Modelling of the behaviour of beam-to-column connections at elevated temperature

Transcription

1 Modelling of the behaviour of beam-to-column connections at elevated temperature K. S. Al Jabri Department of Civil and Architectural Engineering, Sultan Qaboos University, Sultanate of Oman Abstract Beam-to-column connections are one of the structural elements which were found to be of great significance in enhancing structural behaviour at ambient and elevated temperatures. In general, laboratory experiments provide acceptable results that can describe the behaviour of the beam-to-column connections. However, in many cases experiments are either not feasible or too expensive. Numerical modelling of connections at elevated temperature provides an alternative to experimental testing in investigating the connections behaviour. Therefore, in recent years, various numerical techniques have emerged to simulate the connection response ranging from simple behaviour prediction procedure, to more complicated finite element models. This paper addresses the current developments in the numerical methods that have been developed to simulate the connection behaviour at elevated temperature which could help in providing thorough understanding of the major contribution connections can play in the high performance of structures in fire. Keywords: connections, elevated-temperatures, fire, finite element, models, moment-rotation. 1 Introduction Beam-to-column connections are one of structural elements, which were found to be of great significance in enhancing structural behaviour at ambient and elevated temperatures. Observations from damaged structures [1] confirm that connections have a considerable effect on the survival time of structural members in fire due to their ability to distribute forces. Accurate prediction of the structural behaviour of steel beam-to-column connections, by estimating the

2 32 High Performance Structures and Materials II local deformations and induced stresses, is necessary to assess the capacity of the connections and prevent their failure. Laboratory experiments provide acceptable results that can describe the behaviour of the beam-to-column connections. However, in many cases experiments are either not feasible or too expensive. Although of high importance, they are always limited in number of geometrical and mechanical parameters, which obviously would not provide thorough understanding of connection performance. With the advent of computing nowadays, it is possible to simulate complex real life cases involving the need for the variation of a wide range of parameters difficult to consider all of them in the lab. Numerical models are one of the most suitable mean to investigate the effect of all parameters considered in lieu of experimental testing and can provide acceptable and accurate results. Use of analytical models in modelling the connection behaviour at elevated temperature has attracted interest in recent years due to scarcity of experimental data and difficulty in the modelling when the connection is subjected to fire. An accurate modelling of connection elements as well as a realistic simulation of degradation of connection characteristics with increasing temperature are required in order to achieve acceptable results. In general, the behaviour of connections is usually described by momentrotation characteristics up to failure. At elevated temperatures it is necessary to determine such characteristics at different temperatures. In the most sophisticated analysis it may be necessary to include the complete moment-rotation characteristics. However, it may often be adequate to use simple connection models, representing key parameters such as stiffness, capacity and ductility. Various forms of analysis and modelling methods have been suggested including simple curve fitting techniques, simplified component-based models and sophisticated finite element models for both bare-steel and composite connections. 2 Simplified representation of connection characteristics at elevated temperature Simplified mathematical expressions were developed in order to enable the utilisation of connection characteristics obtained from laboratory experimental tests within the numerical models. Such expressions should be capable of describing the connection behaviour over the entire range of rotation. Early modelling of connection characteristics was largely based on the assumption that the behaviour is linearly elastic over the entire moment-rotation range, thus making the overall structural response elastic [2,3]. However, due to complicated nature of connections, the moment-rotation relationships are generally non-linear. Such behaviour can be represented in a number of different ways with various levels of complexity. Therefore various forms of representation have been suggested such as bi-linear approximations [4,5], tri-linear and multi-linear forms of curve fit as proposed by Moncarz and Gerstle [6] and Poggi and Zandonini [7] and polynomial expressions as

3 High Performance Structures and Materials II 321 suggested by Sommer [8] and Fry and Morris [9]. An improved form of the polynomial expression was developed by Richard and Abbott [1] based on the least-squares curve-fitting procedure in which only four parameters are required to establish the moment-rotation characteristics of a particular connection. Ang and Morris [11] proposed an alternative expression following the same procedure while utilising a Ramberg and Osgood [12] function which was originally developed to define the non-linear response of stress-strain characteristics. More complicated forms of expression to represent the response of the connection were developed as the use of computers in analysing the behaviour of steel framed structures became popular. Jones et al. [13] suggested a cubic-b- Spline technique from which the connection rotation is divided into a finite number of smaller ranges. A cubic function is fitted within each range, with first and second derivative continuity maintained between ranges. Chen and Liu [14, 15] proposed an exponential model which provides a comparable representation. However, the model requires four or more constants to describe effectively the moment-rotation characteristics. The Chen-Liu exponential model was further refined by Kishi and Chen [16] to accommodate linear components and deal with both loading and unloading for the full range of rotation. Under fire conditions structural members undergo a considerable deformation far in excess of that normally occurring at ambient temperature and thus the adjacent connections experience high levels of rotation. When modelling the connection characteristics for fire conditions, it is very important to select the form of curve-fit that represent accurately the actual connection response throughout the entire range of rotation and temperature. Selecting simple forms of curve-fitting expression will yield conservative representation of the actual connection behaviour. In order to achieve a representation of the connection behaviour at elevated temperature that reflects the actual behaviour of the connection, El-Rimawi et al. [17] modified the Ramberg-Osgood function [12] to represent the momentrotation response of the connection at elevated-temperatures. The Ramberg- Osgood moment-rotation function is: n M M φ = +.1 (1) A B where, φ, M = Connection rotation and the corresponding level of moment respectively; A, B and n = Temperature dependent parameters. The stiffness and strength of the connection may be degraded with increasing temperatures by modifying the temperature dependent parameters A and B respectively. This form of expression will enable the experimental data to be incorporated in the development of analytical models. Recently, Leston-Jones [18] and Al-Jabri [19] used the suggested expression to represent the moment-rotation-temperature behaviour of different connection types and carried out studies into the effect of actual bare-steel and composite

4 322 High Performance Structures and Materials II end-plate connections on frame behaviour at elevated temperatures. Fig. 1 shows a family of moment-rotation-temperature curves derived for two connections [19]. Moment (knm) 4 (a) Flush End-plate C 2 C 4 C 5 C Moment(kNm) (b) Flexible End-plate C/1 C C 7 C 4 2 Curves at 1 C intervals Rotation (Millirads) Rotation (Millirads) Figure 1: Moment-rotation-temperature curves for typical connections. Based on these findings and knowledge about the degradation of connection characteristics at elevated temperature a simple procedure was proposed by Al- Jabri et al. [2] to predict the moment-rotation-temperature response of connections. The proposed procedure was based on the actual degradation of the connection stiffness and strength with increasing temperatures and the ambient temperature response of the connection. An acceptable degree of accuracy was achieved when comparing the predicted results with experimental tests as clearly shown in Fig. 2. This procedure can be incorporated easily in simplified and numerical modelling of steel frame structures, in cases where the effect of restrain to thermal expansion of members is not likely to be serious. 3 Elevated temperature component-based models Component-based or spring-stiffness models became popular due to their simplicity and ability to predict the ambient temperature connection behaviour to an acceptable degree of accuracy. These models are based on dividing the connection into its basic elements of known mechanical properties. Each connection's element is represented by a spring of known stiffness as shown in Fig. 3. The overall connection response may be obtained by assembling the stiffnesses of individual elements in the tension and compression zones. The elevated temperature response of the connection may be predicted by allocating individual temperature-stiffness profile to each element at a given bolt row, allowing the modelling of any form of temperature distribution based on test

5 High Performance Structures and Materials II 323 data. Only those parameters representing the stiffness and strength are degraded with increasing temperatures. Moment (knm) Rotation (Millirads) Figure 2: 2 C 4 C 6 C Experimental Postulated Moment (knm) C 5 C 6 C Experimental Postulated Rotation (Millirads) Experimental and predicted elevated temperature responses for bare-steel connections. P tt,1 K tt,1 δ tt,1 p δ tt,2 D ep P tt,2 K tt,2 h 1 M conn P cwt K cwt h 2 tep Figure 3: Idealised representation of bare-steel connection component model. Elevated temperature component-based models are rare probably due to the lack of experimental data that describes the connection behaviour. An elevated temperature component model was developed by Leston-Jones [18] to predict

6 324 High Performance Structures and Materials II the response of bare-steel and composite flush end-plates connections. Comparison with experimental data [18] showed that there was a close agreement between the results for bare-steel flush end-plate connections. However, the composite model showed a significant difference in the rate of degradation compared with experimental results for elevated temperatures. A similar component model has recently been proposed by da Silva et al. [21] for the behaviour of steel joints at elevated temperatures. The proposed model was restricted to bare-steel flush end-plate joints. Comparison with experimental results [19] available in the literature has shown good agreement with the proposed method. Al-Jabri [22] adopted similar approach to model the behaviour of bare-steel and composite flexible end-plate connections. Comparison of the bare-steel component models with existing test data generated good results especially in the elastic zones illustrated in Fig. 4. Also the predicted rate of degradation of the connection stiffness and capacity compares well with the experimental results. For composite connections the predicted and the measured responses compared well for ambient temperature. Results were also encouraging for elevated temperatures, but in some respects more experimental data is required to draw positive conclusions. Beam Flange Temperature ( C) knm 16 knm Experimental Results Component Model Figure 4: Rotation (Millirads) Comparison of predicted elevated temperature response with baresteel connection test results. In general the component model is capable of predicting the connection response at both ambient and elevated temperatures to a reasonable accuracy especially in the elastic zone. The use of component-based models proved desirable due to their simplicity and efficiency. They can easily be modified to account for alternative connection types and arrangements.

7 High Performance Structures and Materials II Finite element modelling of connections at elevated temperature Finite element technique represents, in principle, a powerful tool capable of accurately predicting connection response. Despite the fact that a large number of finite element models are available which describe the connection behaviour at ambient temperature, very little work has been conducted so far into modelling the behaviour of the different types of connection in fire. This is attributed to scarcity of experimental data and difficulty in the modelling when the connection is subjected to fire. An accurate modelling of connection elements as well as a realistic simulation of degradation of connection characteristics with increasing temperatures are required in order to achieve acceptable results. Factors affecting the accuracy of finite element modelling include the meshing of the configuration (the optimum mesh size), simulation of bolts, choice of elements, material behaviour and most importantly modelling of the contact and gap elements. Early finite element modelling of connections at elevated temperature was performed by Liu and Morris [23,24,25,26,27] who developed a finite element model; FEAST, to simulate the various types of connection in the event of fire. The beam, column, end-plate and stiffeners were modelled using eight-noded shell elements including the consideration of material plasticity and degradation with temperature, non-uniform thermal expansion across a section and large deflections at very high temperatures. The response of bolts and the contact link between the column flange and end-plate was simulated using a beam element with special characteristics to take into account the behaviour of bolts during the course of expansion. A close comparison was found with experimental results. A three-dimensional finite element model has been developed by El- Houssieny et al. [28] to simulate the response of extended end-plates at both ambient and elevated temperatures. Close agreement was obtained with experimental work and subsequent parametric studies were conducted to investigate the influence of connection behaviour at normal and elevated temperatures. Spyrou et al. [29] modelled T-stub specimens at elevated temperatures using the finite element program ANSYS. Results demonstrated that 3-D analyses generated more accurate modelling than 2-D analyses. A close agreement was found between the experimental results and 3-D analyses. The finite element code, ABAQUS was recently used by Al-Jabri et al. [3] to simulate the behaviour of flush end-plate connections at elevated temperature. The connection elements were assumed to behave nonlinearly under high temperature. Eight nodded reduced integration brick elements were selected to simulate the connection components due to their reliable performance. The bolts were preloaded using the special command bolt load available in ABAQUS. However, they are allowed to slip inside the end-plates and column via bolt-tohole clearance of 1mm. Friction between the contact surfaces at the connection is modelled using the classical coulomb model where the friction coefficient was

8 326 High Performance Structures and Materials II taken as.1. Material non-linearity was considered for steel members and connection components. Degradation of steel properties with increasing temperatures was taken according to data presented in the design code based on experimental connection fire tests. A good agreement between the experimental and numerical results in terms of the failure mode and moment-rotationtemperature characteristics of the connection was achieved as shown in Figs. 5 and 6. Figure 5: Predicted failure mode of the connection from the finite element analysis. Moment(kNm) Rotation (Millirads ) 2º C 4 º C 5 º C 6 º C 7 º C F.E Model Figure 6: Comparison of predicted moment-rotation-temperature response with experimental results. 5 Conclusion This paper reviewed the analytical models which were developed to simulate the behaviour of connections in fire conditions. Both simple and sophisticated models were addressed which demonstrated that such models can be used

9 High Performance Structures and Materials II 327 effectively to predict the connection behaviour at elevated temperatures and provide a good alternative to experimental connection fire tests. References [1] Robinson, J., Fire A Technical Challenge and A Market Opportunity, Journal of Constructional Steel Research, 46:1-3, Paper No. 179, [2] Baker. J. F., Second Report, Steel Structures Research Committee, Department of Scientific and Industrial Research, HMSO, London, [3] Rathburn, J., Elastic Properties of Riveted Connections, Trans. Amer. Soc. Civil Engr, 11, pp [4] Lionberger, S. R., and Weever, W., Dynamic Response of Frames with Non-Rigid Connections, J. Engng Mech. Div., ASCE, 95(EM1), pp [5] Romstad, K. M., and Subramanian, C. V., Analysis of Frames with Partial Connection Rigidity, J. Struct. Div., ASCE, 96(ST11), pp , 197. [6] Moncarz, P. D., and Gerstle, K. H., Steel Frames with Non-Linear Connections, J. Struct. Div., ASCE, 17(8), pp , [7] Poggi, C., and Zandonini, R., Behaviour and Strength of Steel Frames with Semi-Rigid Connections, Connection Flexibility and Steel Frames, W. F. Chen (Ed.), Proc. ASCE, pp , [8] Sommer, W. H., Behaviour of Welded Header Plate Connection, MS Thesis, University of Toronto, Canada, [9] Fry, M. J., and Morris, G. A., Analysis of Flexibly Connected Frames, Can. J. Civ. Engng., 2(3), pp , [1] Richard, R. M., and Abbott, B. J., Versatile Elastic-Plastic Stress-Strain Formula, J. Engrg. Mech. Div., ASCE, 11(4), pp , [11] Ang, K. M., and Morris, G. A., Analysis of Three-Dimensional Frames with Flexible Beam-Column Connections, Can. J. Civ. Engng., 11(2), pp , [12] Ramberg, W., and Osgood, W. R., Description of Stress-Strain Curves by 3 Parameters, Technical Report 92, National Advisory Committee for Aeronautics, [13] Jones, S. W., Kirby, P. A., and Nethercot, D. A., The Analysis of Frames with Semi-rigid Connections - A State-of-the-art Report J. Construct. Steel Res. 3(2), pp. 2-13, [14] Chen, W. G., and Lui, E. M., Column with End Restraint and Bending in Load and Resistance Factor Design, AISC Journal, Third Quarter, pp , [15] Lui, E. M., and Chen, W. G., Analysis and Behaviour of Flexibly Jointed Frames, Engrg. Struct., 8(2), pp ,1986. [16] Kishi, N., and Chen, W. F., Database of Steel Beam-to-Column Connections, Structural Engineering Report No. CE-STR-86-26, School of Civ. Engrg., Purdue University, West Lafayette, Ind., 1986.

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