Analysis Response Spectra?

The response spectrum is a function of period, the reciprocal of circular natural frequency, and damping ratio. It is developed using Duhamel’s integral for a single degree of freedom harmonic oscillator to develop equations for displacement, velocity and acceleration. The values in the appropriate spectrum are the maximum absolute values from these equations.

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5. Elastic Dynamic Analysis What is Period ( Eigen value Analysis )?

The period is the time of the vibration of the structure in a particular mode.

Modes of vibration of the structure


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5. Elastic Dynamic Analysis What is Period ( Eigen value Analysis )?

The period is the time of the vibration of the structure in a particular mode.


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5. Elastic Dynamic Analysis How to Obtain

Combination of Response Spectrum and the period

Mode 2: Period: 1.04, Wg = 1.25*g

Mode 1: Period: 2.41, Wg = 0.75*g

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5. Elastic Dynamic Analysis Results Combination:

The analysis is performed for all modes using the dynamic equation and then the results are combined using one of the following methods:

AASHTO Specification

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5. Elastic Dynamic Analysis Steps of Elastic Dynamic Analysis:

Response Spectrum Functions

Response Spectrum Load Cases

Response Spectrum Results


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5. Elastic Dynamic Analysis Procedure of Elastic Dynamic Analysis:

Eigenvalue Analysis

Frequency Mode Shapes

Period Modal Directional Factor

Effective Modal mass and ratio

**Eigenvalue Analysis is must.

R S Analysis

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5. Elastic Dynamic Analysis Load

Response Spectrum Analysis

Design Spectrum in the database of Midas Civil can be used

Normalized Acceleration : Spectrum obtained by dividing the acceleration spectrum by the acceleration of gravity Acceleration : Acceleration spectrum Velocity : Velocity spectrum Displacement : Displacement spectrum

Response Spectrum Analysis Functions


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Response Spectrum Analysis Functions

In Midas civil you can specify the Response Spectrum Functions as per the site class


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Response Spectrum Load Cases

Excitation Angle When the seismic excitation direction is parallel to the X-Y plane (Direction='X-Y'), the sign of the seismic loading angle [Degree] is referenced to the Z-axis using the right hand rule. The angle is zero at the GCS X-axis.


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5. Elastic Dynamic Analysis

Here the user can select the CQC as required by SDC. Complete Quadratic Combination (CQC) method: This combines the spectral results using structural damping and a weighted ratio of relative frequencies. The act of combination removes the sign of the result, thus leaving only a magnitude for the final answer.

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5. Elastic Dynamic Analysis The damping can also be considered in Elastic Dynamic Analysis: The following types are supported. Modal User defines the damping ratio for each mode, and the modal response will be calculated based on the user defined damping ratios. Mass & Stiff Prop. Damping coefficients proportional damping damping.

are computed for mass and stiffness proportional

Strain Energy Prop. 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.


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4. Elastic Dynamic Analysis For finding the spectral curve for different damping ratio the following Methods are used:

1.

Correction by Damping Ratio :

When a single spectrum is selected, a modifying equation is used to adjust the spectrum to apply to each mode having a corresponding damping ratio.

Interpolation of Spectral Data Select the method of interpolating the response spectrum load data. Linear : Linear interpolation method Logarithm : Log-scale interpolation method


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Open Model for Response Spectru m Analysis. Model 1_RS

(SIDL and SW already applied)

Load>Static Load Cases

1.

Enter SW, SIDL as Dead Loads.

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Procedure 2: Inelastic Time history analysis Time History Analysis can be performed with no fewer than three recorded earthquakes

Discussed in detail in other session.

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6. Capacity Determination

Step 2: Capacity Determination


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6. Capacity Determination Step 2: Displacement Capacity


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6. Capacity Determination Displacement Capacity


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7. Non Linear Static Analysis Pushover Analysis: Static Non Linear Analysis: > Is a technique by which a structure is subjected to a incremental lateral load of certain shape > The sequence of cracks, yielding, plastic hinge formation and failure of various structural components are noted. >The structural deficiencies are observed and rectified.

1

2

3

4

1

2

3

4

1

2

3

4

1

2

3

4

Model

Incremental Loading

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7. Non Linear Static Analysis Non Linear Material Behavior:

The Structural Material has non linear material behavior, thus after a specified loading, the elements responds non linearly.

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7. Non Linear Static Analysis Pushover Analysis:

Combines the Increments of loads with Non Linear behavior.

1

2

1

2

1

2

1

2

+

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7. Non Linear Static Analysis Pushover Curve:

r o i v a h e B r a e n i L

Non Linear Behavior


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7. Non Linear Static Analysis Performance of the Structure:


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7. Non Linear Static Analysis Procedure of Pushover Analysis:

Define Pushover Global Control

Define Load Cases

Define Hinge Properties

Assign Hinge Properties

Results


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7. Non Linear Static Analysis Design

Pushover Analysis

Select the load case as initial load for pushover analysis

Stiffness Reduction Ratio for the Skeleton Curve

Pushover Global Control


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7. Non Linear Static Analysis Design

Pushover Analysis

Pushover Load Cases

Use Initial Load : Accumulate the reaction/story shear/displacement due to the initial load to the pushover analysis result. Reaction / Story Shear by Initial Load : Accumulate the reaction/story shear due to the initial load Displacement by Initial Load : Accumulate the displacement due to the initial load


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7. Non Linear Static Analysis

Increment Method: Load Control Displacement Control

Load Pattern Load Pattern: Select the load pattern out of Mode Shape, Modal and uniform acceleration Mode: Select the mode


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7. Non Linear Static Analysis Design -> Pushover Analysis -> Pushover Hinge Properties

Interaction Type:

Select None for Beam elements Select P-M-M in Status Deformation for Column Elements Components:

Always Select Fx for columns ( PMM interaction)


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7. Non Linear Static Analysis


1997v05 Hangar Design

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