SEARCHING FOR NEW ARCHITECTURAL FORMS OF STEEL ARCH FOOTBRIDGES

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1 Footbridge th International Conference Footbridges: Past, present & future SEARCHING FOR NEW ARCHITECTURAL FORMS OF STEEL ARCH FOOTBRIDGES Jan BILISZCZUK Prof., Civ. Eng. Wrocła Univ. of Technology Research and Design Office MOSTY-WROCŁAW Wrocła, Poland jan.biliszczuk@pr.roc.pl Tomasz KAMIŃSKI Ph. D., Civ. Eng. Wrocła Univ. of Technology Research and Design Office MOSTY-WROCŁAW Wrocła, Poland tomasz.kaminski@pr.roc.pl Summary Noadays, in Poland as ell as in the hole orld many footbridges over motorays or ring roads of cities are being constructed to improve the safety of pedestrians. An important issue becomes the architectural diversification of neighbouring structures. In the paper a project of an unusual steel structure of an arch footbridge over motoray ith span exceeding 50 m is presented. A specific solution for hangers is proposed here originally shaped 8 mm thick steel shells are applied. For this kind of structure numerical analysis by means of to types of Finite Element models is performed and its selected results are presented and discussed. To represent the geometrical nonlinearity in the behaviour of a thin shell subject to transverse loads the application of an advanced FE model of the hanger taking into account large deformation theory is indispensable. A special attention is paid to fatigue analysis of the shell hanger subject to lateral ind action. The results of analyses confirm that the steel shell may be quite freely shaped to achieve the architectural purpose. In the paper various possibilities of shaping the steel shell are also shon. The proposed solution seems to be relatively attractive and at the same time to be cheaper than structures ith traditional hangers made of steel ire ropes or rods. Keyords: footbridge; structural design; FEM; nonlinear analysis; fatigue. 1. Introduction The described footbridge is predicted to be located in the north-east part of Poland over S8 motoray beteen Wyszkó and Ostró Mazoiecka. Location of the footbridge in the vicinity of border beteen to provinces imposed the need to create an unusual and architecturally attractive structure hich could play a role of a structural landmark indicating to users of the motoray crossing of the border. An investor of the footbridge is the General Directorate of National Roads and Motorays in Poland. The investor defined required parameters of the footbridge hich include: superstructure crossing the hole obstacle ith one span (exceeding 50 m), 3 meter ide deck for pedestrians and heelchair ramps. Presented study concentrates on superstructure of the main span hich is the most interesting part presenting a unique structural solution in bridge engineering. 2. Description of structural details 2.1 Superstructure The analysed footbridge is a steel structure ith the static system corresponding to the through arch. The shape of the arch is unusual: it has a curvature in the central part of the span only and has long straight end parts of the profile reaching the supports. The straight part are subject mainly to the axial force (the bending moment generated by the member s self eight is negligible). General shape of the footbridge is presented in figs. 1 and 2. The main load carrying element of the deck is a multi-cell steel box girder hile the arch is composed of to closed tubular sections of 508 mm of diameter. The arches are inclined toard each other at an angle of about 12 degrees. The height of the box girder of the deck is variable over its idth and reaches at maximum 850 mm.

2 Fig. 1 General vie of the footbridge Fig. 2 Cross-sections of the footbridge In the considered case the superstructure is supported by concrete substructure composed of RC columns and equipped ith access ramps. Hoever the proposed self-equilibrated system of the superstructure can be applied ith any substructure providing support to vertical reactions. 2.2 Suspension of the deck An innovative structural solution is a pair of steel shell hangers suspending the deck to arches in the middle of the span. In their central parts the shells are 8 mm thick hile at the top and the bottom edges hich are elded to arches and the deck the thickness increases to 12 mm (see fig. 3).

3 Such a suspension system is significantly different from traditional hangers made of steel ire ropes or rods being usually applied in several cross-sections at constant distances along the span. Hoever it seems to be relatively attractive and cheaper solution. Fig. 3 Details of the hanger s connection to the arch (left) and the deck (right) 3. Numerical analysis 3.1 Applied numerical models During the analysis of the footbridge to types of independent finite element models ere applied: 3-dimenional model representing the hole superstructure and a plane model representing a single hanger (see fig. 4). The global model is composed of bar and shell elements hile the plane model is consisted of shell elements only. The model of the hole structure as applied to initial global linear elastic analysis of all structural elements except the shell hangers subject to different types of load combinations according to the table 1. The plane model as used in non-linear analysis of the shell hanger subject to ind load to check hether the expected fatigue problem can affect this element. Fig. 4 Finite element models applied in analyses: global model (left) and detailed model of a hanger (right) 3.2 Global analysis During the global analysis Ultimate and Serviceability Limit States of the main structural elements ere checked. Among the load types the folloing actions ere considered: self eight of the structure, crod load, lateral ind pressure and uniform (positive and negative) temperature changes. Considered combinations of the loads (according to [1]) as ell as partial (γ) and combination (ψ 0 ) safety factors applied to them are presented in table 1.

4 Table 1 Partial (γ) and combination (ψ 0 ) safety factors applied in load combinations according to [1] Load Types of loads Combination self eight crod ind temperature / / / / / / Envelope of extreme normal stresses x in to main load carrying elements i.e. the arch and the deck girder resulting from all load combinations are shon in Fig. 5. Envelopes of vertical component stresses zz on both outside and inside surface of the hanger coming from all loads except those acting directly on it (self-eight and ind) are shon in Fig. 6. Fig. 5 Envelope of extreme stresses in the arch and the deck girder resulting from all load combinations Fig. 6 Envelopes of vertical component stresses zz ithin the shell hanger on its outside surface (left) and inside surface (right) resulting from loads not directly acting on it

5 3.3 Analysis of the hanger Analysis of the hanger as carried out by means of the plane finite element model representing a half of it taking into account symmetry of its shape as ell as symmetry of its loads and boundary conditions. In the load scenario the self- -eight and the lateral ind pressure ere considered; the latter action as found to be the most unfavourable load case and to generate the highest strains and stresses in the hanger. The analysis carried out ith application of the linear-elastic model of the hole footbridge shoed unreasonably high stresses (at least one order higher than can occur in reality) related to bending moments ithin the shell hangers caused by ind load acting directly on it. Hence a need to perform non-linear analysis has arisen hich could take into account large deformation theory to represent membrane behaviour of a thin shell here axial force dominates hereas bending moments become less important. a) b) c) d) West East WIND WIND WIND WIND Fig. 7 Distribution of vertical component stresses 22 ithin the hanger on est surface generated by ind: a) W E, b) E W; on east surface generated by ind: c) W E, d) E W Distribution of vertical component stresses 22 on both outside (est) and inside (east) surface of the hanger is shon in fig. 7. According to the maps of stress distribution the extreme values of 22 appear at the bottom edge of the shell at connection to the deck girder. The extreme stresses on est surface are as follos: 22,W max = 41 MPa, 22,W min = -34 MPa and on east surface are: 22,E max = 52 MPa, 22,E min = -27 MPa. The extreme transverse displacement u 3 of the shell (in the middle of its height) reaches 7 cm. The nonlinear analysis confirmed feasibility of the hanger in the form of a thin steel sheet. Hoever concentration of the stresses related to high bending moments at fixed edges imposed the need to increase gradually the thickness of the shell at connections to the deck girder and to the arch up to 12 mm (according to fig. 3). 4. Fatigue analysis Further analysis related to of the hanger s performance is concentrated on its fatigue resistance. It as decided to present in details a proposed approach to verification of this unusual problem especially because it is not fully covered by current European standards (Eurocodes) dedicated to design of bridge structures. Both the level of stresses ithin the hanger as ell as (hat is even more important) their variation generated by any loads not directly acting on it (i.e. except the self-eight and the lateral ind pressure of the hanger) are relatively lo hat is visible at envelopes of vertical component stresses zz obtained from the global model shon in Fig. 6. Therefore the loads considered in the fatigue study consist of combination of to actions only: the permanent action of self-eight G k,sup and frequent value of lateral ind pressure ψ 1Q k (here ψ 1 = 0.2 according to [1]). Characteristic value of the total ind force acting on the hanger as calculated according to simplified method for bridges from the folloing formula (1) given in [2]:

6 here: ρ the density of air (taken as 1.25 kg/m 3 ), Q k 1 2 b C Aref.x q k Aref.x (1) 2 ν b the basic ind velocity (equal to 22 m/s for the considered region of Poland), C ind load factor (assumed as the maximum value equal to 6.7 corresponding to narro and high structure of the hanger and the reference height above ground loer than 20 m), A ref,x reference area of the hanger, q k unit ind pressure. Hence, the frequent value of unit lateral ind pressure is equal: ψ 1q k = = 0.4 kpa. The stresses ithin the hanger generated by this load acting in both directions (assuming the most unfavourable case) together ith self-eight action of the shell are shon in fig. 7. The extreme load variation Δ is found at est surface equal to 79 MPa. In the analysed case equivalent constant amplitude stress Δ E,2 is equal to Δ according to formula (2) given in [4]: Δ E,2 = λ Φ 2 Δ = Δ (2) here: λ damage equivalence factor (taken as 1.0), Φ 2 damage equivalent impact factor (taken as 1.0), Evaluation of the fatigue strength as based on geometric (hot spot) stress method assuming the joint of the bottom hanger s edge performed by means of butt elds ith full penetration and ground flush to plate surface. According to [3] this kind of construction detail corresponds to the detail category Δ C = 112 MPa (being the fatigue strength at 2 million cycles). The fatigue resistance is then verified by means of formula (3) taken from [3]: γ Ff Δ E,2 Δ C/γ Mf (3) here: γ Ff partial factor for fatigue loads (according to [4] recommended to be equal to 1.0), γ Mf partial factor for fatigue strength (equal to 1.15 for damage tolerant method and high consequences of failure, according to [3]), In expression γ Ff Δ E,2 stress concentration factor as omitted according a note from [3]. By putting the calculated values to formula (3): = 79 MPa < 112/1.15 = 97 MPa the inequality is satisfied and thus the fatigue resistance of the hanger at the ind action is provided. 5. Architectural study Proposed unusual structural solution of the hangers formed by means of steel shells has also an important advantage providing a possibility to create easily attractive and diverse architectural forms of the footbridge. Taking into account the fact that according to the results of analysis the central part of the shell undergoes relatively lo stresses (see fig. 6 and fig. 7) it can be shaped quite freely. For instance, it allos creation of various openings in the shells hoever devoid of any sharp angles. Some exemplary solutions are given in fig. 8. Hence an additional advantage of the hangers form is a possibility to locate on them any content hich may have an essential meaning to users of the road belo, for example informing about crossing some border or reaching a specific destination as ell as presenting some local symbols, emblems or crests.

7 Fig. 8 Various architectural forms of the shell hanger 6. Conclusions Within the scope of the presented study possibility to apply a thin steel sheet as a hanger suspending a footbridge deck as verified. The level of stresses ithin the hanger generated by loads not directly acting on it as found to be very lo. The biggest doubts related to ability of the hanger to ithstand the lateral loads acting on it directly ere dispelled ith application of a non-linear analysis. Also resistance of this element to fatigue as successfully checked and provided. To avoid concentration of stresses in steel shell hanger it could be considered to construct structural hinges at connection of

8 the hangers to the deck girder and to the arch. Hoever such a solution ould disturb the initially assumed simplicity of the structure. The proposed structural solution can be distinguished by several advantages: - lack of expensive and numerous sophisticated elements of hangers and their anchorages, - easiness of construction (devoid of assembly and tensioning of hangers), - providing a linear support to the deck and stiffening the hole structural system of the superstructure (the deck ith the arch), - original and unusual form, - possibility of a free and diverse forming of the shell hanger, - easy and inexpensive possibility to locate any content on the bridge making it a landmark structure. 7. Acknoledgements The study has been financially supported by research project Innoacyjny Transfer co-financed by European Social Fund ithin the Human Capital Programme. This support is gratefully acknoledged. 8. References [1] Eurocode 0 EN Basis of structural design. National Appendix A2. [2] Eurocode 1 EN Actions on structures. General actions. Part 1-4: Wind actions. [3] Eurocode 3 EN Design of steel structures. Part 1-9. Fatigue. [4] Eurocode 3 EN Design of steel structures. Part 2. Steel bridges.