Bridge analysis: Analysis

Bridge load optimisation is selected in the Analysis wizard.

Analysis of bridge structures consists of a number of stages:

• Influence analysis
• Optimisation
• Expansion
• Static analysis

For method A as described in the References entry on bridge loading all these stages are usually carried out in a single operation, while for method B it is more likely that only the influence analysis will be carried out initially and the other operations will be done using the tools described.

The influence analysis is carried out by applying a unit load across the width of the path at a series of positions along each path, the result for each influence effect being extracted for each load position. As this involves solving for many sets of loads the influence analysis can be quite slow.

The influence analysis is selected in the Analysis wizard. The influence analysis is carried out by applying a unit load across the width of the path at a series of positions along each path, the result for each influence effect being extracted for each load position. As this involves solving for many sets of loads the influence analysis can be quite slow.

The optimisation uses the path loading and the influence results to determine the most onerous load positions (those that maximise the response at the positions of the influence effects) and creates a set of static bridge loads.

The third stage in the bridge analysis is to carry out a static analysis of the structure subject to the static bridge loads determined by the optimiser. The first stage in this analysis is to expand the bridge loads Model > Bridge modelling > Expand bridge loading menu command. This converts the bridge loads defined in the Bridge loads table into loads on the structure. The static analysis is then selected in the Analysis wizard.

Influence analysis

For bridge loading, where large concentrated loads move across a structure, it is often useful to plot influence lines to determine the optimum position of a load to maximise an effect.

Each point on an influence line is the magnitude of a specified effect (e.g., moment, displacement, reaction etc) at a specified point on the structure (node or position on element) of a unit load, plotted at the point of application of the load. An influence line is the line joining these points along the line of travel of the load.

The influence analysis option in GSA produces influence lines along the centre of every path specified in the Paths module (or on key automatically generated paths), for each effect specified in the Node influence effect and Element influence effect modules.

The influence lines are produced by analysing the effect of a knife edge load (KEL) at approximately 100 points along each path, and storing the specified effects only.

All the influence lines produced by this analysis are stored in a single analysis case, and can be viewed in graphical or tabular form. As an aid to optimisation, details of each lobe of an influence line, where a lobe is generally the section of the influence line between points of zero influence, can also be tabulated. For lane paths only, lobes are split where the effective lobe length (the base length of a triangle with the same maximum value as the lobe) would be less than 90% of the actual lobe length.

No other results are available for this analysis case.

Lane by lane path optimisation

The path load optimisation tool uses the results of an influence analysis to generate a series of Static bridge loads, based on the loading information specified in the Path loading module.

For each influence effect and each entry in the *Path loading module, the optimiser produces two groups of static bridge loading, to give the maximum (most positive) and minimum (most negative) effect.

Path loading can be a standard (code dependant) load type, or a user defined load type. For details of the application of standard type loading the user should refer to the relevant code, details of the versions of codes used are given in the description of path loading. User defined path loading can be made up of vehicles, KELs, and VUDLs.

The following rules are used for optimisation, these are based on the UK loading code (BD37) but are generally applicable:

• Unless noted otherwise in the definition of Standard bridge loading only one KEL or vehicle will be placed in each path, across the width of the path.
• VUDLs will always be applied over complete lobes of an influence line (except when placed outside a vehicle exclusion length, see below) and over the full width of the path.
• For Vehicle + VUDL loading, the VUDL will be placed starting at the specified exclusion length either side of the midpoint of the vehicle (if effect at this point is adverse, or at the start of the next adverse lobe if not). Loaded length for calculating intensity of VUDL is the total length of adverse lobes, including each adverse lobe in the exclusion length.
• Intensity of VUDL will be calculated for the sum of the lengths of the adverse lobes. The worst case from 1, 2 or more lobes loaded will be determined.