FIREDESIGNOFBOLTEDBEAM-TO-COLUMNJOINTS螺栓连接梁柱节点的消防设计.doc

FIRE DESIGN OF BOLTED STEEL BEAM-TO-COLUMN JOINTS Aldina Santiago; Lus Simes da Silva ISISE - Department of Civil Engineering, University of Coimbra, Portugal aldinadec.uc.pt; luisssdec.uc.pt Paulo Vila Real LABEST - Department of Civil Engineering, University of Aveiro, Portugal pvrealcivil.ua.pt ABSTRACT In this paper, the main approaches used for developing a practical consistent methodology to predict the behaviour of bolted steel beam-to-column joints under a natural fire are presented and discussed. This methodology incorporates the influence of the transient temperature variation on the time-varying forces that act on the joint and gives design guidance on how to avoid the failure of the joint throughout the fire event (heating and cooling phase). Validation of the proposed model is carried out by comparison against the available results obtained from an experimental programme of steel sub-frames under a natural fire undertaken at the University of Coimbra, Portugal (Santiago et al., 2008). 1. INTRODUCTION Under a natural fire conditions, the behaviour of steel joints within a structure highly depends on the redistribution of internal forces with time as a result of the global behaviour of the structure. In this situation, the actual behaviour clearly deviates from the results of isolated joint tests, being subjected to a full 3D stress state (N, My, Mz, Mt, Vz and Vy), resulting from local, distortional or global instability of the connected members that could lead to the failure of the tensile components (such as bolts or end-plates). This paper gives a brief description of a consistent methodology to predict the behaviour of bolted steel beam-to-column joints under a natural fire. This methodology incorporates the influence of the transient temperature variation on the time-varying forces that act on the joint and gives design guidance on how to avoid the failure of the joint throughout the fire event. Validation of the proposed model is carried out by comparison against experimental results (Santiago et al., 2008). 2. BEHAVIOUR OF JOINTS IN FIRE Based on the studies previously described, it is confirmed that it was in the last fifteen years that the subject of steel joints under fire conditions suffered its main developments. Several experimental tests were performed in different typologies of joints and under different boundary and loading conditions, and analytical and numerical models were developed, which tried to reproduce adequately the behaviour of such tested joints. However, some of these experimental tests were concentrated on predicting the behaviour of isolated joints at high temperatures under monotonic bending loading, while other tests used this known bending- rotational behaviour as boundary conditions, in order to study the behaviour of the heated connected beams. Despite the evident importance of modelling the behaviour of beam-to-column joints under a natural fire, as part of a frame structure, low experimental studies concerned with this matter have yet been published in the open literature. In a research projected developed at the University of Coimbra (Santiago et al., 2008; Santiago, 2008), some fire tests on a sub-frame beam-to column were carried out (Figure 1). The structural definition consisted of two thermally insulated HEA300 cross-section columns (S355) and an unprotected IPE300 cross-section beam (S355) with 5.7 m free span, supporting a steel-concrete composite slab. The mechanical loading applied at room temperature corresponded to the self-weight and the concentrated loads equal to 20 kN at 700 mm from the mid-span cross- section; the thermal loading corresponded to a heating-cooling curve applied to the beam and joints.The parametric study is focused on the beam-to-column joint configuration (Table 1). IPE 300 1210 HEA 300 1129 5700 300 HEA 300 Y Z X Figure 1. Structural model (mm). Table 1. Beam-to-column joint configuration. Test IDJoint typology End-plate dimensions (mm) and steel grade Bolts / Weld FJ01(32020010); S2752 bolt row M20, 8.8 FJ02(32020016); S2752 bolt row M20, 10.9 FJ03 Flush end-plate (32020016); S2752 bolt row M20, 8.8 EJ01Extended end-plate(38520016); S2753 bolt row M20, 8.8 HJ01Header plate(2601508); S2754 bolt row M20, 8.8 WJ01Welded-af = aw = 10 mm 3. COMPONENT METHOD IN FIRE 3.1Overview Over the past three decades, a considerable effort was undertaken to give consistent predictions of the steel joints at room temperature using the component method (Jaspart, 2002); however due to the large number of parameters that need to be taken into account when modelling the joints response in fire, very little research work has been conducted in fire situation; exception should be mentioned to the work developed by the University of Coimbra (Simes da Silva et al., 2001), the University of Sheffield (Block et al., 2007) and the Imperial College London (Ramli Sulong et al., 2007). From the available methods(Simes da Silva et al., 2005), the component-based approach is also chosen in this work to model the connection behaviour because of its computational efficiency and capacity to provide a reasonable representation of the full range of response starting from the actual geometrical and mechanical properties. 3.2Proposed component method Considering the evidences reached from the experimental tests and the numerical simulations (Santiago et al., 2008 and Santiago, 2008), some important aspects were identified as relevant for the formulation of any component methodology to analyse steel joints under fire: i) components characterization; ii) material properties dependency with temperature; iii) variable combination of bending moment and axial force; iv); non-conservation of linear cross-sections; v) loading-unloading-reloading that characterise the changing temperatures; vi) effective length of the components. The spring model chosen in this work corresponds to the one developed by Cerfontaine (Cerfontaine, 2004) to analyse joints under bending moment and axial force at room temperature. Figure 2 depicts the proposed model to a flush end-plate joint; the number and location of each component depends on the joint typology. For a bolted joint, the compression components (beam flange in compression and column web in compression) are located at the level of the beam flanges axis and the tension components (column web in tension, column flange in bending, end- plate in bending, bolts in tension and beam web in tension) are located at the level of the bolt rows axis. Additionally, the shear column components are located independently of the tension-compression system, as suggested by Cerfontaine. However an important difference should be highlighted; in the Cerfontaine model, the axial force and bending moment is monotonic increased and proportional throughout the analysis; but under a natural fire, the axial force changes from compression to tension and the bending moment from hogging to sagging. compression components (beam top flange) compression components (beam bottom flange) tension components (2nd bolt row) tension components (1st bolt row) column web in shear Figure 2. Proposed model to a flush end plate joint. For the performed experimental tests, the columns were maintained at low temperatures, and its deformability, compared with the global deformability of the joint, was much reduced (Santiago, 2008). So, on the application of the proposed model, the column web components could be disregarded: column web in shear, compression and tension. The application of the proposed model is feasible when the component response is introduced as a force displacement curve. Due to the reduced number of studies on the component characterization at high temperatures, a bilinear law was assumed in this study: the plastic resistance and initial stiffness at room temperature were calculated according the EN 1993-1-8-2005; once the component was loaded beyond its yield capacity, post-limit stiffness defined on literature was adopted (Santiago, 2008). For each step, the degradation of the strength and stiffness of each component material with temperature was considered using the reduction factors proposed by EN 1993-1-2-2005, and the component temperatures corresponded to the experimental measurements (Figure 3). The effective length of each component remains constant throughout the analysis and corresponds to the value calculated by the EN 1993-1-8-2005 at room temperature. 0 150 300 450 600 750 900 020406080100120140160180 time (min) temp. (C) beam bottom flange (joint) beam w eb (joint) beam top flange (joint) beam bottom flange (beam) beam w eb (beam) beam top flange (beam) 0 150 300 450 600 750 900 020406080100120140 160180 time (min) temp. (C) bolts end-plate Figure 3. Temperature applied to the FJ03 model. The variable combination of bending moment and axial force, derived from the finite element models, was introduced in the spring model as axial forces at the level of each component (Santiago, 2008). To respond to the changing loading-unloading-reloading characteristic, a modified Masing rule has also been implemented into the model. Masing rule assumes that a material like steel unloads with a stiffness equal to the initial stiffness of the loading curve, and then follows a hysteresis curve meeting the mirror image of the point at which unloading started in the opposite quadrant. However, if the temperature changes between loading and unloading, this process becomes more complicated because the components response is temperature dependent. In this case, the assumption that the plastic strain is not affected by the temperature distribution should be employed (Franssen, 1990). The main underline of this assumption it that each force-displacement curves at different temperature unloads to the same plastic deformation, p (Figure 4). One of the main problems of this approach originates from the fact that the tensile and compressive forces in the connection do not share the same line of action. So, it was assumed that the compression springs are plastically deformed and unload until the end-plate loses contact with the column flange, the compression springs are deactivated and the tension springs start taking load from this deformed position. However, if the tension springs are deformed plastically and unload to initial position, it is assumed that all subsequent compression forces in the tension spring is taken by the compression spring row adjacent to the unloading tension spring row. Another problem inherent to a fire situation is the large deformations developed on the beam. After large deformations, the well known Bernoullis hypothesis, according to which plane cross-sections remain plane in the deformed state of the beam, is not valid, as observed in the experimental tests (Santiago et al., 2008). The component method presented in the EN 1993-1-8 assumes that the cross-section remains always plane, even at large deformations. Here, the same simplifying assumption was adopted. FRd,1 FRd,0 FEd,1 Deformation, Force, F O p0 0 1 1 0) O A A FEd,0 B Figure 4. Force-displacement paths for loading with increasing temperature. 3.3Application to a bolted end-plate beam-to-column joints The connection element has been validated against the experimental results (Santiago et al., 2008). The active components were chosen according the variation of the axial stresses integrated in a beam cross section near the connection and the axial stresses of the bolts; Figure 5 illustrates it for the flush end-plate joint FJ03: The active beam components were divided in five periods: t 12 min - compression in the lower zone and tension in the upper zone; 12 t 27 min - compression in the lower and upper zones; 27 t 90 min - compression in the lower and tension in the upper zone; t 90 min - tension in the lower and upper zones. -600 -400 -200 0 200 400 600 0255075100125150175200 t (min.) Fx (kN) compression in the upper zone tension in the upper zone tension in the lower zone compression in the lower zone 0 40 80 120 160 200 0255075100125150175200 t (min.) Fx (kN) tension in the 2nd bolt-row tension in the 1st bolt-row Figure 5. Forces introduced in the component model (joint FJ03). Applying the axial forces and the bilinear force-displacement response of the active components at each temperature (Figure 6), the main quantities relevant for the FJ03 joint, for some representative times, are set out in Tables 2 and 3. For t 27 min; no active component reached its capacity. Between 27 t 90 min. the beam bottom flange exhibits a decrease of the compressive force and the upper connection zone changes from compression to tension. This change of forces is shown in the active components during this period: the components reached their highest temperature leading to a relevant decrease of their resistances and to the yielding of the beam bottom flange in compression and beam web in tension (top). 0 150 300 450 600 750 900 0.00.20.40.60.81.0 dx (mm) F (kN) end-plate in bending bolts in tension beam flange in compression beam web in tension column flange in bending Figure 6. Force-displacement response of each component at room temperature. Table 2. Proposed model applied to the bolted joint FJ03 (27 t 90 min). t (min)temp. (C)FRd,t (kN)FEd,t (kN) t (mm)note 27.0700.0188.4189.00.396yield 42.0849.569.851.10.396elastic beam bottom flange in compression89.0686.5215.027.20.396elastic 27.0206.4370.441.20.027elastic 42.0378.7318.5110.80.090elastic 1st bolt-row in tension 89.0414.5294.877.80.067elastic 27.0291.1336.233.00.015elastic 42.0518.2243.287.10.057elastic end-plate in bending (top) 89.0502.5259.7113.90.069elastic 27.095.4390.741.20.008elastic 42.0302.7390.7110.80.028elastic column flange in bending (top)89.0404.9390.777.80.023elastic 27.0636.0250.833.00.000elastic 42.0790.979.187.10.423yield Beam web in tension (top) 89.0572.6362.9113.91.609elastic From Figure 5 it is observed that between 90 t 165 min, only the tension components are active. According the proposed methodology, there was one component that reached its plastic resistance: end-plate in bending (bottom) at t = 131 min, FRd,t = 336.2 kN and FEd,t = 358.2 kN, with a corresponding displacement of t = 0.93 mm (Table 3). The last active component that reached its maximum capacity was the 2nd bolt-row in tension at t = 165 min, FRd,t = 376.7 kN and FSd,t = 377.1 kN, with a corresponding displacement of t = 13.6 mm. It should be referred that on the experimental test, this component failed at t = 190 min. For each bolted end-plate beam-to-column joints, Table 4 summarizes the components that reached their plastic capacity. 4. RECOMMENDATIONS FOR DESIGN RULES In the previous section, a methodology for the evaluation of the response of steel joints under fire loading based on the component method was developed and applied. It was able to reproduce with sufficient accuracy the transient response of the steel joints throughout the fire development and to identify the failure modes of the joint. This procedure provides an adequate basis for incorporation in advanced Table 3. Proposed model applied to the bolted joint FJ03 (90 t 165 min). t (min)temp. (C)FRd,t (kN) FEd,t (kN)t (mm)note 1st bolt-row in 90.0389.1313.286.40.072elastic 131.0256.5364.0183.80.128elastic tension 165.0159.3376.7275.60.173elastic 90.0467.1286.6118.90.067elastic 131.0300.9336.2186.50.083elastic end-plate in bending (top) 165.0192.9336.2234.90.093elastic 90.0379.2390.786.40.024elastic 131.0241.3390.7183.80.043elastic column flange in bending (top) 165.0161.2390.7275.60.059elastic 90.0515.8478.0118.91.609elastic 131.0292.3653.7186.51.609elastic Beam web in tension (top) 165.0153.2653.7234.91.609elastic 90.0389.1313.235.90.030elastic 131.0256.5364.0299.20.209elastic 2nd bolt-row in tension 165.0159.3376.7377.113.60yield 90.0455.0276.70.00.000elastic 131.0314.1336.2358.20.930yield end-plate in bending (bottom)165.0196.6336.2497.95.105plastic 90.0379.2390.735.90.010elastic 131.0241.3390.7299.20.070elastic column flange in bending (bottom)165.0161.2390.7377.10.081elastic 90.0515.8653.70.00.000elastic 131.0292.3653.7358.20.000elastic Beam web in tension (bottom) 165.0153.2653.7497.90.000elastic Table 4. Sequence of yield or failure (bolts) of the components to each bolted end- plate beam-to-column joints. acting forces Top T Bottom - C Top C Bottom - C Top T Bottom - C Top T Bottom - T HeatingCooling FJ01 -t = 22 (beam bottom flange in compression) t = 32 (end plate in bending - top) t = 99 (end plate in bending - bottom) FJ02- t = 22 (beam bottom flange in compression) t = 44 (beam web in tension - top) t = 123 (column flange in bending - bottom) t = 141 (column flange in bending - top) t = 170 (failure of the 2nd bolt-row in tension is imminent: FEd,t = 0.99 FRd,t) FJ03- t = 27 (beam bottom flange in compression) t = 42 (beam web in tension - top) t = 131 (end-plate in bending - bottom). t = 165 (2nd bolt-row in tension) EJ01- t = 34 (beam web in tension - bottom)- t = 110 (end-plate in bending 3rd bolt-row) t = 141 (beam web in tension - 3rd bolt-row) t = 190 (3rd bolt-row in tension) calculation methods through the development of specialized joint finite elements. However, for conceptual and pre-design, the proposal of simple design recommendations is a desirable goal. Although the number of tests carried out in this research work is clearly insufficient to validate wide-ranging simplified rules, it is nevertheless enough to propose a framework and a methodology for future simplified rules. Focussing on bolted end-plate beam-to-column joints, simplified design rules should take into account two distinct design points (on top of the fulfilment of the cold-design criteria): (i) design period A that corresponds to the critical period during the heating phase; and (ii) design period B that corresponds to the crit