Equivalent Lateral Force vs Response Spectrum Analysis

Estimating seismic demands on buildings and structures is complex because of random nature of excitations. We have already learned how seismic demands on structure varies on the basis of nature of excitation, if you still want to learn about resonance you can refer to the blog post here:

In reality all buildings and structures will undergo inelastic demands during extreme seismic events, but are they designed to capture this nonlinear response and understand the extent of this non-linearity? Well, sort of, because you have two options to analyze the structure. Linear analysis or nonlinear analysis. Now nonlinear analysis is complicated and it takes a long time to run a complicated model. So if we have a small, regular building, we can do linear analysis on the bases of few parameters that are presented in building codes. These parameters are constructed assuming that the buildings are suppose to achieve a minimum strength under design level earthquake. Understand the word "minimum" over here, we are designing the buildings so that they will not collapse in case of seismic events but they could be damaged beyond repair. We can achieve higher performance by carefully accessing the building using many different critical parameters, but let us keep that for another article.

Linear elastic seismic analysis of structures is dependent on many assumptions. First assumption is, all the buildings will behave more or less the same under a particular sets of rules. For example, all shear wall buildings will have similar amount of ductility demand. Which in reality is not true. There are some building codes which understand this scenario and they assign additional factors to be incorporated in the building forces, which amplifies the seismic demands. There are some limitations to this method as well but it is still better in predicting the seismic demands than building codes which do not understand this amplified seismic demand.

The seismic demands on the structure is estimated by different methods. Elastic method and inelastic method. In elastic method, we consider that the structure remains elastic and the seismic demands on the structure is reduced using response reduction factor which assumes that the structure has the capacity to go beyond elastic limit but the performance is never checked. While in inelastic method, actual seismic demands are tested against the force resisting capacity and inelastic deformation capacity of the structure. In this scenario a true performance of the structure is tested and made sure it meets all the criteria of collapse prevention under maximum considered earthquake.

Want to read more about response reduction factors do refer to this post here:

Equivalent Lateral Force (ELF) Analysis & Response Spectrum Analysis are types of linear elastic analysis but the difference is, one is static analysis while the other is dynamic analysis.

Equivalent Lateral Force (ELF) Analysis

ELF analysis is based on an assumption of static cantilever beam. There is a slight effect of second mode of the structure taken into consideration in the story shear distribution but nothing more than that. The amount of seismic base shear consider for designing the building is on the basis of approximate period of the building, site specific ground acceleration and response spectrum curve, site class of the site and type of building system used to resist the lateral forces. This type of analysis should only be used when the building is symmetric, torsion is minimal, no vertical or horizontal irregularities and no discontinuities in the system and where the primary mode of the structure governs the structural dynamics. This means that ELF analysis leads to a fairly accurate results for short and very symmetric and regular buildings. Something like this one:

In ELF analysis, story force is generated as per the height at which the story is located from the seismic base. Higher the story up in the building, more loads will be generated by that story. But the drawback of this method is, the if there is a significantly heavier story near the base of the building, let us say Level 2 or 3, the contribution from this heavier story present close to the bottom of the building is significantly less. The only reason is because the equations are developed in such a way that it gives more weight to the height of the story from the base as compared to the story weight itself. This was just an example of drawback of ELF analysis. And so, it is always recommended that ELF analysis should be carried out on structures that are very regular and symmetric and do not exhibit any complex behavior.

Response Spectrum Analysis (RSA)

RSA is dynamic analysis of a structure. It is referred as dynamic analysis because it considers mode shapes and modal mass participation of the structure for different building frequencies. Every building has different frequencies of vibration and not just one frequency and when an earthquake occurs, the response of the building is a combination of different natural frequencies of the building. You have got to understand that, no structure man-made or natural will never respond to earthquakes outside of its natural frequency. These frequencies of the structure are known as eigenvalues and the shape each mode generates is known as eigen-vector. Now only first few natural frequencies are important to capture the overall response of the structure. Generally codes require 90% of modal mass participation to capture the overall response of the system.

Now to understand response spectrum analysis, you have to understand the mode shapes and modal mass participation factor. You can refer it on my blog here:

Because RSA is based on mode shapes and natural periods of the building, this captures more accurate “natural” response of building under seismic shaking. Because the story forces are generated on the basis of eigenvectors and story accelerations and mass of the story, it provides a more realistic “dynamic” response of the building.

RSA should always be carried out no matter what the building type is. It will always give you a better insight into building performance and demands on the structure, not just in terms of base shear but also in terms of story shear as well as moments in the building.

RSA is must when a building has re-entrant corners, irregularities in floor plan, horizontal and vertical discontinuities in lateral system, off centered core where center of rigidity is way off from center of mass and where torsional mode of the building may govern, when a building is significantly tall like 5–6 stories or more, when there are multiple types of lateral system present in the building. All these different aspects adds complexity to the natural and “ideal” behavior of the structure. Because it is important to capture these “unusual” behavior, RSA should be performed.

Another important thing to understand the difference between two analysis is the difference in flexure demands under both the analysis. Because ELF is based on a cantilever type of load distribution and because the load distribution does not consider significant impact of higher mode of the structure, the moment demands are quite large. While that is not the case with RSA.

Let me clarify this, a wall designed using RSA will definitely perform much better than the one designed with ELF analysis. ELF analysis overestimates the moments at the base of the structure as it ignores the higher modes of the structure. This will be reflected in significantly more flexure reinforcing in the walls which will be unrealistic and will lead to inefficient energy dissipation mechanism during an earthquake.

We want buildings to dissipate energy through inelastic actions in protected zone. If those zones will have much higher capacities, so seismic demands will get transferred to unprotected zones and there could be a potential brittle failure of the structure. In seismic engineering we trust on ductility and protected zones. For example hinge zone of shear wall is completely confined to achieve higher ductility. Now let us say that we design the hinge zone for static moments then in reality the structure may never yield there as dynamic properties suggest that the moments are only 40% of static. This means that hinge zone will never dissipate inelastic energy.

It is important for buildings to dissipate energy in seismic event and apart from dampers and damping energy there other source to dissipate this energy is inelastic energy in members. Because hinge zone is never going to go in inelastic state, this will in turn lead to potential hinge formation up in the building which may not be designed for inelastic demands. Thus increasing the chance of collapse.

I hope this article gave you a clear enough difference between RSA and ELF methods of analysis.

Thank you