Pushover Curve

Using the interaction of the base shear and the displacements calculated from the results of a Pushover analysis, the capacity curve and capacity spectrum of a structure are calculated. The demand spectrum is also generated for a design seismic load using the design response spectrum.

The Performance Point, which represents the state of maximum inelastic capacity of the structure, is found through the cross point of the Capacity Spectrum and Demand Spectrum for a given damping ratio.    

From the Main Menu select Design > Pushover Analysis > Pushover Curve.

Pushover Curve dialog box

Pushover Load Case

Select a load case applied to pushover analysis.

Note

If Pushover Load Case acting in GCS Z-direction is specified, only Load Factor vs. Displacement becomes activated in Plot Type.

Plot Type

Select the type of pushover result curve to be produced.

Capacity Curve (MDOF)

Base Shear vs. Displacement

Shear Coefficient vs. Displacement: Shear coefficient (Lateral load/Total weight) vs. Displacement

Shear Coefficient vs. Drift: Shear coefficient vs. inter-story Drift

Load Factor vs. Displacement

Note 1

If Load Factor vs. Displacement is specified in Plot Type, Capacity Spectrum becomes inactivated.

Note 2

Pushover Curve due to vertical (gravity) load can be produced.  An example of application may be an arch structure subjected to vertical displacement in relation to the total reaction.

Additional Curves at other Nodes: Nodes numbers for which additional curves will be produced

Capacity Spectrum (SDOF)

For Performance Point (FEMA) : Load (Base Shear) - Displacement of the pushover analysis is transformed into the Spectral Acceleration (Sa) vs. Spectral Displacement (Sd) curve.

For Target Displacement (EC8/Masonry): Target displacement is a the seismic demand derived from the elastic response spectrum considered in terms of the displacement of an equivalent single-degree-of-freedom system.

• When Capacity Spectrum (SDOF) :  For Performance Point (FEMA) is selected

  

   

  Demand Spectrum

   

  

  In order to apply the design response spectrum to prepare the demand spectrum, define a design spectrum specified in a design standard.

   

  Demand Spectra at Damping Ratios (%)

  Using the specified damping ratio, produce the demand spectrum.

   

  Constant Period Lines at Period (sec)

  Produce the corresponding period lines for the specified periods.

   

  Evaluation of Performance Point

  Using the effective damping ratios suggested in ATC-40, evaluate the inelastic demand spectrum and compare it with the capacity spectrum to find the performance point.

   

  Procedure-A: The effective damping ratio for inelastic behavior of a structure is evaluated first, and a corresponding demand spectrum is created. The performance point is found through a repetitive process.

   

  Procedure-B: Assuming the ductility demand curve and using the corresponding effective period and effective damping ratio, the path of the performance point is evaluated and the intersection with the capacity spectrum is found.

   

  Damping Parameters

   

  Enter the parameters determining the effective damping ratio.

   

  Inherent + Additional Damping (%)

  Specify the total damping ratio (%) reflecting the inherent damping ratio and additional damping resulting from physical devices installed in the structure.

   

  Structural Behavior Type

  Select A, B or C to obtain a reduction factor applicable for effective damping.

   

  Note

  Structural Behavior Type is classified in the table below.

   

  Shaking Duration	Essentially New Building	Average Existing Building	Poor Existing Building
  Short	Type A	Type B	Type C
  Long	Type B	Type C	Type C

   

  For example, if 5% is specified for the damping of the structure, the effective damping becomes,

  

  Refer to ATC40 for the definitions of the variables.

   

  Performance Point

   

  It provides the information on the performance point on the spectrum and the performance point transformed into a multi-degree of freedom system. 

   

  V, D

   

  Maximum base shear and maximum displacement of the inelastic structure by the performance point 

   

  Sa, Sd

   

  Spectral Acceleration (Sa) and Spectral Displacement (Sd) at the performance point   

   

  Teff, Deff

   

  Inelastic effective period and effective damping at the performance point

   

   

Revision of Gen 2011

• When Capacity Spectrum (SDOF) :  For Target Displacement (EC8 / Masonry) is selected

   

  

   

  Demand Spectrum

   

  Design Spectrum: Select the design spectrum (i.e.= The elastic response spectrum associated with a reference return period of 475 years) to be applied to calculate the target displacement for the Limit State of Significant Damage (SD).

   

  Eurocode-8(2004)

  User Defined: Predefined user-defined response spectrum function can be selected.

   

  Revision of Gen 2011

  Transformation Factor (Gamma) Calculation

   

  Gamma can be calculated in the following two ways:

   

  1. Based on 2D Behaviour (EC8-1:2004 Annex B):

  2D Behavior is based on EC8 -1 :2004 Annex B and determines the value of gamma by  only considering the direction in which pushover analysis is performed .

  Hence the value of gamma is :

   

  

   

   

  2. Based on 3D Behaviour: 3D Behavior determines the gamma  by considering lateral deflection in all the possible directions.

  Hence the value of gamma becomes:

       

   

   

  Target Displacement

   

  The target displacement of a structure is determined through the transformation to an equivalent single degree of freedom system. For the detailed formula, refer to ANNEX B DETERMINATION OF THE TARGET DISPLACEMENT FOR NONLINEAR STATIC (PUSHOVER) ANALYSIS, EN 1998-1:2004. The target displacement, which is obtained from the above, corresponds to the seismic demand of the Limit State of Significant Damage (SD). Target displacement of the Limit State of Near Collapse (NC) is taken equal to that of SD multiplied by 1.5. Target displacement of the Limit State of Damage Limitation (DL) is taken equal to that of SD divided by 2.5.

   

  Note

   

  When transforming MDOF system to SDOF system, midas applies different modal participation factor to each direction for the 3 dimensional structure. The direction of each mode is determined based on the maximum Modal Participation Mass. For example, if Modal Participation Mass is as follows, Modal Participation Factor for mode 1 and 2 is applied to X-direction and Y-direction, respectively.

   

  Mode	Modal Participation Mass (%)
  	TRAN-X	TRAN-Y	ROTN-Z
  1	66.23	15	3
  2	13	60.85	1.06
  3	5	7	45

   

  Demand: Roof displacement corresponding to the target displacement for the seismic action is considered. Note that this is the target displacement for the MDOF system, while the vertical lines on the pushover curve represent the target displacements for the equivalent SDOF system.

   

  Capacity: Global capacity of the masonry structure in terms of roof displacement (Master node). Only applicable to Masonry material models.

   

  Global capacity of the Limit State of Significant Damage (SD) is taken equal to the roof displacement at which total lateral resistance (base shear) has dropped below 80% of the peak resistance of the structure, due to progressive damage and failure of lateral resisting elements.

   

  Global capacity of the LS of Damage Limitation (DL) is taken as the minimum value between a) displacement corresponding to the maximum base shear in the pushover curve and b) displacement corresponding to the story drift of 3/1000.  

   

  Step: The nearest increment step to the target displacement

   

  Remark: Assessment of the result in terms of the global response for the masonry structure. Only applicable to Masonry material models.

   

  Limit State of SD: The assessment is OK if the global capacity of the Limit State of SD is greater than the target displacement of the Limit State of SD   and   is less than 3. is the ratio between the acceleration in the structure with unlimited elastic behavior  and in the structure with limited strength .

   

  

   

  Limit State of DL: The assessment is OK if the global capacity of the Limit State of DL is greater than the target displacement of the Limit State of DL (i.e.= Target Displacement of the Limit State of SD divided by 2.5.

   

   

   

   

   

   

   

   

   

   

   

Revision of Gen 2011

• When Capacity Spectrum (SDOF) :  For Target Displacement (NTC 2008) is selected

  

   

   

   

  Demand Spectrum

   

  Demand Spectrum : The demand spectrum must be defined for each of the limit states.

  The demand spectrum can be defined in Load > Response Spectrum Analysis Data > Response Spectrum Functions. User defined Spectrum can also be specified for individual limit states. The target displacement for each of the limit states is determined on the basis of the response spectrum defined for that limit state.

  Revision of Gen 2011

  Transformation Factor (Gamma) Calculation

   

  Gamma can be calculated in the following two ways:

   

  1. Based on 2D Behaviour (EC8-1:2004 Annex B):

  2D Behavior is based on EC8 -1 :2004 Annex B and determines the value of gamma by  only considering the direction in which pushover analysis is performed .

  Hence the value of gamma is :

   

  

   

   

  2. Based on 3D Behaviour: 3D Behavior determines the gamma  by considering lateral deflection in all the possible directions.

  Hence the value of gamma becomes:

       

   

  Target Displacement

   

  Target Displacement:The target displacement of a structure is determined through the transformation to an equivalent single degree of freedom system.

   

   

  Note

   

  When transforming MDOF system to SDOF system, midas applies different modal participation factor to each direction for the 3 dimensional structure. The direction of each mode is determined based on the maximum Modal Participation Mass. For example, if Modal Participation Mass is as follows, Modal Participation Factor for mode 1 and 2 is applied to X-direction and Y-direction, respectively.

   

  Mode	Modal Participation Mass (%)
  	TRAN-X	TRAN-Y	ROTN-Z
  1	66.23	15	3
  2	13	60.85	1.06
  3	5	7	45

   

   

  Capacity

   

  Capacity: The capacity is determined for Global Verification and Local Verification.

   

  Capacity for Global Verification: Capacity for Global Verification for limit state SLD is determined as the displacement of the master node ( control node ) for the pushover step when the interstory drift reaches 0.005h. For limit state SLO capacity is determined when the interstory drift becomes greater than 2/3 of 0.005h. The assessment of a structure is done by comparing the capacity and the demand values. The assessment is OK when the capacity is greater than demand.

   

   

   

Additional Pushover Step for Story Drift

Define the additional pushover steps in order to check the pushover analysis results for the steps which have not been defined in Pushover Load Case. [Details…]

Text Output

Pushover analysis result graphs can be saved as text files.

Note

When Performance Point is found, an additional step for Performance Point is added in text file.  

Draw

Display Capacity Spectrum produced by Performance Point / Target Displacement.  

Note

If the user click on Draw button, an additional step for Performance Point is added into Additional Step dialog box.   

Graph Display Option