# Equivalent Lateral Forces (esas.26)

esas.26

The seismic Equivalent Lateral Forces (ELF) analysis is the most well known method for the seismic analysis of structures. Although it is quite conservative, its simplicity makes it a very popular method for seismic design.

• The ELF method is a static analysis method.
• It requires the input of some data related to dynamic analysis: masses and at least one combination of mass groups.
• The calculation is based on the distribution of masses in the structure.
• The calculation of storey forces is based on the definition of storeys as well as on the reduced system, which must therefore be defined.

## Calculation of the Equivalent Lateral Forces

• The user is able to select from methods for calculation of equivalent lateral forces.
• These method are in compliance with the European and American standards - EN 1998 and ASCE 7-10.
• ELF are calculated in the background after a modal analysis.
• Calculated equivalent lateral forces are applied as one concentrated force at the mass centre of each storey.

Possibility to select how the acceleration is distributed in the building:

• Linear distribution of accelerations (EN 1998-1 clause 4.3.3.2.3 eq. (4.11) )
• Polynomial distribution of accelerations (ASCE 7-10 12.8.3)
• Distribution of accelerations from eigenshape (EN 1998-1 clause 4.3.3.2.3 eq. (4.10) )

Linear distribution

Distribution from eigenshape

## Application of the storey forces to the model

• The calculated storey forces are applied to the structure using the reduced system.
• The transformation matrices of the IRS method make it possible to "smear" the concentrated storey forces in such a way that the resultant of each storey force is applied at the mass centre of the corresponding storey. It is therefore not necessary to define diaphragms to apply storey forces.
• The loads are, however, applied in a distributed way to the entire storey, hence avoiding any numerical singularity, as would be the case if point loads would be applied in a conventional way.

## Results

All standard result output can be used in SCIA Engineer, without any restriction. Also, because it is a static load case, none of the issues related to the loss of sign due to the modal superposition apply here.

#### Brief comparison of ELF and response spectrum method

##### Equivalent lateral forces

Pros

• easy to use, intuitive

• static analysis, which implies the following advantages:

• results easy to check

• signed results & concomitant results

• non-linear analysis possible (not available yet in SCIA Engineer)

Cons

• limited to regular buildings (acceptance criteria defined in the design codes)

• only fundamental mode is taken into account

• conservative (in applicable cases)

##### Response Spectrum Method (modal superposition)

Pros

• applicable to all types of buildings (including irregular ones)

• multiple modes taken into account

• less conservative than ELF, more realistic

Cons

• requires understanding of modal analysis

• only elastic linear analysis (2nd order possible)

01/02/2016