Numerical and experimental assessment of thermal stresses in steel box girders

Transcription

1 NSCC2009 Numerical and experimental assessment of thermal stresses in steel box girders H. De Backer, A. Outtier & Ph. Van Bogaert1 1 Bridge Research Group, Civil Engineering Department, Universiteit Gent, Gent, Belgium ABSTRACT: Thermal loading has a fundamental influence on the behaviour of large structures. This type of loading is generally characterized by the deck average temperature and the thermal vertical gradient. The available knowledge concerning these parameters is quite limited, when it comes to steel box girders. Hence, the quantification of the thermal gradients working on steel box girders becomes quite important. In this context, long term measurements are being undertaken on the Vilvoorde Viaduct in Belgium. This is oriented in such a way that both deck plate and web are directly subjected to solar radiation. The measurement data are compared with results from detailed finite element models of the steel box girders, including stiffeners, diaphragms and wearing courses. Modelling all thermal fluxes within this system, including solar radiation, radiation with the environment, mutual radiation, convective airflow, allows verification of the temperature variations in the steel box during a 24-hour cycle as well as during a longer period. 1 INTRODUCTION Steel box girders, equipped with an orthotropic bridge deck and constructed using stiffened plates are one of the most frequently used concepts for road bridges and flyovers spanning between 80 and 160 m. Similar sections are often applied for arch cross-sections of bridges spanning 200 m or more. They are a very economical solution and are easy to build thanks to the modern construction techniques. A new problem has arisen in recent international research, that was not taken into account for the design until now, which can heavily influence the behaviour of the bridge. During a 24-hour cycle, a closed box girder is susceptible to heating, caused mainly by the radiant heat of the sun, but also by heat transfer by convection in the air inside the box girder and by the good thermal conductivity of the steel. The radiant heat of the sun, which acts primarily on the surface of the bridge, is captured by the surfacing and transmitted to the supporting steel structure. Once the steel section of the box girder heats up by thermal conduction, it will then on its turn start to heat up the air inside of the box girder, which will result in an internal heat convection system in the girder. The natural ventilation because of the manholes in these types of girders can never be influential enough to create a cooling airflow substantial enough to countermand this effect, taking in mind the typical dimensions of such a structure. As soon as the external heating source of the surfacing and the effects of the radiant heat decrease, the surface layers will start cooling. The interior 65

2 of the box however, will nevertheless keep heating the surface layers for a considerable amount of time, but now from the inside working outwards, because of the thermal inertia of the system. This in turn will induce new and in-verse thermal gradient in the box girder. This quick succession of heating and cooling and the resulting thermal stresses will have an extremely negative effect on the behaviour and the cohesion of the surfacing to the steel deck plate. The effect of this thermal gradient is not fully included in the design process at this moment. The gradient can result in a temperature difference between different parts of the box girder section of up to 35 C as was shown by Emerson (Emerson 1980), because of the thermal inertia of the system. On top of this, the thermal heating force with its temporarily delayed working will be causing an additional inverse temperature gradient from the one being assumed at the design phase. One can rightly pose the question if such a cyclic thermal force will not put too high a demand on the classical wearing courses and water-proofing layers which are installed beneath, so that it might become necessary to start using other types of wearing courses. When doing this, it is important to keep in mind that a certain dispersion of the concentrated traffic loads on the deck remains necessary at all times for orthotropic deck plates. The dispersion will not have high enough values for thin wearing courses. This means without a doubt that it is important to incorporate the combined influence of traffic loads, support structure and actual temperature effects in the choice of the wearing courses and waterproofing layers, especially since the surface structure and colour of the surfacing are determining parameters for the absorption of the sun s radiant heat. The state of the art nowadays does not take this into account, since it is not really possible with the actual design theories. This paper describes a new research project which focuses on the quantification of this thermal effect. The objective of the proposed research is to reach a new and fundamental insight in the given problem and the behaviour of closed steel box girders with orthotropic stiffeners, subjected to a variable thermal load, and the repercussions of such a loading combined with the live load on the stability of the box section, be it the main arch of the bridge or part of the deck structure. Figure 1. Vilvoorde Viaduct The heating and thermal regime of closed steel box girders has been measured experimentally on the steel part of the Pont de Normandie, as documented by Lucas (Lucas 2001, Lucas, Berred & Louis 2003, Lucas, Virlogeux & Louis 2005). These tests clearly indicate at the existence of considerable temperature effects in these types of box girders, although they were not considerably larger than de-sign values in this specific case. The cross section of the bridge has a small height, which means that it isn t a typical example of the classical box girder. The forces in higher boxes will be much higher. The thickness of the wearing course is only 40 mm on top of that, so the heat absorption and the delayed temperature effect because of the warm air inside of the deck will not be strong enough when compared with the overall cooling effect of the bridge. Temperatures were also measured during longer periods in several locations of the box girders of the West-Gate bridge in 66

3 Australia and on the Benchley viaduct in the United Kingdom (Emerson 1980). These bridges, with box girders of a more considerable height, are installed on a lower altitude above the water surface and can benefit less from the cooling effect of the wind. The temperature gradient in these bridges resulted in a temperature difference between the up-per and lower plate of the box girder of more than 35 C. In the aftermath of a scientific research project for the Flemish Community about the damage to the surface of the Viaduct of Vilvoorde, see Figure 1, by the authors, the different causes of the damage were identified as a combination of effects of an entirely different nature such as the unevenness of the substrate, sub par waterproofing layers and extremely thick layers of wearing courses. As a secondary cause, the heating of the steel boxes was identified as a contributing factor, since the temperatures that were mentioned reached much higher values than is normally assumed in literature. Temperature differences such as this will try to deform the box girder section. This deformation will result in additional thermal stresses, since it is unevenly distributed over the box girder section, because of the comparable temperature distribution, and since it is opposed by the boundary conditions. Simulations using highly simplified calculation models in (Lucas 2001), simulating the behaviour of the steel box section, lead to the assumption that these additional stresses will have values of 40 MPa or more. These initial findings as well as the damages which were visible on the surface of the Via-duct of Vilvoorde, leads to the preliminary conclusion that further fundamental research into the workings of the noticeable temperature gradient and its combination with the other actions in the bridge could lead to the development of alternative construction methods for these kinds of situations, which will arise ever more frequently in large viaducts. 2 FINITE ELEMENT MODELING OF TEMPERATURE EFFECTS Calculations concerning the thermal behaviour of steel boxes, having thermal characteristics and subjected to thermal loading that can vary with time and temperature, have to be made within the framework of Fourier s, Darcy s and Arrhenius assumptions. The thermal effects that need to be studied are: - Solar radiation, resulting in a positive heat flux to the steel box girder; - Heat exchange between the external or internal surfaces of the steel with the surrounding or internal air flow, by convection of heat; - Heat loss because of radiation between the structure and the environment; - Mutual radiation between the external and internal surfaces of the steel structure. Generalizing, the modelling problem can thus be reduced to a problem of correctly modelling the heat radiation and the convection effect for a steel box section. 2.1 Radiant heat The finite element models developed for this research have the possibility to model mutual radiation between the different objects within the model and the surrounding environment. This surrounding space is modelled in part as the influence of solar radiation and in part as mutual radiation with a black body, representing the almost infinite absorption capacity of the environment. The radiation characteristics of the materials are given using its absorptivity and emissivity coefficients, while the possible transmissivity is neglected, assuming all surfaces to be opaque. The software also uses a gray body approximation, which implies that the emissivity of the surface is considered to be a constant value over the entire spectrum. This is a valid assumption for studies concerning most commonly used construction materials and subjected to the to-be-expected temperatures. The influence of solar radiation can be seen as mutual radiation with a radiation source located at infinity, represented in the model by a random node. The resulting flux will flow from the sun in the direction of each element surface. However, only modelling the influence of the solar radiation would result in a constant heat flow to the finite element model, resulting in an ever increasing tem- 67

4 perature, without reaching equilibrium. Because of this, radiation losses to the environment are modelled as a black body at the same temperature as the environment. 2.2 Heat convection Heat transfer by convection between the exterior surfaces of the finite element model and the surrounding air, can be modelled as a boundary condition, the thermal flux of which is determined by Newton s law: Q c c ( T T ) = h A (1) S A where h c equals thermal exchange coefficient for convection, T S the surface area, TS the surface temperature and T A the temperature of the surrounding air. The value of the coefficient h c is dependent on temperature, nature of the exchange medium and air velocity v. Some values have been proposed in literature (Recknagel et al. 1974) for this coefficient: h c = 4.2 v + 6.2, v < 5 m s (2) 0.78 h c = 7.15 v, v 5 m s (3) Since the air trapped inside of the box girder by the diaphragms will also heat up, an additional convection flow will start influencing the internal surface of the elements of the box. This second heat transfer by convection can be characterized by an exchange coefficient of h c equals 3 Wm -2 K -1, according to [2]. 3 RESULTS OF THE THERMAL FINITE ELEMENT CALCULATIONS All of the above considerations have been used to develop a finite element model of a typical steel box girder. The geometry is comparable to that of the Vilvoorde viaduct. The box is 8 m wide and 5 m high, with side flanges of 5 m each. The thickness varies between 18 mm for the top plate to 48 mm for the bottom plate. An epoxy asphalt layer of 5 mm is assumed to be installed on the entire upper surface of the box girder. The temperature distribution in such a steel box girder on a sunny summer day at noon is shown in Figure 2. The asphalt layer is not shown on this figure. It is immediately obvious that an important temperature difference can arise between the upper and lower part of the box girder. For this specific example, the temperature difference rises to a value of more than 40 C. Studying the a top view of the deck plate of the bridge, as shown on the right side of figure 2, the influence of the underlying structure is quite obvious. Since the parts at the side of the box girder are completely surrounded by air, and the able to cool down by way of a convective air flow with the environment, they remain fairly cool. The middle part however starts to heat up, partly because the convective flow at the inside of the box girder is almost negligible, and partly because mutual radiation between the steel parts of the box will keep heating the deck plate from the inside out. The influence of the diaphragms in the box in conducting the heat away from the top is also quite obvious, since they can be noticed in figure 2 by the lower temperature of the deck plate. The deck plate remains also a bit cooler halfway between the sides of the box, since the influence of the secondary radiant heat sources, being the sides of the box girder, is smaller. 68

5 Figure 2. Temperature distribution in the steel part of a typical box girder bridge ( C) 4 STRUCTURAL IMPLICATIONS Once the results of the thermal analysis is known, it is possible to introduce these temperatures, as shown in Figure 2, as thermal boundary conditions into a finite element model and perform a classic linear elastic calculation. The resulting displacements and Von Mises stresses are displayed in figure 3. These values due o thermal loading seem quite considerable. The thermal loads cause a rotation of the side flanges of the box, while the girder as a whole is susceptible to an enlargement, which becomes more important closer to the deck plate. Figure 3. Modulus of the displacement vector for of a typical steel box girder bridge due to thermal loading (mm) (left) and Equivalent Von Mises stresses in the deck plate, due to thermal loading (MPa) (right) The resulting stresses in the deck plate reach values of up to 25 MPa. These additional stresses seem to be the smallest in the deck plate zone above the diaphragms and above the sides of the box girder, since these parts of the structure help to disperse the solar heating to the cooler parts of the structure, thus resulting in a smaller thermal loading. This conclusion points to the possibility of separating the functional and practical functionalities of the wearing courses. 5 EXPERIMENTAL VERIFICATION During the spring months of 2008, an autonomous monitoring system for temperatures was implemented in the southern box girder of the Vilvoorde Viaduct. Instead of using classic thermocouple sensors, the choice was made to use small-scale integrated circuits, with an in-built temperature sensor, normally used to monitor temperatures in computer and network systems. 69

6 One cross-section of the southern box girder of the Vilvoorde Viaduct was equipped with four similar measurement devices, one on each side of the girder, as shown in Figure 3. The location of the cross-section along the length of the viaduct was chosen in such a way that the section is relative to the movement of the sun so that it would be subjected to the largest temperature effects, based on the finite element calculations mentioned above. After a first evaluation period of the experimental setup, the sensors were replaced with updated and more stable components and the number of measurement locations was doubled to eight, to get a clearer view of the temperature distribution in the cross-section. It is the intention that this setup will remain in operation for several years, in order to allow for a statistical verification of the results of the finite element models. Figure 3. Installation of the temperature sensors in the box girder of the Vilvoorde Viaduct Figure 4. Continuous temperature measurements during May 2008 on the steel box girder of the Vilvoorde Viaduct ( C) 70

7 The results of the temperature measurements during the first four days of May 2008 are shown in figure 4. The daily variation is quite clearly visible. In addition, it can be seen that a substantial temperature difference occurs, of up to 8 degrees between two different points of one cross-section. Which is of importance is that this maximal difference, as well as the maximal temperature occurs around eight o clock in the evening. This clearly illustrates the validity of the claim that a second internal heating will take place, due to mutual radiation and heat conduction, after the solar radiation has reached its peak. Furthermore, it can be seen that the average daily temperature of the steel box girder rises slightly every day. This measurement period corresponds with days having stable weather conditions with clear skies and average temperatures varying between 12 and 24 C. Especially the open skies resulted in optimal conditions for heating due to thermal radiation. Since this positive heat flux was more important than the negative flux due to heat loss to the environment in the night, the overall temperature could rise continuously. It is the expectation that during warm periods in the summer months, this effect will be even more important, but this will need to be validated by additional measurement data. Figure 5. Continuous temperature measurements during February 2009 on the steel box girder of the Vilvoorde Viaduct ( C) The measurements have been continued all through the winter. Figure 5 shows the temperature results for a 15-day period, during the coldest part of the past winter. When a very cold period is combined with sunny weather, it can be seen that the temperature gradient in one cross section can reach values of almost 15 C, while the temperature variation over one period of 24-hours, can be more than 20 C. This is purely due to the influence of direct solar radiation on parts of the box girder resulting in immediate heating, while most of the rest of the cross-section remains close to environmental temperature. 71

8 6 CONCLUSIONS This paper tries to focus on the importance of temperature effects and thermal loading for the design and behaviour of steel boxes. In box girder as well as in closed arch sections (Outtier, De Backer & Van Bogaert 2006, De Backer, Outtier & Van Bogaert 2007), solar radiation will result in important temperature differences between parts of the cross section. This thermal loading will have an important impact on the cohesion of wearing courses and will thus also influence the fatigue effect in steel box girders equipped with an orthotropic plated bridge deck, but to a lesser degree. The starting point of further research is thus to allow differential displacements between wearing courses and the supporting structure in those regions where the traffic induced deformations are considerable, and to realize the connection at the zones with minimal deformations. By doing this, a separation of two actions which when combined can cause fatigue damage in the wearing course, as well as in the steel deck will be carried out. By separating these actions, as well in location as in functioning, it must be possible to develop a more balanced design. 7 REFERENCE De Backer, H., Outtier, A. & Van Bogaert, Ph., The influence of temperature gradients on stiffened arch box sections, Proceeding of 5th International Conference on Arch Bridges, Madeira, September Emerson, M., 1980, Steel box bridge temperatures in Australia and the United Kingdom, Supplementary report 611, Crowthorne House, Transport and Road Research Laboratory. Lucas, J.M., 2001, Actions thermiques dans un caisson métallique orthotrope: modélisation et mesures sur le Pont de Normandie, Université du Havre, (in French). Lucas, J.M., Berred, A. & Louis, C., Thermal actions on a steel box girder bridge, Proceedings of the Institution of Civil Engineers: Structures & Buildings, Vol. 156, 2003, pp Lucas, J. M., Virlogeux, M. & Louis, C., Temperature in the box girder of the Normandy Bridge, Structural Engineering International, Vol. 3, 2005, pp Nunn, D. E. & Morris, S. A. H., 1974, Trials of experimental orthotropic bridge deck panels under traffic loading, Laboratory report 627, Crowthorne House, Transport and Road Research Laboratory. Outtier, A., De Backer, H. & Van Bogaert, Ph., Lateral Buckling of a steel tied arch, Proceedings of 10th East Asia Pacific conference. on Structural. Engineering. & Construction, Vol. 4: Real Structures and Tall Buildings, Bangkok, 3-5 Augustus 2006, pp Recknagel, Sprenger, Hönman & Schramek, 1995, Le Recknagel, Manuel pratique du génie climatique, tome 1 : Données fondamentals, PYC Edition livres (in French). 72