## Client:

Sintagma S.r.l. - Perugia (IT)

Bridges with steel-concrete deck from 1 to 6 spans, 30 – 90 m, 2 longitudinal beams, Abutments and piers in reinforced concrete. Seismic isolation. Calculation report for executive project.

Main FE modelling approaches in the design of steel-concrete decks are:

- Grillage of steel-concrete beams
- Concrete slab modelled with shells and steel members with eccentric beams
- Concrete slab and steel web with shells, flanges and bracings with beams

Approach 2 or 3 in modelling a composite bridge, is currently easy to set up in advanced FE software, and they allow to deal with curved girder structures, where significant torsional stresses arise and to get directly from the model the design stresses in the bracings.

Up to now, a large shortcoming in modelling the concrete slab and eventually the web of the steel beam with shell elements, was in the loss of direct availability of full set of design forces and moments in the composite beams, needed for code of practice checks.

The joined use of LUSAS and PontiEC4 overcomes this shortcoming; an application to a deck designed by Alhambra srl for Sintagma srl on a motorway in Sicily is presented. The deck has 2 longitudinal beams curved in plan, 4 spans 75-87.5-87.5-75 m, K-shaped reticular transverse beams supporting an intermediate beam, and torsion bracing members.

The analysis of the structure is performed by modeling with the finite element method, adopting the LUSAS system.

The structure was modeled by discretizing the slab and the beams webs with 4-node shell elements QTS4 type, the flanges with beam elements BMI21 type. This allowed the modeling of the real position of the reticular transverse trusses and of the torsion braces, also modeled with BMI21 beam elements and with the release of the bending moments at the ends. The intermediate beam is also inserted in the model, modeled with BMI21 beam elements. The portion of the slab straddling the supports, for an extension equal to 15% of the span of the respective spans, was assumed to be cracked.

Below is a rendered three-dimensional view of the complete model and one of the elements in steel.

The identification of the traffic load positions suitable to give the maximum / minimum design actions on the various elements of interest is carried out through an automated procedure, typical of the LUSAS finite element system, which involves the processing of the surfaces of influence of the various stress characteristics, in the points of interest through a “Direct Method Influence” (DMI) analysis, preliminar to the search for the most unfavorable traffic load positions, through a “Vehicle Load Optimization” (VLO) analysis.

The stresses N, T, M in the points of interest of a beam-shell model are obtained by integrating the results on “slices” of the model placed independently of the mesh; the influence surfaces, defined in order to evaluate the maximum / minimum bending and shear stress on the most stressed longitudinal beam, can be calculated, either in correspondence of the mesh nodes or of the slices.

The following figure shows, through red rectangles, the schematic positioning of the various “slices” on which the surfaces of influence have been made (only 2 spans of the deck has been studied for symmetry).

*“Slices” positions for influence surfaces (red rectanguls)*

The “Vehicle Load Optimization” analysis generates as many loadcases as there are maximized / minimized stresses at a given slice.

The following figure shows the load pattern, generated by the VLO, which maximizes the bending moment on the girder placed on the outside curve, in correspondence with the support of the pile P1; the arrows in red represent the tandem loads while those in magenta the distributed loads, segmented on the roadway according to the indications of the surface of influence.

*Traffic load pattern generated automatically by the “Vehicle Load Optimization” analysis – Loadcase that maximizes My of the girder placed on the outside of the curve on the P1 pile*

The “slices” allow us to have the stresses in significant and a priori chosen sections according to our needs, making the visualization phase of the results concise and fast without losing the precision of the representation of the diagrams of the stress even with a small number of sections, as shown by the following diagram of the moment My.

*My trend along the external and intermediate girder for the fundamental ULS*

The definition of the slices in the Composite Design Member of LUSAS is useful because it allows you to automatically create the verification sections in PontiEC4, nesting each one in the corresponding segment and load the corresponding design stresses, otherwise the sections and segments must be defined directly in PontiEC4 and the stresses imported from an Excel folder.

*PontiEC4 Geometry window – Section definition*

Based on the abscissa of the section, PontiEC4 software associates with the section the width of the slab actually collaborating, to be considered in the checks, due to the shear lag effect.

The effect of shear lag was evaluated in the following form where a reduction in the collaborating width of the slab is noted, when you get closer to the supports.

*PontiEC4 shear lag data window*

The variation of the collaborating width of the slab is represented in the graph generated by PontiEC4 below.

*Collaborating width of the slab along the whole viaduct*

**ULS, SLS & fatigue calculations**

- Section properties
- Primary (isostatic) effects of shrinkage and temperature change
- Creep & shrinkage coefficients (EN1992-1-1, App B)
- Classification of sections (EN1993-1-1, Table 5.2)
- Ultimate bending check for Class 1 & 2 sections (EN1993-1-1, 6.2.5)
- Stress checks for Class 3 & Class 4 sections (EN1993-1-5, Section 4)
- Ultimate shear & web buckling (EN1993-1-5, Section 5)
- Bending-shear interaction (EN1993-1-5, Section 7)
- SLS stress checks (EN1994-2, 7.2.2 (5) & EN1993-2, 7.3)
- SLS web-breathing check (EN1993-2, 7.4)
- RC crack checks (EN1994-2, 7.4.3)
- ULS, SLS and fatigue checks for connectors (EN1994-2, 6.6 & 6.8)
- ULS, SLS and fatigue checks for bolted connections (EN 1993-1-8)
- Fatigue checks for both structural steel and reinforcement components (EN 1993-1-9, EN 1994-2, EN 1993-2)
- Longitudinal and transversal stiffeners check (EN 1993-1-5, 9.2.1, (4), (8), (9), 9.3.3 (3))

All check results are available as graphs of utilization ratio in all sections along the beam into analysis

A multi-page form gives the summary results from the checks for each section.

**Conclusion**

“The possibility of obtaining forces and moments N, T, M diagrams from a series of sections of a beam-shell model, coupled with the availability of generating influencing surfaces for the same sections, allowed to model the bridge with transverse beams and torsion braces in their real position, fully considering the effects of the curved plan. The joined use of LUSAS and PontiEC4 allowed a fast and excellent optimization of structural steel and of reinforcement steel.”

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*Fabrizio Durastanti – Technical Manager Sintagma srl (Perugia)*