Concerning the difference between Linear Dynamic Analysis, which was understandably Response Spectrum Analysis (RSA) and Non-linear Dynamic analysis, which was on the other hand, is understood to be Non-linear Time History Analysis (NL-THA). RSA and THA are like chalk and cheese. The linear procedure that corresponds to NL-THA is obviously the Linear Time History Analysis (Lin.THA). Then which non-linear procedure corresponds to RSA? This is what made me try to resolve by posting this thread. I’m just putting forward what I think I know. Please post your opinions, if opposing, freely.
In general, the methods of seismic analysis can be classified as (1) Static and (2) Dynamic. Dynamic analysis can further be classified as (i) Dynamic Characteristics based (static) Analysis and (ii) Time Domain Analysis. All of the above categories have their (a) Linear and (b) Non-linear counterparts.
1) Static Analysis
2) Dynamic Analysis
Rahul Leslie
rahul.leslie@gmail.com
In general, the methods of seismic analysis can be classified as (1) Static and (2) Dynamic. Dynamic analysis can further be classified as (i) Dynamic Characteristics based (static) Analysis and (ii) Time Domain Analysis. All of the above categories have their (a) Linear and (b) Non-linear counterparts.
1) Static Analysis
a) Linear
• Seismic Coefficient Method (SCM)(IS:1893, Cl.7.5.3 & 7.7.1): Here the seismic base shear for the building is determined by using an empharically determined time period, and distributed over the stories as lateral load proportional to an assumed mode shape, which is parabolic (but interestingly with 100% mass participation assumed). Here lateral load determination is all formula based, no modal analysis is required, and the method is therefore STATIC.
b) Non-linear: This is done by running a non-linear analysis on a non-linear building model. Non-linearity is incorporated in the analysis model in form of non-linear hinges inserted into an otherwise linear elastic model which one generates using a common analysis-design software package.
• Non-linear Static Analysis (NSP) or Pushover Analysis (FEMA-356, Sec.3.3.3; ATC-40, Ch.. Unlike as SCM (where the lateral load of a calculated intensity is applied in whole - in one shot), in NSP, analysis model is gently 'pushed over' by a monotonically increasing lateral load applied in steps up to a predetermined value or state. Here also seismic base shear for the building is distributed over the stories as lateral load proportional to an assumed mode shape, which is either uniform (FEMA-356, Sec.3.3.3.2.3-2.1) or a power distribution (FEMA-356, Sec.3.3.2.3-1.1) with the value of k* determined to be a value between 1 (inverted triangular distribution) and 2 (parabolic distribution) by an empharical method. You know why it is the method is ‘therefore’ STATIC.
*(k is the power of h shown with k=2 in the formula under IS:1893, Cl.7.7.1)
2) Dynamic Analysis
a) Linear
i) Dynamic Characteristics based (static) Analysis
• Response Spectrum Analysis (RSA) (IS:1893, 7.8.4) – Here a DYNAMIC (modal) analysis is done to get the dynamic characteristics of the building (natural frequencies and mode shapes) from which the lateral loads corresponding to each mode shape is calculated, with which a STATIC analysis is performed for each mode, the results (BM, SF, etc.) of which are then combined (SRSS) to get the design forces.
ii) Time Domain Analysis
• Linear Time History Analysis (Lin.THA). (IS:1893, Cl.7.8.3): In THA, the support points of the model is oscillated back and forth in accordance to a recoded ground motion of an actually occurred earthquake (as recorded by a seismograph, and available in tabular form of time vs. acceleration). The results (BM, SF, etc.) are usually taken as the maximum enveloped over time (ie., the max. BM on the mid span of a particular beam in the maximum among all the BMs, each corresponding to each time point over the duration of earthquake).
b) Non-linear : As said above, this is done by running a non-linear analysis on a non-linear building model.
i) Dynamic Characteristics based (static) Analysis
• Non-linear Static Analysis (NSP) or the same Pushover Analysis mentioned above, but with the 1st mode proportionate lateral loads (FEMA 356, Sec.3.3.3.2.3-1.2) or more rightly, a combination (SRSS) proportionate lateral loads (FEMA 356, Sec.3.3.3.2.3-1.3). Please note that unlike the RSA, it’s not the results corresponding to each mode shape that is SRSS’ed, but the loads themselves. [Of course, methods have been developed and papers published on how to SRSS the pushover results corresponding to each mode shape, but not yet been standardized (by agencies like FEMA, ATC or ASCE)].
No one considers putting this version of pushover analysis under Non-linear Dynamic Analysis (and as the non-linear counterpart of RSA), but this is my starting point and the reason for posting this classification in the first place.
ii) Time Domain Analysis
Author from SEFI• Non-linear Time History Analysis (NL-THA). (FEMA356, Sec.3.3.4.2.3). This is same as the Lin.THA, but here since the structure has non-linear hinges inserted, the members can undergo and stiffness degradation, strength deterioration – in general, damage, as a real building would, during the progress of an earthquake.
Rahul Leslie
rahul.leslie@gmail.com








