Additional Information

See the adjacent Software Information links for general details regarding LUSAS Bridge software products and options.

Linear / Nonlinear Buckling Analysis

Buckling analysis of structures to codified requirements is often over-conservative. For existing structures, assessment or load rating to regional design codes often shows they ‘fail’ buckling checks, but detailed buckling analysis with LUSAS can often reveal additional ‘hidden’ capacity. 

For new plate girder, box or tub girder bridge designs, linear and nonlinear buckling analysis using LUSAS can investigate the girder stability during erection, look at the effects of a slab casting sequence, and also help to optimise the size of the web and flange plates, bracing, stiffeners and position of any temporary supports used.

Linear buckling

To obtain an indication of a structure’s potential to buckle under a particular loading a linear buckling analysis can be undertaken. Linear buckling analysis can estimate the maximum load that can be supported prior to structural instability or collapse. A LUSAS analysis therefore provides load factors based on classic elastic buckling. Where the type of structure isn’t covered by the design code, and where P-delta, lift-off and yielding effects are not significant in the loading range up to buckling, a linear buckling analysis should give a more accurate assessment of member resistance than would be obtained from a code of practice. However, imperfections and nonlinearities tend to prevent most ‘real’ structures from achieving their theoretical elastic (or "Euler") buckling strength, so the eigenvalue buckling load factors are therefore somewhat overestimated. To get a more accurate answer nonlinear analysis can be undertaken.

Nonlinear buckling

For a detailed structural buckling assessment a geometrically nonlinear analyses should be carried out. With this, material and boundary nonlinearity can also be investigated if found to be required. With a geometrically nonlinear analysis the stiffness matrix of the structure is automatically updated between loading increments to incorporate deformations which affect the structural behaviour (sometimes described by engineers as P-delta effects). 

Nonlinear buckling can be performed on the original structure without imperfection, or by automatically adding an imperfection based upon a scaled deformed shape which could be from a linear buckling model.

 

A structure may also experience some material nonlinearity during a buckling event (yielding for example) and/or some boundary nonlinearity (lift-off supports, perhaps). Generally it is recommended that modelling of nonlinear effects is done progressively in order to evaluate the results of each additional modelling at each stage. This helps in developing an understanding of the structural behaviour and helps to identify the cause of any potential failed analyses.

Nonlinear modelling of a plate girder in shear

Erection analysis

A nonlinear buckling analysis with LUSAS can investigate the stability of girders under self-weight loading, imposed construction loads such as slab pours, and wind loads. From the results obtained, members can be re-sized accordingly and, if necessary, temporary bracing and supports can be inserted into the model and tested to reduce the structural response.

For some clients, buckling analysis erection checks with LUSAS have highlighted that for some open box girder designs with narrow bottom flanges a standard design approach is just not valid.

 
Mesh sensitivity analysis

With finite element analysis, it is good practice to carry out a mesh sensitivity check to ensure that results are not unconservative. Mesh density should be checked to ensure enough elements of the type chosen are being used. Coarse mesh patterns could produce under conservative results; fine mesh patterns may take longer to solve and be no more accurate. Similarly quadratic elements will generally produce better results than linear elements with nonlinear capabilities. Unlike some software systems, with LUSAS, mesh patterns can be easily refined and manipulated without losing any assigned supports and loading - making it ideal for this type of work.

As an example the plate girder shown was meshed with 0.2m mesh divisions and then had 0.1m mesh divisions assigned for a mesh refinement check. The results showed that the change of displacement and the difference in maximum stress differed by less than 1% - meaning that, for this model at least, the initial mesh definition was sufficiently fine enough to achieve good results.

 

Nonlinear buckling analysis procedure with LUSAS
  1. Carry-out an initial linear analysis and check the stress levels for factored loading.
  2. Perform a mesh sensitivity analysis
  3. Run a linear eigenvalue buckling analysis to give load factor at which the critical buckling may occur.
  4. Save the model and define an initial imperfection (if necessary)
  5. Add nonlinear controls
  6. Run an initial geometric nonlinear buckling analysis
  7. Add additional nonlinear material or boundary conditions as necessary.

Nonlinear analysis of U-frame showing Ultimate Limit State collapse deflection

Buckling analysis summary
  • Linear buckling analysis enables an assessment of the buckling resistance of a structure, and may be particularly useful for structures not falling within the scope of codes of practice. 
  • In some instances, a linear buckling analysis may appropriate to satisfy checks against buckling, in others, it may only provide a good starting point for a thorough nonlinear buckling analysis.
  • Nonlinear buckling analysis provides a detailed buckling assessment and can include geometric, material and boundary effects.
  • LUSAS provides all the facilities required for linear or nonlinear buckling analysis, and has the ability to consider nonlinear buckling effects throughout a staged erection analysis.

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Any modelling and analysis capabilities described on this page are dependent upon the LUSAS software product and version in use.