## Bridge analysis methods

For bridge analysis the live load requirements are very different to those for ordinary structural analysis. A number of tools are available in GSA to simplify the generation of these load cases. Three different ways of using the tools are available for different design codes and different situations:

## Buckling analysis

A buckling analysis is required where it is important to investigate the potential effects of buckling on the structure. These effects can be significant well before a structure actually buckles.

## Dynamic Analysis

Dynamic analysis covers a range of analysis options from determining the dynamic characteristics of a structure, through looking at linear response, to full nonlinear dynamic analysis.

## Envelopes analysis wizard

An analysis envelope is a stored envelope of results produced in way similar to other analysis options. I.e Analysis envelopes are requested by setting up an appropriate analysis task via the Analysis Wizard and then analysing this. The envelope is produced by comparing results from cases described in the syntax of a standard enveloping combination case. Since it is stored it is very much quicker to display than the alternative combination envelope that is produced by examining all effected analysis case results at the time of display. The disadvantage of analysis envelopes is that derivation of other results from those stored is not possible.

## Environmental Impact

The Environmental Impact feature enables environmental impact parameters to be assigned to the structure, and for the environmental impact of the structure to be reported both as a summary and to be represented graphically.

## 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:

## Harmonic Analysis

Harmonic analysis of structures is to calculate the maximum elastic response of a structure subjected to harmonic loading at steady state. The structure responses include nodal displacements, velocities and accelerations as well as element forces and moments etc. The harmonic loading is the load that varies sinusoidally along with time. Harmonic analysis is based on modal dynamic analysis results (frequencies, mode shapes and modal masses etc). It calculates the maximum structure responses for the given harmonic loads using modal superposition method.

## Linear Static Analysis

For most users the most common use of GSA is for linear static analysis. The Getting started manual guides a new user through the stages of building and carrying out a linear static analysis. In all cases a knowledge of linear static analysis is a pre-requisite for the more advanced analysis options.

## Linear Time History Analysis

Linear time history analysis is to calculate the linear responses of structures that are subjected to dynamic loads (force excitation) or base accelerations defined by the combination of the applied loads or base acceleration and load curve. The structure responses include nodal displacements, velocities and accelerations as well as element forces and moments etc at the chosen time intervals. If it is force excitation, the magnitude and locations of the dynamic loads are defined in the same way as that for static analysis and the variation of the dynamic loads along with time is defined by load curve in the unit of time versus load factor. If it is base acceleration, the load curve should be acceleration recordings of the ground motions in the unit of time versus acceleration, the ground accelerations varying with time given by the load curve can be scaled by a scaling factor that can be defined in the analysis wizard.

## Members and Design

For design to work, it is necessary for Member definitions to be complete and consistent. The recommended approach for creating a GSA model is to define members first, and then to create elements from them. This approach is also more efficient when coordinating the GSA model with a BIM model. The Create elements from members tool (under Model > Coordination menu) generates elements from Members.

## Modal P-delta analysis

A modal p-delta analysis is similar to a modal analysis, only the deflected shape is the mode shape. The same model (with a few changes) can be used for both. The difference in the case of p-delta analyses is that the stiffness is modified to include geometric stiffness effects.

## Nonlinear Static Analysis

There are several different types of nonlinear analysis, but there are two different effects that need to be considered.

## P-delta Analysis

For some structures it is important to be able to take account of the changes in the stiffness of a structure due to the load. When a column is subjected to an increasing compressive axial load its ability to carry transverse load is reduced until the Euler load is reached when it can no longer carry any transverse load.

## Periodic Load Analysis

Periodic load analysis is to calculate the maximum responses of structures that are subjected to periodic loads. The structure responses include the maximum nodal displacements, velocities and accelerations. The periodic loads are generic and the dynamic load factors of each of the harmonic components of the periodic loads at a given frequency are defined by the users through dynamic load factor table.

## Raft analysis

Raft analysis is a soil-structure interaction analysis, iterating between a solution of the structural problem and the soil problem until convergence of nodal displacements is achieved. See Raft analysis (Theory) for more information on how GSA iterates for a solution.

## 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.

## Response Spectrum Analysis

Response spectrum analysis is a method for estimating the seismic response of a structure from a set of modal dynamic or Ritz analysis results along with a response spectrum which capture the frequency content of an expected earthquake.

## Ritz P-delta Analysis

A Ritz P-delta analysis is similar to a Ritz analysis, only the deflected shape is the mode shape. The same model (with a few changes) can be used for both. The difference in the case of P-delta analyses is that the stiffness is modified to include geometric stiffness effects.

## 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.

## Summary

Analyse