Bridge analysis, design + assessment

Case Study 

Making the most of Eurocodes for critical buckling analysis

  • Investigations into the implications of changing to Eurocodes for bridge design

  • Comparison of analysis of first and second order effects for critical buckling analysis

  • Increased load factors obtained - especially for nonlinear analysis

Atkins, the UKís largest engineering consultancy, has been carrying out investigations into the implications of using the new Eurocodes for UK bridge design. As part of its study finite element test models were created in LUSAS Bridge to assess particular aspects of the new codes. From analyses carried out, significant benefits have been seen when using the new Eurocodes for linear and nonlinear investigations into critical buckling analysis of steel girder structures with transverse stiffeners.


The use of Eurocodes for bridge design in the UK requires engineers to make greater use of first principles as fewer rules and formulae are given compared to the BS 5400 code. The new codes have, in effect, moved away from being equation-based to becoming more analysis driven, and this, in many cases, will lead to the greater use of finite element analysis to model particular types of structures.

First order or second order?

The default analysis in the new Eurocodes is second order (nonlinear), and considers p-delta effects. But, in almost all cases where first-order (linear elastic) analysis with BS 5400 was used previously, first order analysis with the Eurocodes can be used just as successfully, if not more so. However, when finite element software with a nonlinear capability is used to investigate second-order effects, design to the Eurocodes really comes into its own and great benefits can be obtained both in economy of new designs and in assessments of existing structures over BS 5400 methods.

Evaluating the Eurocodes

Atkins carried out trial calculations for the Highways Agency and other clients on existing concrete and steel-concrete composite bridges. These trials indicated that, on average, when the basic application rules are applied the Eurocodes give a small increase in economy in the design. Chris Hendy, Head of Bridge Design and Technology at Atkins said: "For concrete structures, there is a systematic saving in flexural reinforcement and shear reinforcement for reinforced concrete structures, but generally little difference for prestressed structures." He continues: "For steel design, there is more economy to be obtained from using the Eurocodes for stiffened structures, which reflects a greater confidence in behaviour as a result of recent testing and of some nonlinear parametric studies that have been undertaken. Economy can be improved further if nonlinear analysis with software such as LUSAS Bridge is employed."

Transverse stiffener investigation

A model of a plate girder with a central load was one of many set up by Atkins on behalf of the UKís Highways Agency to investigate the Eurocode rules for transverse stiffeners resisting shear. The model was created in accordance with the requirements of EN 1993-1-5 and modelled the geometry of an actual physical test specimen that was tested in the 1980s. Chris Hendy said: "Not only did the nonlinear LUSAS model give results almost identical to the actual physical test specimen but it also showed that the EN 1993-1-5 rules for stiffeners were very conservative for this particular beam, and the BS 5400 Part 3 predictions even more so."

Nonlinear modelling of a plate girder in shear

Nonlinear modelling of a plate girder in shear

Critical buckling modelling

In another investigation, Atkins used LUSAS Bridge to model a pair of steel beams during concrete placement, prior to the concrete slab providing lateral restraint to the beams. For this situation the new Eurocodes give no formula to derive the critical bending moment. In LUSAS, thick shell elements represented the plate girders, and beam elements modelled the bracing members. One span was loaded with wet concrete such that the lateral torsional buckling would govern the resistance of the beam group. From an eigenvalue buckling analysis the critical buckling moment was seen to be caused by the 20th mode, but at a load factor 50% greater than that predicted by BS 5400.


Nonlinear analysis of a pair of braced beams

Elastic critical buckling analysis for a pair of braced beams (20th mode shape)

Nonlinear analysis

A nonlinear analysis carried out for the same paired beams with material behaviour based upon Eurocode recommendations, and with initial imperfections based on the elastic critical buckling results, gave even better results. A collapse deflection similar to that for elastic buckling was obtained but a large increase in resistance was achieved by using nonlinear analysis instead of the former linear analysis as shown in the results table. This greater resistance could be attributed to a number of factors including: partial plastification of the tension zone; conservative code buckling curves for this mode of buckling; and also redistribution of moment away from the span to the supports.

Nonlinear analysis of a pair of braced beams

Nonlinear analysis of a pair of braced beams

U-frame investigation

Atkins also examined the lateral torsional buckling of U-frame bridge. Hand calculations using EN 1993-2 clause and EN 1993-1-1 buckling curves gave a MbRk of 54358 kNm but by using LUSAS to run a nonlinear analysis the MbRk value was increased to 72340 kNm. This was a significant improvement over BS 5400 for several reasons: the effect of moment variation along a beam is better accounted for; the partial plastification of the tension zone is accounted for; and strain hardening allowed flange stresses to increase about 7% above yield values.

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

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

In summary

Elastic critical buckling analysis using the new Eurocodes is more efficient than BS5400 Part 3. When linear buckling analysis is used comparable, and often more beneficial results are obtained from using the Eurocodes, but when second-order effects are considered using software with a nonlinear analysis capability, such as that provided by LUSAS, even greater economy is achieved.

"Not only did the nonlinear LUSAS model give results almost identical to the actual physical test specimen but it also showed that the EN 1993-1-5 rules for stiffeners were very conservative for this particular beam, and the BS 5400 Part 3 predictions even more so."

Chris Hendy, Head of Bridge Design and Technology, Atkins

Reference: Eurocode / BS 5400 comparison



Equivalent BS 5400 part
  • EN 1990 Basis of Structural Design
BS 5400 Part 1 and 2
  • EN 1991-1-1 Densities, self weight and imposed loads
  • EN 1991-1-4 Wind loads
  • EN 1991-1-5 Thermal loads
  • EN 1991-1-6 Actions during excavation
  • EN 1991-1-7 Accidental actions
  • EN 1991-2 Traffic loads on bridges
BS 5400 Part 2
  • EN 1992-1-1 General rules and rules for buildings
  • EN 1992-2 Bridges
BS 5400 Part 4
  • EN 1993-1-1General rules and rules for buildings
  • EN 1993-1-5 Plated structural elements
  • EN 1993-1-8 Design of joints
  • EN 1993-1-9 Fatigue
  • EN 1993-1-10 Brittle fracture
  • EN 1993-2 Bridges
BS 5400 Part 3
  • EN 1994-2 General rules for bridges
BS 5400 Part 5

Listing of Eurocode parts needed in the design of a steel-concrete composite bridge


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