The influence of continuing reinforcement on the load capacity of a RC beam previously exposed to high temperatures

The paper describes the RC beam model development and the influence exerted by the main longitudinal reinforcement overlapping and transverse reinforcement (ties) on the bearing capacity of a RC load bearing structure for several cases of load, with an emphasis on the influence of high temperatures. Several RC beam models are made and relevant calculations and results are presented, which show the influence of the reinforcement method on the bearing capacity of structures, i.e. of the mainreinforcement continuing as related to the one-part reinforcement, as well as the influence of transverse reinforcement (ties).


Introduction
The behaviour of reinforced concrete structures exposed to fire and high temperatures, with observation of the damage and usability rating of structures during and after the effects of such types of load, is currently considered to be one of the main and highly topical research issues worldwide.Understanding behaviour of reinforced concrete structures during and after exposure to fire, with simultaneous exposure to continuous and moving load, is very important for the safe and rational sizing of structures.In the first place, it is important to understand the behaviour and characteristics of certain materials forming the load bearing structure (concrete, steel...), as well as their interaction.The development of simple and efficient numerical models that take into account the effects of high temperatures, especially if these models have been confirmed by experimental tests, forms the basis for a more detailed study of stochastic processes, such as fire and consequences of its actions on load bearing structures, and for further updating of standards and regulations so as to enable more efficient and safer design of structures.Most of today's regulations and standards provide rather simplified approach and guidelines related to dimensioning and resistance to fire activity.The standards and regulations used in this paper are listed in [2][3][4].It should be noted that obstacles in the observed structure present a problem, because most regulations are based on the behaviour of simple static systems.In reality, such a simple bearing element is a part of a continuous beam and structure, which can cause unexpected behaviour and response of the structure.Extensive fire tests conducted in 1995-1996 [5] show that a static system, as part of a bearing structure, can have significantly higher fire resistance than when considered as a separate static system.Although it is known that, in comparison to other materials, reinforced concrete structures exhibit a relatively good behaviour during fire or high temperatures, it should be observed that, after the effects of such load, changes in the initial characteristics of material occur, i.e. significant features of structural materials are affected [6,7].The occurrence of these degradation mechanisms causes damage to the load-bearing structure during and after fire, which results in a reduced bearing capacity of the reinforced concrete structure [8], as well as in mechanical and temperature damage to concrete [9,10].
The paper shows results of numerical analysis aimed at determining behaviour of a reinforced concrete beam at high temperatures and various loads, i.e. for beam load without the action of fire and high temperatures, and for beam load after exposure to fire.The modelling and geometrical characteristics of the reinforced concrete beam are based on the paper by Ožbolt et.al. [7], where a similar static model of reinforced concrete beam, loaded at four points by bending, was studied.Unlike the concept presented in paper [7], the objective of this paper is to study the effect of different reinforcing methods on the loadbearing capacity of structures after previous simulation of fire activity and material degradation as a result of high temperature.The modelling of all RC beam models presented in this paper, i.e. insertion of model geometry, description of material characteristics, and loading and analysis of these models, was performed using computer programmes FEMAP® and MASA (Macroscopic Space Analysis) [11].The finite-element computer programme MASA is used for non linear calculation and analysis of three dimensional (3D) finite elements of structures made of quasi-fragile materials, such as concrete, stone, ceramics, etc.Although different types of materials can be analysed, the programme is mostly intended for non-linear analysis of concrete and reinforced concrete in the framework of the continuum mechanics theory, taking into account damage of material [7,12,13,14], e.g.cracking of concrete or flow of reinforcement.
The programme can be used to analyse and solve mechanical problems, i.e. to conduct static and dynamic analyses of loadbearing structures.It may also serve for solving non-mechanical problems, such as the analysis of transport processes in porous media, analysis of corrosion on a reinforced concrete structure, or analysis of fire action and exposure to high temperatures.The knowledge and understanding of such computer programmes enable creation of different models and loads, i.e. prediction of behaviour of load-bearing structures and response to actual load in real environment and time.This kind of research is still much cheaper compared to creation of prototypes and conduct of physical tests and experiments on real elements.The finiteelement analysis aims to reduce the time and cost required for development and improvement.

RC beam modelling
A thermo-mechanical model [7,12,15,16] of the reinforced concrete beam, loaded at the mid span of the girder, was developed for the purpose of this testing, using the threedimensional (3D) finite element method.The thermo-mechanical model is required so as to simulate response of the loadbearing structure after degradation of mechanical properties due to high temperature effects.A more detailed description of the thermo-mechanical model is presented in paper [7].This model ensures that mechanical properties of materials (concrete) depend on the temperature, while temperature distribution is not dependent on such properties.Concrete was modelled using the so-called planar micro model [17], while a plastic model served for reinforcement by applying von Mises criterion [18].The so-called "Crack band" regularization method was applied to make sure that results are not dependent on the size of finite elements [19].The computer programme FEMAP® is used for preparing input data and for analysing finite-element results after calculation.The program allows us to use the finite-element method to generate nodes and connect them to create a network of finite elements.It also allows us to set boundary conditions of the model, to define various ways of loading, and to select and describe various materials.The load setting method is incremental, i.e. it is divided into a number of steps, depending on the force or predetermined increments.
The influence of continuing reinforcement on the load capacity of a RC beam previously exposed to high temperatures

Geometrical properties of structural member
The reinforced concrete beam is rectangular in cross-section and measures 4.0 m in total span, while its dimensions are b/h = 200/300 mm.It is reinforced in the upper and lower zones with rod-shaped reinforcement 12 mm in diameter, i.e. by four rods in the lower zone and two rods in the upper zone and by ties 10/200 mm in diameter.The concrete cover is 26 mm in thickness.Due to complexity of the model and to simplify calculation, as well as to reduce the total number of finite element networks (shorter calculation time), a quarter of the model was developed, because the symmetry of the model itself provides such possibility.The model of the simulated beam is rectangular in cross section and measures 2.0 m in span, while its dimensions are b/h = 100/300 mm, as shown in Figure 1.

Figure 1. Beam model with corresponding cross section
The main longitudinal reinforcement is modelled as a solid body made of three-dimensional (3D) finite elements, while the ties (transverse reinforcement) are dimensioned as one-dimensional elements (bar elements).For realistic modelling of reinforcement splicing details, the bars should fully be modelled by 3D finite elements.The 3D elements allow realistic description of stress state in the zone of reinforcement splicing: bond, radial and tangential stresses in concrete around the reinforcement.Such stress states can not be described realistically using common bar elements.Transverse reinforcement (ties) can be modelled using bar elements, because this modelling is sufficient for simulation of lateral adherence which the ties provide.It is not realistic to model the connection between the ties and the main reinforcement by fixed connection, because in reality the ties are not welded to main reinforcement, but are only held in place.Therefore, in this paper they are modelled separately from the main reinforcement.The main longitudinal reinforcement in the overlap zone is modelled in the same way.Main reinforcement anchoring (at the end of the reinforced concrete beam) is modelled so that the concrete elements at the end of the reinforcement are assigned linear properties, and as such they actually simulate hooks.A 1 mm thick layer of elements, called contact elements, is modelled around longitudinal reinforcement.Contact elements serve only for modelling the surface zone between concrete and steel reinforcement, or to simulate connection at the contact of two materials, and can transfer the shear and compressive stress only.Three-dimensional elements with eight nodes and eight integration points (hexahedron three-dimensional (3D) finite elements HexMesh solids) are used for spatial discretization of steel (reinforcement, contact elements, and steel plates).The transverse reinforcement (consisting of steel ties) is modelled by means of one-dimensional bar elements.The biggest 20 mm tetrahedral element of concrete is defined when specifying the number of elements by each model geometry line, or when modelling the finite element network of concrete.It is very important to devote enough time to modelling such networks of tetrahedral and hexahedral three-dimensional finite elements, in order to avoid mistakes and gain more realistic results.For successful creation of the finite element network, it is necessary to control that all finite elements (tetrahedral and hexahedral) interconnect (continue) in their nodes only.The dimensions of reinforcing bars forming the main longitudinal reinforcement are 2 x 1000 mm and 2 x 1600 mm for the simulated beam 2 m in span, Figure 4.The diameter of all longitudinal reinforcing bars is 12 mm, while ties are 10 mm in diameter.The overlap of longitudinal reinforcement in the tension zone is 600 mm (50 x Ø [mm]).The minimum length of overlap necessary to ensure the transfer of force from one rod to another, prescribed by HRN EN 1992 (l 0 = α 1 α 2 α 3 α 5 α 6 l b,rqrd ≥ l 0,min ), was reduced by GRAĐEVINAR 68 (2016) 12, 967-978 Krešimir Ninčević, Joško Ožbolt, Ivica Boko 30 % in this study.Two steel plates were modelled to simulate real conditions.One of them was placed at the bottom at the beginning of the beam, at the position of the bearing, and the other was placed in the centre of the beam.Its role was to better assume and transfer the load, but also to avoid possible local damage to concrete during application of load, Figure 5. Steel plate dimensions are 100/100/25 mm.

Reinforcement models
The analysis was conducted for several distinct models of similar geometrical characteristics, but differing in the form of reinforcement: reinforced concrete beam with one-part longitudinal reinforcement in the bottom tension zone and with transverse reinforcement (ties), as shown in Figure 6 reinforced concrete beam with two-part longitudinal reinforcement in the lower tension zone (reinforcement overlap), and with transverse reinforcement (ties), as shown in Figure 7 reinforced concrete beam with two-part longitudinal reinforcement in the lower tension zone (reinforcement overlap), but without transverse reinforcement (ties), as shown in Figure 8.For simplicity reasons, detailed results will be given only for the model of reinforced concrete beam with two-part longitudinal reinforcement in the lower tension zone (overlapping reinforcement) and transverse reinforcement (ties), and a table with calculation results will be shown for all models in conclusion.

Note:
The distribution of ties is equal in the first and the second models, and the main longitudinal reinforcement in the tension zone is equal in the second and third models.The main longitudinal reinforcement in the pressure zone is equal for all models, Figure 9.

Material characteristics of reinforced concrete beam
Temperature dependence of the planar micro model is described so that the macroscopic properties of concrete (Young's modulus, compressive and tensile strength, and energy fracture) are variable due to elevated temperatures, based on experimental data [7, 13, 14], Figures 10, 11  Krešimir Ninčević, Joško Ožbolt, Ivica Boko Young's elasticity modulus, as shown in Figure 12.Although these two characteristics are reduced due to high temperature, experiments show that yield point of steel can be restored, unlike that of concrete where degradation of material is irreversible [21].The longitudinal and transverse reinforcement exhibits the following characteristics: yield strength f y = 480 MPa tensile strength f u = 580 MPa -Young's modulus of elasticity E = 210 000 MPa -Poisson's ratio n = 0.33

Application of load
Two basic ways of applying load were used in the analysis of reinforced concrete beams: load by controlled displacement at the centre of the beam (incremental procedure) high temperature load and fire simulation (beam heated from three sides).
Two groups of model tests were established for model loading.In the first group, load was applied to the model only by displacement and the bearing capacity was monitored until collapse.The second group is a combination of the two loads, which means that all models were originally exposed to high temperatures and simulation of fire, cooled to the desired temperature according to the specified heating and cooling protocol, and then subjected to displacement load in order to check bearing capacity (Figure 13).The ISO-834 curve (standard fire curve) [4] was adopted as temperature load.The temperature of the fire-affected area increased in the first 30 minutes to 850 °C, and in the next 90 minutes to about 1050 °C.

Temperature distribution in reinforced concrete beam
For simplicity reasons and due to very similar results of temperature distribution in reinforced concrete beams, the temperature analysis is restricted to a single model of reinforced concrete beam, with continuous longitudinal reinforcement of the lower tensile zone (overlapping reinforcement) and transverse reinforcement (ties), as shown in Figures 14 to 21  The influence of continuing reinforcement on the load capacity of a RC beam previously exposed to high temperatures GRAĐEVINAR 68 (2016) 12, 967-978 The analysis of temperature field in the beam shows that after 5 minutes, or between 5 and 10 minutes, a significant temperature rise is registered in peripheral elements of the beam, particularly at the lower edge of the beam (the beam is heated from the external and bottom sides).

Presentation and comparison of results
Two groups of model tests were established for model loading.In the first group, load was applied to the model only by displacement and the bearing capacity was monitored until collapse.The second group is a combination of the two loads, which means that all models were originally exposed to high temperatures and simulation of fire, cooled to the desired temperature according to the specified heating and cooling protocol, and then subjected to displacement load in order to check bearing capacity Therefore, all test and calculation results, and their comparison, will be presented in the conclusion.

Note for Figures 23 to 30:
LEFT SIDE -models subjected to displacement load only; RIGHT SIDE -models exposed to displacement load after being subjected to high temperatures and cooling.The range of displayed stresses in reinforcement can vary from 0 to 480 N/mm 2 .The main tensile stress (cracks) in concrete is shown by relative deformation in the range from 0.0 to 0.10, where deformation of 0.01 corresponds to the crack width of 0.2 mm for the average length of finite element of 20 mm.Cracks formed in concrete after the tensile strength was exceeded.According to the limit state of cracks in RC structures, the critical crack width is w g =0.3 mm.It can be seen from the shown state of stress in RC beam ties that there was no flow of reinforcement, and that maximum strength was not exceeded, even immediately before the fracture and failure of the structural member.The peeling of the protective layer of concrete occurs due to the heating and cooling of the reinforced concrete beam, as can be seen in Figures 28 to 30 to the right, and as confirmed in other studies [6,7].The nonuniform degree of heating, and temperature gradient through cross-section of the RC element, result in temperature strain and stress, which leads to peeling and damage of concrete.Greater exposure to high temperature causes major damage to concrete, as well as additional damage during cooling.Water found in concrete starts to change its physical state at the temperature of 105°C.Further temperature increase causes cement dehydration.The destruction of cement gel occurs at temperatures between 800 and 900°C.The behaviour of concrete at high temperatures also depends on the type and mineralogical composition of aggregate, because of possible loss of water in the aggregate, and change of properties.This can be explained by the fact that compressive stresses are also generated inside the reinforced concrete due to heating, e.g. in the direction of the longitudinal axis of the beam, and these stresses influence fracture energy of concrete, which increases and hence contributes to the increase in ductility of the beam.The influence of continuing reinforcement on the load capacity of a RC beam previously exposed to high temperatures GRAĐEVINAR 68 (2016) 12, 967-978

Conclusions
The tests and calculation results presented in the paper show that the expected damage and degradation of the reinforced concrete beam material was caused by high temperature and fire simulation, and by a significant decline in bearing capacity.The comparison of the two models reveals the influence of different ways of reinforcing using longitudinal reinforcement in the lower tension zone.The model with the main longitudinal overlapping reinforcement exhibits a considerably larger displacement immediately before failure in the numerical model, while the final force value is slightly higher.The reason for such slight increase in force can be explained by the fact that the reinforcement overlapping zone is closer to the bearing than to the zone of impact of maximum moments.The consequence of reinforcement overlapping is an increased share of steel in RC beam and a higher reinforcement coefficient.This results in an increased ductility (toughness) of structural elements and hence in greater displacement.Ductility is important as a means of avoiding sudden demolition of a structure due to load expected during the life and use of the structure.Higher ductility means higher deformability in nonlinear field.Tests have also shown the impact of transverse reinforcement, i.e. significant decline of bearing capacity can be observed in the model without transverse reinforcement (ties).Such an outcome is quite expected because the observed model is a statically determined system, i.e. a freely supported simple beam, subjected to vertical displacement load.All described tests were performed on the presented numerical models and their results are used to predict the behaviour and response of the bearing structure or structural member subjected to load testing in real time and environment.However, the number of these and other experimental studies is still insufficient for production of more reliable and accurate test results, which is mostly due to difficult working and measurement conditions under the effect of high temperature, and to high cost of testing.

Figure 2 .
Figure 2. Finite element of reinforcement and contact element

Figure 4 .Figure 5 .Figure 6 .Figure 7 .Figure 8 .
Figure 4. Longitudinal and transverse reinforcement of reinforced concrete beam , and 12.The reinforced concrete beam with the following characteristics of concrete is analysed: characteristic compressive strength of f ck = 25.0MPa tensile strength f t = 2.0 MPa -Young's elasticity modulus E c = 28000 MPa -Poisson's ratio v = 0.18 fracture energy G F = 0.08 N/mm.Experiments show that mechanical properties of steel change and are subject to changes at elevated temperatures [20].This phenomenon is taken into account in the model through application of reduced diagrams for the yield point of steel and

Figure 22 .
Figure 22.Points used for temperature distribution and heating and cooling curves Figures 23 to 27 show detailed results of reinforcement stress and concrete damage for only one model of reinforced concrete beam, with two-part longitudinal reinforcement in the lower tension zone (overlapping reinforcement) and transverse reinforcement (ties).

Figures
Figures 31 to 35 show all forms of RC beam bearing capacity.As can be seen in Figures31 to 35, the bearing force of the reinforced concrete beam for the model that was exposed to high temperature prior to loading by displacement, is lower due to damage to concrete during fire action.However, immediately before the failure of the RC beam, the displacement is in this case considerably bigger.

Figure 31 .
Figure 31.Bearing capacity diagrams (displacement -force) of reinforced concrete beams subjected to displacement load only