Introduction of N2 method The N2 Pushover Method of ...admin.midasuser.com/UploadFiles2/105/Pushover N2 method.pdf · The N2 Pushover Method of Eurocode8-1:2004 and NTC2008 Introduction

Contents

Introduction of N2 method

Normalization of mode shape

Determination of lateral

The N2 Pushover Method ofEurocode8-1:2004 and NTC 2008

load pattern

Determination of time period, yield force and yield displacement

Determination of target Determination of target displacement

Verification

Midas Information Technology Co., Ltd.

Program Version Gen 795 (R1)

Revision Date 2011.11.07

http://kor.midasuser.com/building

The N2 Pushover Method ofEurocode8-1:2004 and NTC2008

IntroductionStep

00

In Gen 795, N2 method has been completely implemented for the determination of the target

displacement and capacity for the EC8/Masonry and NTC 2008.

Pushover analysis is a non linear analysis carried out under conditions of constant gravity loadsPushover analysis is a non linear analysis carried out under conditions of constant gravity loads

and monotonically increasing horizontal loads. It may be applied to verify the structural

performance of newly designed and the existing buildings for the following purposes:

(a) to verify the over strength ratio values.

(b) to estimate the expected plastic mechanism and the distribution of damage.

(c) to assess the structural performance of existing or retrofitted buildings(c) to assess the structural performance of existing or retrofitted buildings.

(d) as an alternative to the design based on linear analysis which uses the behavior factor q.

In that case the target displacement should be used as the basis for the design.

Prominent Features:

The N2 method combines the advantages of the visual representation of the capacity

spectrum method with the physical basis of inelastic demand spectra.

The N2 method leads to a transparent transformation from a multi – degree of freedom

(MDOF) model to an equivalent single degree of freedom model (SDOF).

The N2 method takes into consider the period range of the structure for the determination of the

Procedure of the N2 method:

The N2 method takes into consider the period range of the structure for the determination of the

target displacement.

Normalization of mode shape

Generation of lateral load pattern for pushover analysis

MDOF system to SDOF system

Determination of idealized elasto –perfectly plastic force displacement relationship.

Determination of time period and yield force of the SDOF system

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Determination of time period and yield force of the SDOF system

Determination of target displacement of the MDOF system corresponding to the response

spectrum.


Step

00 New Load Pattern

For the implementation of the N2 method a new load pattern Normalized Mode Shape * Mass

has been added to the Pushover Load Cases.



Step

02 Normalization of Mode Shape

The mode shape for which the pushover analysis has to be done is obtained by the eigenvalueanalysis of the structure.

In midas Gen normalization is done on the basis of the master node ( user defined) and hence after normalization the mode shape becomes such that the Φ at master node becomes 1.

Pushover analysis is stopped when the displacement of the master node reaches the specified i di l tmaximum displacement.

The lateral loads are applied on the centre of mass and the lateral load pattern is obtained by the normalized Ф values of centre of mass.

Normalization example has been provided for the following 3D structure.The obtained values of Ф for the mode shape 1 for the master node and the centre of mass of the stories are specified in the table along with the normalized valuesstories are specified in the table along with the normalized values.

Master nodeCentre of Mass

3F

Roof

1F

2F

3F

StoryMode Shape

ФNormalized Mode Shape

Ф

Normalization of Mode Shape

y Ф Ф

Roof (Master Node) .0621 1

Roof (Centre of Mass) .0346 .557

3F (Centre of Mass) .0326 .5249


1F (C f M ) 1948



*It is recommended that the master node be the node at the centre of mass . Otherwise in some cases, the normalized Ф of the roof may not be 1 as in the table.


Step

02 Normalization of Mode Shape

Example of normalization for a 2D model:

.87

.65 .74

1

Defined Master Node

.54

.21

.63

.24

Model Mode Shape Normalized Mode Shape

StoryMode Shape Normalized Mode Shape

Normalization of Mode Shape

Story Ф Ф

Roof (Master Node) .87 1

Roof (Centre of Mass) .87 1


2F (Centre of Mass) 54 632F (Centre of Mass) .54 .63




Step

03 Lateral Load Pattern

The Lateral Load Pattern is required to generate the Pushover Curve for the SDOF model. Lateral loads are applied at each story ( mass centre) and the roof displacement is obtained .

The load is applied to till the point when the displacement of master node reaches the maximum Displacement.

The lateral load pattern is obtained by multiplying the mass of the story with the respective normalized Ф and then normalizing it with the force obtained for roof story.

m = 4001

1m4 = 400

.74

.63

.24

1

.55

.31

06

m3 = 300

m2 = 200

m1 = 100

Model Normalized Mode Shape

.06

Load Pattern

m1 100

Story Story MassNormalized Mode

ShapeФ Calculation Load Factor

Roof (Centre of Mass) 400 1 (1X400)/(1X400) 1

3F (Centre of Mass) 300 74 ( 74X300)/(1X400) 55

Lateral Load Pattern

3F (Centre of Mass) 300 .74 (.74X300)/(1X400) .55





Step

04 Time Period and Yield Force

The yield force and the yield displacement is obtained from the bilinearized pushover curve .The F* and the d* values are obtained from the Pushover Curve generated for the SDOF model.

They yield force fy* ,which represents the ultimate strength of the idealized system, is equal to the base shear force at the formation of the plastic mechanism. The initial stiffness of theid li d i d i d i h h h d h l d h id li didealized system is determined in such a way that the areas under the actual and the idealized force – deformation curves are equal.

Based on this assumption, the yield displacement (dy*) of the idealized SDOF system is given by:

where Em* is the actual deformation energy up to the formation of the plastic mechanism

dy*

AnnexB of EN 1998-2004 midas Gen - Determination of dy*

After determining the values of Fy* and dy*, the time period is calculated as:



Step

05 Target Displacement

The target displacement of the structure for the MDOF model is obtained by first determiningthe target displacement for the SDOF mode and then multiplying it with Г.

where

The target displacement for the SDOF model is obtained by first determining det*

Where: Se(T*) is the elastic acceleration response spectrum at the period T*

The target displacement is determined by determining whether the structure is in the short g p y gperiod range or the medium and long period range. The range is determined by comparing the values of T* and Tc where T* is the time period and the Tc is the corner point between the short and the medium period range in the response spectrum.

Short Period Range Medium and Long Period Range



Step

05 Target Displacement

(a). T* < Tc (Short Period Range)

Where:

(i) If Fy*/m*> Se(T*) , the response is elastic and thus:

(ii) If Fy*/m* <Se(T*), response is nonlinear and thus:

Where:

(b) T*> Tc (Medium or long Period Range)(b) T Tc (Medium or long Period Range)

Target displacement for the MDOF model is obtained by multiplying the value obtained for the SDOF model by Γ



Step

05

Target Displacementcalculation for NTC 2008

Demand and Capacity

Text file containing the values of m*, T*,Fy* and target displacementdisplacement



Step

06 Safety Verification for NTC 2008

Safety Verification is divided primarily into two different groups:

Global VerificationLocal Verification Capacity for Global Verification

The capacity for SLD is obtained as the displacement of the master node when the interstorydrift becomes .005h , where h is the story height.

The capacity for SLO is 2/3 the capacity for SLD

Global verification is performed by comparing target displacements (as obtained in the previouspages) and interstory drift capacity for both SLD and SLO limit states.For example:The following table shows the story drift table for a structure for different storiesThe following table shows the story drift table for a structure for different stories.

Story Drift Table for 1st floor

Story Drift Table for 2nd floor

Story Drift Table for 3rd floorStory Drift Table for 3rd floor

Story Drift Table for 4th floor


It can be realized that the lowest step is obtained as the step 43 for which the inter story drift in1st and second floor reaches more that .5%. Hence the capacity for global verification will beobtained by determining the displacement of master node at 43rd step which is the capacity forSLD, capacity for SLO = 2/3 SLD


Step

07 Capacity Determination NTC 2008

Capacity Determination for Local Verification

The capacity is determined as shown in the table.

The demand (force, moment or rotation) for a member is obtained for the pushover step which is nearest to the target displacement in the spectral demand curve.

Eqn A.1

The local verification is done automatically in the program by generating the safety verification table.When the demand exceeds capacity the table shows NG for the particular element.



Step

08 Safety Verification Table

Capacity values for different limit states can now be seen along with the user defined stepThe limit state for capacity can be defined along with the user defined step.

Safety Verification Table


Documents

Introduction of N2 method The N2 Pushover Method of ...admin.midasuser.com/UploadFiles2/105/Pushover N2 method.pdf · The N2 Pushover Method of Eurocode8-1:2004 and NTC2008 Introduction