## Footfall Induced Vibration Analysis

Footfall induced vibration analysis is to evaluate the responses of structures subjected to the actions of human footfalls. The structural responses include nodal accelerations, velocities and response factors etc. The human footfall loads are considered as periodical loads which are represented by a number of harmonic loads according to Fourier series theory. The detailed descriptions of human footfall loads can be found from references 35, 29 and 1 in the Bibliography which are also listed below. Footfall induced vibration analysis utilizes dynamic analysis results (frequencies, mode shapes & modal masses etc) to calculate the structure responses . The outputs of footfall analysis are the maximum responses of the structure for the given ranges of walking frequencies etc. The following three design guides of footfall analysis can be considered:

## Modelling Implications

The analysis stage facility allows the elements, element properties, restraints and constraint conditions to be specified for particular analysis cases. It is provided to allow the results from models differing in these ways to be combined (e.g. for the analysis of construction stages).

## Modelling Implications

Defining the structure

## Modelling Implications

In most cases a buckling analysis follows on from a linear static analysis, so a model set up for static analysis is the normal starting point. As buckling effects are three dimensional, it is inadvisable to define global restraints on the structure, as this can potentially provide an artificial degree of stiffness to the model.

## Modelling Implications

Proceed in the same way as for a nonlinear static analysis except that the elements can have Form-finding Properties assigned as well as, or instead of, their true physical properties. The solver looks for the appropriate form-finding property for each element, and if none is defined it uses the normal property. Therefore the model can include a mixture of stiff “real” elements and form-finding elements.

## Modelling Implications

Some structures can only be adequately modelled using 2D elements. For examples cores (where deformations in the plane of the element dominate) or floor slabs (where deflections normal to the plane of the element dominate). This section gives an introduction to 2D elements for linear analysis. Nonlinear analysis using 2D elements is discussed later.

## Modelling Implications

Cases

## RC Slab Reinforcement Design

The RC slab reinforcement design process calculates reinforcement areas for RC slabs modelled using 2D elements of uniform thickness, subject to any combination of in-plane compression and/or shear force and out-of-plane bending moment and torsion. The process ignores through thickness shear.

## Seismic Analysis

There are many different approaches to seismic analysis. The main approaches implemented in GSA are Equivalent Static Procedures, Response Spectrum Analysis, Linear Time History Analysis, and Nonlinear Time History Analysis. In general the response spectrum method is recommended in the various seismic codes as this is based on a dynamic analysis of the structure. However at times the simpler equivalent static method which ignores the actual dynamic response of the structure may be useful.