Case Study
Raith Bridge box girder assessment
- steel box girder diaphragm assessment
- extraction of stresses using LUSAS scripting language
- checking with design codes
When the diaphragms of a steel box bridge do not comply with
assessment code criteria, finite element analysis using LUSAS Bridge will allow a
detailed analysis to be performed in order to help prove the integrity of the design. In
one such example, an assessment of Raith Bridge by Scott
Wilson Scotland Ltd, had identified that the pier and abutment diaphragms of the
box girders did not comply with the geometric requirements of the bridge assessment code
BD 56/96, so an in-depth analysis using LUSAS Bridge was carried out.
Raith Bridge carries the 6 lane, M74 motorway across the River Clyde and
comprises two, three span, twin steel box girder bridges with an in-situ concrete deck.
Whilst the steel diaphragms were the main area of interest, the whole bridge was modelled
in LUSAS. This allowed the distribution of load from the webs onto the diaphragms to be
calculated and eliminated the need for otherwise complex boundary conditions. It also
enabled global effects, such as the torsional effects from the behaviour of the whole
structure to be considered. Due to symmetry only one diaphragm at an abutment, and one at
a pier needed to be investigated in detail.
The finite element model
was constructed from three and four noded thick shell elements supplemented by thick
engineering beam and 3D continuum elements. Two spans were modelled in detail with shells
representing the steel box and concrete slab. Beam elements were used to represent the
contribution from the longitudinal stringer beam, transverse beams and vertical and
transverse stiffeners. Within this section of the model, a pier and abutment diaphragm
were modelled in detail with a finer mesh to allow the behaviour of individual components
to be examined. The third span was included as beam elements with appropriate geometric
properties. Self weight, surfacing, parapet, and vehicle loads were applied to the five
notational lanes in accordance with the "Design Manual for Roads and Bridges"
document BD 21/97.
The model was required to generate elastic stresses that could be
extracted and compared to criteria in the code of practice to ensure that the steel
components will not yield or buckle under the combined permanent and vehicle loadings. A
twin box model was used to examine the way live load applied over one box was distributed
between the two boxes. This showed that there was little difference in the distribution of
diaphragm stresses between the two models. The single box model was then used for detailed
stress determination because of the lower analysis times. The diaphragms were supported on
a layer of 3 dimensional solid continuum elements that represent the bearing plates
beneath the box. At the pier diaphragm, the deck model was supported on representation of
the leaf pier, which was included as a series of shell elements. At the abutment, the deck
was supported on an array of points that represented the distributed support from the
abutment. These techniques avoided the unrealistically high stresses that can result from
the use of point supports in this type of model.
Stress plots
in global axes were produced from LUSAS for specific load cases and using the LUSAS
scripting language, results were assembled for output to spreadsheets to determine
compliance with the various requirements of BD 56/96. The code is complex and, with
reference to the buckling criteria, it was not clear which plates would be critical since
high stresses were concentrated on small panels and larger panels were less highly
stressed. The use of the spreadsheets allowed easy checking of all panels, and stress
changes in critical panels could be rapidly identified for different load combinations.
The allowable stresses were determined and checked against buckling and yield criteria in
the assessment document and areas of non-compliance with yield criteria were highlighted.
The use of LUSAS in conjunction with scripting and spreadsheets gave a
rapid analysis of the structure and a comparison of results with code requirements. The
detailed model ensured that the correct distribution of load from the webs, through the
diaphragms to the bearing was obtained. Results showed that the diaphragms were vulnerable
to the assessment loading and may require further nonlinear analysis to prove the capacity
of the structure.
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