Fire Resistance of Concrete Structures - The Global Behaviour

Transcription

1 Fire Resistance of Concrete Structures - The Global Behaviour Tiago Filipe Domingos Gonçalves M.Sc. thesis summary 1 Introduction As it is known, concrete presents a good resistance when exposed at high temperatures. It is noncombustible and has a slow rate of heat transfer, which makes it a highly effective barrier to the spread of fire. Most International Codes and Standards allow performing member analysis, thus neglecting the effects of the indirect fire actions. This method does not take into consideration the arising of members internal forces and can lead to non conservative results. The increase of shear force in the columns induced by thermal expansion of beams and slabs can cause the collapse of the structure. The main objective of this work is to understand the global behaviour of concrete structures when exposed to fire. Hence, it is performed a simplified analysis to a building that suffered a fire. This analysis consists in the application of temperature variations (uniform and linear gradient) to the slabs and beams of the building and comparing the results with those verified in-situ. It is used a commercial computer programme named SAP2000 for the modelling of the structure and for the application of temperature variations. 2 Methods of Assessment of Fire Resistance and General Procedures for the Verification of Fire Resistance The fire resistance of concrete structures can be assessed by one of the five distinct methods, listed in order of increasing complexity [1]: standard fire tests; tabulated data (largely prescriptive but also increasingly based on calculations); simplified calculations, neglecting complex effects such as thermal stresses; advanced calculations, that can be used on simulation of global behaviour of the structure, parts of the structure (frames) and isolated elements (beams, columns or slabs), neglecting the interaction between them; full scale fire tests. According to Part 1-2 of Eurocode 1 [2], fire resistance of structures should take into account the following steps: definition of the thermal action; definition of the mechanical actions in fire situation; 1

2 calculation of the temperature evolution θ d in structural elements; determination of the design value of the relevant effects of actions in the fire situation at exposure time t, E fi,d,t ; determination of the design value of the relevant resistance in fire situation at exposure time t, R fi,d,t ; verification of the fire resistance, that can be done in three different domains: 1. in time domain: 2. in strength domain: 3. in temperature domain: t fi,d t fi,requ (1) R fi,d,t E fi,d,t (2) θ d θ cr,d (3) Where, t fi,d - is the design value of the fire resistance; t fi,requ - is the required fire resistance time; θ d - is the design value of material temperature; θ cr,d - is the design value of the critical material temperature. 3 The Global Behaviour When a member analysis is done, the indirect actions arising in the structures due to thermal expansion are not taken into consideration which, in case of statically-indeterminate members, can lead to non conservative results. P. Riva, referred in [4], performed an extensive study in order to analyse this problem in frames. In this kind of structures, the continuity of the beams with the columns may induce a non negligible axial force in the beams, which in turn may generate high shear forces in the columns and cause a possible shear failure, as often observed in real fires. This study is summarized in the following. 3.1 Parametric study of frames In this study, it was considered two different fire exposures to the columns of the frames: fire on three sides, with the fourth side at ambient temperature, and fire on one side, with the remaining three sides at ambient temperature. The first case represents a column with the external side flush with the wall of compartment in fire, and the second case a column with the internal side flush with the wall of the compartment. The existence of the upper floors has been introduced by considering a portion of the columns above the fire compartment, assuming that the inflection points are located at mid-height between two continuous storeys, and by applying to the columns an axial force N sd = 1000kN representing the effects of the upper floors 2. The columns belonging to the upper floor, being outside the fire compartment, are assumed to be at ambient temperature. In the base, the columns are considering as fully clamped. 2

3 1 - Time domain. 2 - Strength domain. 3 - Temperature domain. Figura 1: Verification of the fire resistance [3]. Figura 2: Parametric study of frames [4]. 3

4 The analysed frames are shown in figure 2. The geometry of the frames and the reinforcement of the critical sections satisfy the tabulated values in [5] for R60. In the following, the results of the analysis carried out on a frame with a 6 m span beam having rectangular section and with the column heated on one side are discussed. With the obtained results, which are shown in figure 3, the following comments can be drawn: Both bending moment and shear force increase dramatically in the columns for the first 30 minutes, because of the heating of the beam. However, no further increase is observed later on, because of the progressive damage of the beam. Figura 3: R/C frame with the columns exposed to fire on one side and with 6 m span beam (rectangular section) [4]. The bending moments in the lower columns increase approximately seven times because of the thermal deformations of the beam (elongation and end rotation), while the bending moments in the upper columns change sign, and their values increase more than twice of the value at ambient temperature. The shear forces in the lower columns increase approximately four times with respect to ambient conditions. As a result, the columns which are lightly reinforced in shear and not confined, may exhibit a shear failure, as often observed during real fires. Neglecting the effects of beam in the design of R/C frames may lead to highly non conservative results because of the increasing bending moments and shear forces in the columns during the first 30 minutes of fire exposure. 4

5 For practical applications, detailing rules for columns similar to those generally adopted in seismic design are recommended for fire design as well. The adoption of closely spaced hoops is important in improving section strength and ductility in combined bending and axial force, and helps controlling concrete spalling [4]. The column exposure to fire on three sides do not shown relevant differences, except that the increase of the bending moment and shear is less pronounced, due to the smaller temperature gradient in the column. 4 Analysis 4.1 The building A simplified analysis to a building that suffered a fire was conducted. The building has four floors, the ground floor and three elevated floors. The beams and columns of the building were made with in situ concrete and they are structurally connected. The slabs of the ground floor are solid concrete slabs and those of the upper floors are one way slabs with pretensioned beams and ceramic blocks. On the ground floor there is a ramp that connects to the first floor, which is used as truck s access. This ramp was made with concrete beams, a solid concrete slab and is monolithic to some columns. After the real fire, the columns of the ramp were excessively damaged and so far, they did not suffer any repair (figure 4). The connection between the slab of the ramp and the columns lead to an imposed displacement of the columns, with the direction of the ramp, due to the expansion of the concrete resulting from the increase of temperature during the fire. Figura 4: Shear failure in the columns. 4.2 Modelling The structural modelling of the building was done with a commercial computer program named SAP2000. To simulate the beams and the columns, frame elements were used. The slabs were simulated with rectangular finite elements of Shell-Thick type and one meter side length. In the base, the columns are considered as fully clamped. In figure 5 is shown a tri-dimensional view of model. The increase of temperature inside a section can be divided into two parts, one linear and one selfequilibrated (figure 6). In turn, the linear part is divided into the sum of a constant and a linear temperature gradient. 5

6 Figura 5: 3D model view. Figura 6: Temperature linearisation process. In the analysis it was study the influence of the two previous parts separately, with the objective of assessing the global behaviour of the structure, namely in the columns of the ground floor. Hence, two kinds of analyses were performed (temperature variations applied to the beams or to the columns) in three different cases. In the first case, the temperature variations were applied only to beams and then to the slab of the ramp (figure 7). In the second case, all beams and slabs of the ground floor (ramp and ceiling) were separately submitted to temperature variations (figure 8). Finally, in the third case, the same elements of the second analysis were submitted to temperature variations, but considering the building without the ramp (figure 9). Temperature variations were not applied to the upper floors since they were only slightly affected by the fire. Figura 7: Case 1. Figura 8: Case 2. 6

7 Figura 9: Case 3. The load combination considered was: where, E fi,d,t = G k + ψ 1 Q k + A d (4) E fi,d,t - design value of the relevant effects of actions in the fire situation; G k Q k A d - characteristic value of permanent loads; - characteristic value of the leading variable action (overload); - design value of the indirect actions due to the fire, caused by internal or external restraint of deformation. ψ 1 - reduction factor for obtaining the frequent value of the variable action. It was considered ψ 1 = 0 for the roof slab and ψ 1 = 0, 9 for the other slabs. 4.3 Columns strength assessment Figure 10 shows the columns cross section and table 1 theirs resistance forces and moments. Figura 10: Columns cross-sections. The temperature variation part T that causes the section bending failure is obtained by solving the following equation: ( ) MEd,x,(G+ψ1Q) + T M α ( ) Ed,x, T =1 o C MEd,y,(G+ψ1Q) + T M α Ed,y, T =1 o C + 1, 0 (5) M Rd,x M Rd,y 7

8 Tabela 1: Resistance forces and moments of the columns. Column 70x20 cm Column 30x70 cm Direction x Direction y Direction x Direction y Reinforcement (cm 2 ) 25,91 25,91 31,42 31,42 ω tot 0,48 0,48 0,39 0,39 ν 0,21 0,21 0,59 0,59 µ 0,29 0,29 0,25 0,25 M Rd (knm) 135,6 474,6 613,7 263,0 V Rd (kn) 175,3 The temperature variation part T that causes the section shear failure is obtained by solving the following equations: V Rd = V Ed,x,(G+ψ1Q) + T V Ed,x, T =1 o C (6) 5 Analyses results V Rd = V Ed,y,(G+ψ1Q) + T V Ed,y, T =1 o C (7) Due to the amount of the results, it is only shown in table 2 the following points: The values for the occurrence of the first plastic hinge in the columns that are interrupted by the crossing of the ramp (figures 11 and 7). These columns were more damaged with the fire than the remaining. The values for the Case 2 and 3. The values for the application of the uniform temperature variation, because it causes higher forces in the columns than the linear temperature gradient. Figura 11: Plan view of the ramp. 1 The columns length is 5 meters. 8

9 Tabela 2: Analyses results. Column T for plastic hinge ( o C) Type of plastic hinge - section (m) 1 C2S C3S C2B C3B C2S C3S C2B C3B P V y 0 0, 84 M 5 V y 0 0, 84 V y 0 5 P V y 0 1, 66 V y 0 5 V y 0 1, 66 V y 0 5 P M 0 V y 0 5 V y 0 2, 49 V y 0 5 P M 0 M 0 V y 3, 33 5 V y 0 5 P V y 0 0, 84 M 0 V y 0 0, 84 M 0 P V x 0 1, 66 M 0 V y 0 1, 66 V y 0 5 P V x 0 2, 49 M 0 V y 2, 49 5 V y 0 5 P V y 3, 33 5 M 0 V y 3, 33 5 M 0 C2S - Temperature variations applied to slabs of the Case 2 C3S - Temperature variations applied to slabs of the Case 3 C2B - Temperature variations applied to beams of the Case 2 C3B - Temperature variations applied to beams of the Case 3 6 Conclusions With the results of the analyses, the following comments can be made: The existence of a ramp monolithic with the columns in the building was the responsible factor for the premature shear failure in the columns P10 to P13 and P16 to P19. If the ramp slab would be repaired/replaced, it should not be monolithic with the columns this time. These columns should be strengthened or replaced because the seismic safety of the building can be in danger. The results of Case 2 show the significant influence of short column to the premature failure. For Case 3, this phenomenon does not exist and the results are similar of the values for real cases [4]. The thermal expansion of the beams and slabs exposed to fire causes a high increase of the shear forces and bending moments in the columns. Hence, to avoid premature failures, appropriate detailing of the reinforcement is necessary. It should be adopted closely spaced hoops, in order to improve section strength and ductility in combined bending and axial force. The short columns, likely in the seismic design, should be avoided and the detailing rules for columns for fire design should be similar to those generally adopted in seismic design. In case of frame design, the indirect actions arising in the structures due to thermal expansion should be taken into consideration because the individual element analysis leads to non-conservative results. Referências [1] FIB - Fédération Internationale du Béton. State-of-art Report - Bulletin 38 - Fire Design of Concrete Structures - Materials, Structures and Modelling, [2] CEN - Comité Européen de Normalisation. EN , Eurocode 1: Actions on structures - Part 1-2: General actions - Actions on structures exposed to fire, April

10 [3] VILA REAL, Paulo M. M. Incêndio em Estruturas Metálicas - Cálculo Estrutural. Edições Orion, [4] TAERWE, Luc. From member design to global structural behaviour. Proceedings of the International Workshop: Fire Design of Concrete Structures - From Materials Modelling to Structural Permormance, Coimbra, Portugal, [5] CEN - Comité Européen de Normalisation. EN , Eurocode 2: Design of concrete structures - Part 1-2: General rules - Structural fire design, December