- Email: [email protected]
Component-based model of the behaviour of flexible end-plate connections at elevated temperatures
Composite Structures 66 (2004) 215–221 www.elsevier.com/locate/compstruct
Component-based model of the behaviour of flexible end-plate connections at elevated temperatures K.S. Al-Jabri
*
Department of Civil and Architectural Engineering, Sultan Qaboos University, P.O. Box 33, Al-Khod, Post code 123, Oman Available online 5 June 2004
Abstract This paper describes a component-based model developed to predict the behaviour of flexible end-plate composite connections at elevated temperature. In the model the connection elements are treated as springs with predefined characteristics such as stiffness and strength. By assembling the characteristics of individual elements, the connection response can be predicted with increasing temperatures. Only those parameters representing the stiffness and strength are degraded with increasing temperatures. Comparison of the results from the model with existing test data generated good results especially in the elastic zone. Also, the predicted degradation of the connection stiffness and capacity compares well with the experimental results. 2004 Elsevier Ltd. All rights reserved. Keywords: Flexible end-plate; Stiffness; Strength; Temperature; Fire; Component-based model; Composite
1. Introduction Laboratory tests 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. Component-based models started to attract researchers due to their relative simplicity and their ability to model the whole connection behaviour to an acceptable degree of accuracy. Due the improved understanding of the behaviour of connection’s elements at ambient temperature, EC3: Annex J [1] suggested a method for the design of connections at ambient temperature using component model. This method is based on dividing the connection into its basic elements of known mechanical properties. By assembling the contributions of individual components which represent the connection as a set of rigid and deformable elements, the entire behaviour of the connection may be determined. However, elevated temperature component-based models are scarce due to the lack of experimental data *
Tel.: +968-515-335; fax: +968-513-416. E-mail address: [email protected] (K.S. Al-Jabri).
0263-8223/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruct.2004.04.040
that describes the connection behaviour. If such simplified models are developed which has the capability of representing the connection response to an acceptable degree of accuracy, this of course will lead to better understanding of the high performance of steel structures in fire with fraction of testing costs and time. Consequently this will be beneficial in improving the current design codes in which the behaviour of steel structures in fire is inadequately addressed. This paper presents the results from a proposed component model developed to predict the behaviour of flexible end-plate composite connections at elevated temperature.
2. Behaviour of flexible end-plate connections Flexible (partial depth) end-plates are classified as ‘pinned’ connections with the end-plate partially welded to the beam web (Fig. 1). They possess higher flexibility and larger rotational capacity than those connections, which are classified as ‘semi-rigid’. Flexible end-plate connections are widely used in the construction of braced multi-storey steel framed buildings due to the ease of fabrication and assemblage and speed of erection. One of the main characteristics of a flexible end-plate is that the response has two stages:
216
K.S. Al-Jabri / Composite Structures 66 (2004) 215–221
Nomenclature Ar Db Dc Er Ert
fyrt h hb hr hr k Kb Kbt Kc Kcc Kcct
cross-sectional area of the reinforcing bar depth of the steel beam column depth elastic modulus of reinforcement modulus of elasticity of the reinforcement (mesh and reinforcement bars), at a given temperature; yield strength of the reinforcement at a given temperature distance from the beam slab interface to the centre of rotation; distance between centroid of top row of bolts and centre of rotation; distance between the centroid of reinforcement and centre of rotation; distance from the reinforcement to the centre of rotation secant stiffness of one shear stud axial spring stiffness of bolt bolt stiffness at a given temperature stiffness of the bare-steel connection initial stiffness of the composite connection at ambient temperature rotational stiffness of the composite connection for a given temperature;
φ
M conn
Kr Krpt Krt Ks Kst lr M N tb z
a / lr
column flange stiffness at a given temperature column web stiffness at a given temperature end-plate stiffness at given temperature equivalent single stiffness of all components in tension zone at a given temperature axial spring stiffness of reinforcement strain hardening stiffness of the reinforcement at a given temperature, stiffness of the spring representing the reinforcement for a given temperature axial spring stiffness of shear stud stiffness of the spring representing shear connection for a given temperature assumed length of reinforcement (23.8 mm). applied bending moment number of active shear studs temperature of the bolt distance from the centre of rotation to the centreline equivalent spring in the tension zone increase factor (@2) rotation of the composite connection the strain hardening coefficient for the reinforcement ( ¼ 0.05)
bearing the rotation is assumed to take place at the centre-line of the bottom flange as shown in Fig. 1, resulting in an enhanced stiffness and capacity. Due to lack of elevated temperature experimental data for the second stage, only the first stage is accounted for in the model. However, a simple modification of the model is possible to accommodate this response once test data becomes available.
3. The proposed composite model
Centre of Rotation
(a)
Kcft Kcwt Kept Keqt
(b)
Fig. 1. Behaviour of flexible end-plate connection. (a) Before contact and (b) after contact.
stage one: the unobstructed rotation of the connection; stage two: the beam lower flange bears against the column with further rotation. Prior to contact, the connection is assumed to rotate about the lower edge of the end-plate, whilst after
Composite construction has become popular in multi-storey structures in the last two decades, due to its increased structural efficiency allowing the use of lighter sections which leads to cost saving when compared with bare-steel construction. Similarly the performance of bare-steel beam-to-column connections is significantly improved by incorporating a composite slab. A nominal steel mesh is used to control the development of cracks as well as providing resistance to any applied tensile forces. Shear studs are used to ensure that the composite slab and the bare-steel section act compositely. The composite slab, in fire, act as insulation to the top part of the connection, shear studs and reinforcing mesh,
K.S. Al-Jabri / Composite Structures 66 (2004) 215–221
reducing their temperature and thus enhancing the inherent fire resistance of the connection. The principle of component models is based on dividing the connection into its basic elements. These elements are idealised as springs with known mechanical characteristics of strength and stiffness. The composite connection is divided into parts: the bare-steel connection and the composite slab. Bare-steel connection components are simulated by individual springs at each bolt row representing the stiffnesses of the components which are assumed to follow a pre-defined force-displacement relationship. For simplicity, an equivalent single spring stiffness at a given temperature, Keqt is used to represent the stiffness of all components in the tension zone in accordance with EC3: Annex J [1] whilst the compression zone is defined by a separate spring, Kcwt . The tension zone comprises bolt stiffness ðKbt Þ, end-plate stiffness ðKept Þ and column flange stiffness (Kcft ) while column web stiffness ðKcwt Þ represents the connection component in the compression zone. The global rotational stiffness of the bare-steel connection is determined by assembling the stiffnesses in the tension and compression zones to form an equivalent single spring. In the composite model additional springs are incorporated to represent the composite slab components such as reinforcing mesh and shear studs. An idealised representation of the component model of the composite connection is shown in Fig. 2. The elevated temperature component model representing the bare-steel flexible end-plate connections is described in detail elsewhere [2]. The connection characteristics of the composite connection may be assessed by taking into consideration the bare-steel section, reinforcement and shear studs. Therefore, the rotation, of the composite connection, /, at any given moment, M may be expressed as /¼
M Kcc
ð1Þ
where, Kcc is the initial stiffness of the composite connection at ambient temperature.
A number of authors have proposed a simple form of equations in order to predict initial stiffness of the connection at ambient temperature. Aribert and Lachal [3] developed a simple equation for calculating the initial stiffness suitable for flush end-plate composite connections based on eight tests. This may be defined as Kcc ¼ Kc þ
Krt
δ rt δs Kst
Ptt,1
Ktt,1
δ t,1 hr
Ptt,2
Ktt,2
Mconn
δt,2 h1 h2
Pcwt
Kcwt
Fig. 2. Idealised representation of composite connection component model.
Db Dc a þ 2Er Ar hr Nkhb
ð2Þ
where, Kc is the stiffness of the corresponding bare-steel connection, Er is the elastic modulus of reinforcement, Ar is the cross-sectional area of the reinforcing bar, hr is the distance from the reinforcement to the centre of rotation, N is the number of active shear studs, Db is the depth of the steel beam, Dc is the column depth, k is the secant stiffness of one shear stud and a is the increase factor (@2). Anderson and Najafi [4] proposed a model relating rotation and moment using the following expression: /¼
M Kr Ks hr h 2 þ Kb hb Kr þ Ks
ð3Þ
where, h is the distance from the beam slab interface to the centre of rotation, hb is the distance between centroid of top row of bolts and centre of rotation and Kr , Ks and Kb are the axial spring stiffness of the reinforcement, shear stud and bolt respectively. Ren and Crisinel [5] developed a relation between the moment and rotation for composite flush end-plate connections which can be used to predict the initial stiffness of the connection. The derivation of the model assumed that the moment capacity of a connection is the sum of the reinforcement and the bare-steel capacity. The method considers the deformation of the column web due to the compression at the level of the beam bottom flange. The model may be expressed as M hr
/¼ 1 Kr
Prt
217
ð4Þ
þ K1s þ K1c
A more generalised stiffness model has been proposed by Ahmed and Nethercot [6] to predict the initial stiffness for flush end-plate composite connections. The initial stiffness of the connection may be expressed as 1 1 1 1 1 1 2 hhr þ þ þ þhb hb ðhþhr Þ Kb Kcw Kr Ks Kcw Kcw Kcc ¼ 1 1 1 1 1 1 þ þ þ 2 Kr Ks Kcw Kb Kcw Kcw ð5Þ The form of model proposed by Anderson and Najafi [4] has been adopted in the elevated temperature flexible composite connection model. The model has been
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modified to consider the effect of elevated temperatures and to maintain consistency with the bare-steel component model. The stiffness of the composite connection may be obtained by adding the stiffness of the bare-steel connection to that of the reinforcement and shear studs. Therefore, the stiffness of the composite connection may be expressed as follows: 1 Krt Kst hr h 1 Kcct ¼ ðKeqt þ Kcwt Þ z2 þ ð6Þ Krt þ Kst where, Kcct , Krt , and Kst are the rotational stiffness of the composite connection, reinforcement and shear studs for a given temperature and z is the distance from the centre of rotation to the centreline equivalent spring in the tension zone. By introducing temperature-dependent parameters that have the capability of predicting the response of additional components required for composite action, it is possible to follow the entire moment-rotation characteristics in a tri-linear form. The model also requires suitable representations of the composite slab elements such as reinforcement and shear studs. 3.1. Behaviour of reinforcing bars In the model proposed, it is assumed that the concrete has negligible tensile strength, and that the reinforcement resists the internal tensile forces generated in the connection under load. A number of authors [3–6] have suggested that the reinforcement obeys Hooke’s law. Hence, the stiffness of the reinforcement, Krt , at a given temperature is expressed as Ert Ar Krt ¼ lr
ð7Þ
All studs in the hogging moment region should be considered when calculating the stiffness of the shear studs. If the connection has more studs than are required for full interaction the actual number of studs required for full interaction should be utilised. Results from push out tests [7–10] show that the elastic stiffness of shear studs is in the range of 110–350 kN/mm. Therefore an approximate value of 200 kN/mm is adopted to represent the stiffness of the shear studs in the current model.
4. Degradation of connection characteristics at elevated temperature The degradation of stiffness and strength of the connection components was based on the degradation of structural steel at elevated temperature according to EC3: Part 1.2 [11] as shown in Table 1. However, the degradation of bolt stiffness and capacity is based on recommendations presented by Kirby and Preston [12] based on experimental tests using the following expressions: For tb 6 300 C
ð9Þ
where, Krpt is the strain hardening stiffness of the reinforcement at a given temperature and lr is the strain hardening coefficient for the reinforcement ( ¼ 0.05).
ð11aÞ
For tb < 300 C 6 680 C SFR ¼ 1:0 ðtb 300Þ 2:128 103
ð11bÞ
Table 1 Degradation of connection stiffness and strength at elevated temperature Steel temperature, (C)
ð8Þ
where, fyrt is the yield strength of the reinforcement at a given temperature. A reduced stiffness is assumed in the strain hardening zone following the onset of yielding, which may expressed as Krpt ¼ lr Krt
3.2. Stiffness of the shear studs
SFR ¼ 1:0
where, Ert is modulus of elasticity of the reinforcement (mesh and reinforcement bars), at a given temperature and lr is the assumed length of reinforcement (23.8 mm). It is anticipated that the reinforcement will behave elastically until the onset of plasticity. Thus, the force, Frpt that causes yielding in the reinforcement, at a given temperature, may be expressed as: Frpt ¼ fyrt Ar
The force in the reinforcement for a give rotation may be expressed as Krt Kst h / ð10Þ Frt ¼ Krt þ Kst
200 100 200 300 400 500 600 700 800 900 1000 1100 1200
Reduction factors for yield stress, fy and Young’s modulus, Ea , at temperature, ha ky;h ¼ fy;h =fy
kE;h ¼ Ea;h =Ea
1.000 1.000 0.926 0.848 0.775 0.618 0.357 0.169 0.087 0.060 0.040 0.020 0.000
1.000 1.000 0.900 0.800 0.700 0.600 0.310 0.130 0.09 0.0675 0.0450 0.0225 0.000
K.S. Al-Jabri / Composite Structures 66 (2004) 215–221
For tb < 680 C 6 1000 C SFR ¼ 0:17 ðtb 680Þ 5:13 10
4
ð11cÞ
where, tb is the temperature of the bolt and SFR is strength retention factor of the bolt.
219
selected based on tensile coupon tests conducted on structural steel specimens [2]. However, the bolts were assumed to have yield and ultimate stresses of 480 and 600 MPa, respectively. Geometrical properties of the steel sections were based on nominal values. The temperature profile across the connection depth was based on experimental observations [2].
5. Connection geometry and material properties In order to illustrate the behaviour of steel composite connections under fire loading, a cruciform bolted flexible end-plate composite connection tested by Al-Jabri [2] was selected. This major axis connection configuration consists of two 356 · 171UB51 beams connected to a 254 · 254UC89 column by 8 mm thick flush end-plates and eight M20 bolts. The form of the composite slab was namely PMF COMFLOR C70 decking with 130 mm overall slab depth using lightweight concrete of Grade C35 with A142 mesh reinforcement. The length of continuous slab across the connection was 1400 mm and its width was 1200 mm. The length of the slab was enough to allow two 100 mm by 19 mm shear studs at 300 mm centres on each cantilever beam. The composite connection detail is shown in Fig. 3. The elevated temperature tests were performed under anisothermal conditions, the levels of applied bending moment being based on the moment capacity of the connection obtained from experimental test at ambient temperature. The moment capacity of the connection was 102 kNm. Four tests were conducted at loading levels of: 34, 46, 62 and 82 kNm representing 0.32, 0.46, 0.59 and 0.78 of moment capacity of the connection. Two load cases were modeled at loading levels of 34 and 46 kNm which represent the behaviour of the connection in the first stage of rotation. The yield and ultimate stresses of the connection components were taken as 426 and 573 MPa, respectively while a value of 197 kN/mm2 was adopted for the Young’s modulus of structural steel. The yield and ultimate stress values of reinforcing mesh were taken as 487 and 553 MPa, respectively. These values were
6. Validation of the model The connection response predicted by the model is compared with experimental test data at both ambient and elevated temperatures. The rate of degradation of the connection’s stiffness and strength for connection is also compared with the numerical prediction. Five tests were carried out, four at elevated temperature and one at ambient temperature. Two elevated temperature tests were conducted within the first stage of the connection response and used in the validation of the model. Results from the ambient temperature test are compared with the predicted response from the model as shown in Fig. 4. The stiffness of the connection remains constant up to a moment of approximately 45 kNm, after which curved knee response appears in the moment-rotation response due to the yielding of the reinforcement and failure of the composite slab. This is followed by response which is represented by flat plateau due to the significant end-plate deformation until the beam bears against the column at a rotation of approximately 65 mrad. It can be seen from the plotted results that the predicted elastic response of the connection compares closely with the experimental results suggesting that the proposed model is capable of predicting the initial stiffness of the connection accurately. However, the model predicts a more flexible response in the plastification zone up to approximately 15 mrad, beyond which the predicted response becomes stiffer. This difference, in the strain hardening zone, is probably due to the actual Moment (kNm) 80
100x19mm(dia.) shear stud
254x254x89UC(50)
A142 reinforcing mesh 130
70 40 60
100
25
8
700 356x171x51UB(50)
Light weight concrete C35
PMF COMFLOR C70 profiled deck
60
260
60 40
70 60 50 40 30 20 Test Component Model
10
6mm FW to beam web
0
71
All holes 22mm dia. for M20 Grade 8.8 bolts
90 150
Fig. 3. Composite connection detail.
0
10
20
30
40
50
Rotation (Millirads)
Fig. 4. Comparison of predicted ambient temperature response with test results for flexible end-plate composite connection.
220
K.S. Al-Jabri / Composite Structures 66 (2004) 215–221
variation in the material properties as well as lack of data defining the connection components responses in the plastification zone. Despite the slight variation in the response, the model can predict the connection response to a reasonable accuracy. It may be anticipated that the reinforcement and shear studs would remain at a relatively low temperature due to the protection provided by the concrete. It is therefore assumed that this temperature is 20% of the beam bottom flange temperature. The analysis was repeated using the experimental temperature profiles to investigate the ability of the model to predict the performance of the composite connection at elevated temperature. The experimental and predicted rate of degradation of connection’s stiffness and capacity are compared in Figs. 5 and 6. It may be seen from Fig. 5(a)
Stiffness Retention Factor 1
(a) Stiffness
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2
Experimental Results Predicted Degradation
0.1 0 0
100 200 300 400 500 600 700 800 Temperature (˚C)
Strength Retention Factor 1
(b) Capacity
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2
Experimental Results
0.1
Predicted Degradation
0 0
100 200 300 400 500 600 700 800 Temperature (˚C)
Fig. 5. Degradation of composite connection’s (a) stiffness at elevated temperature and (b) strength at elevated temperature.
Beam Flange Temperature (˚C) 700
34 kNm
600
46 kNm
500 400 300 200
Experimental Results Component Model
100 0 0
10
20
30
40
50
60
70 80
Rotation (Millirads)
Fig. 6. Comparison of predicted elevated temperature response with composite connection test results.
that there is close agreement between the predicted rate of degradation of stiffness and that observed experimentally. This demonstrates that the degradation of connection stiffness is primarily controlled by the degradation of the reinforcement in the tension zone since in the first stage of response the exposed column web in the compression zone has little influence on stiffness degradation. Considering connection capacity, it may be seen from Fig. 5(b) that there is a reasonable correlation between the predicted and experimental data, with the proposed model predicting a greater degradation rate than the recorded at intermediate temperatures. This difference is more pronounced at low failure temperatures where the connection is exposed to high levels of loading. This is probably due to the fact that the degradation of capacity adopted in the model was based on a strain level of 0.5% which underestimates the actual rate of degradation of connection capacity. Unfortunately experimental data was not available for temperatures below 480 C, as a result of the levels of moment utilised in testing. The applicability of the model to predict the connection response at elevated temperature is investigated against two elevated temperature tests conducted within the first stage of response. These tests were conducted at moments of approximately 34 and 46 kNm respectively. Experimental results are compared with those obtained from the proposed component model as shown in Fig. 6 based on experimental material properties and temperature profiles. It may be seen that the proposed component model provides a reasonable prediction of the initial stiffness and capacity of the connection for both tests. However, for the first elevated temperature test (i.e. 34 kNm), the model slightly underestimates the yield capacity of the connection at high temperatures, whilst it provides a close prediction of initial stiffness. However, this variation may be attributable to a reversal in the connection rotation in the first test at temperatures between 300 and 500 C due to thermal bowing. The current model does not account for this.
K.S. Al-Jabri / Composite Structures 66 (2004) 215–221
7. Conclusions A simplified component model was presented for modelling the elevated temperature response of flexible end-plate composite connections. Connections were modelled by assembling the contributions of individual components. Tri-linear modelling was adopted, with the separation of the connection into its main components allowing the use of any chosen temperature profile. The main parameters describing stiffness and capacity of the elements were degraded with increasing temperatures. The predicted response of the connection was compared with the response observed from experimental tests. Results showed that there a good agreement between the predicted and the experimental response at low levels of loading. This agreement was more noticeable in the elastic zone. However, at high levels of loading and in the plastic region the model underestimates to some extent the connection response. This may be attributed to the lack of experimental data that describes the connection behaviour in the strain hardening region. The rate of degradation of stiffness and strength was closely predicted by the model for both connections. 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. References [1] EC3: Design of steel structures Part 1.1: Revised Annex J joints and building frames (draft) document CEN/TC250/SC3 N419E. European Committee for Standardisation. 1994.
221
[2] Al-Jabri KS. The behaviour of steel and composite beamto-column connections in Fire. Ph.D. Thesis. Department of Civil and Structural Engineering, University of Sheffield, UK. 1999. [3] Aribert JM, Lachel A. Experimental investigation of composite connections in global interpretation. Proc COST C1 conf on semirigid joints. Strasbourg, France. 1992, pp. 158–169. [4] Anderson D, Najafi AA. Performance of composite connections: major axis end-plate joints. J Construct Steel Res 1994;31(1):31– 57. [5] Ren P, Crisinel M. Prediction method for moment-rotation behaviour of composite beam to steel column connection. In: Bjorhovde R, et al. editors, Connections in steel structures III: behaviour, strength and design, Proc 3rd int workshop, Trento University, Italy, 1995, pp. 33–46. [6] Ahmed B, Nethercot D. A prediction of initial stiffness and available rotation capacity of major axis composite flush end-plate connections. J Construct Steel Res 1997;41(1):31–60. [7] Chapman JC. Experiments on composite beams. The Struct Eng 1964;42(11):369–83. [8] Mottram JT, Johnson RP. Push tests on studs welded through profiled steel sheeting. Struct Engr 1990;68(10):187–93. [9] Lloyd RM, Wright HD. Shear connection between composite slabs and steel beams. J Construct Steel Res 1990;15:255– 85. [10] Mistakidis ES, Thomopolos KT, Avdelas A, Panagiotopoulos PD. Analysis of Composite Beams with Shear Connectors Allowing for Softening. in: Kounadis, editor, Steel StructuresEurosteel ’95. Rotterdam: Balkema; 1995, p. 73–80. [11] EC3: Design of steel structures, part 1.1: Revised Annex J joints and building frames., (draft). Document CEN/TC250/ SC3 N419E. European Committee for Standardisation. 1994. [12] Kirby BR, Preston RR. High temperature properties of hot rolled structural steels for use in fire engineering design studies. Fire Safety J 1988;13:27–37.
Component-based model of the behaviour of flexible end-plate connections at elevated temperatures K.S. Al-Jabri
*
Department of Civil and Architectural Engineering, Sultan Qaboos University, P.O. Box 33, Al-Khod, Post code 123, Oman Available online 5 June 2004
Abstract This paper describes a component-based model developed to predict the behaviour of flexible end-plate composite connections at elevated temperature. In the model the connection elements are treated as springs with predefined characteristics such as stiffness and strength. By assembling the characteristics of individual elements, the connection response can be predicted with increasing temperatures. Only those parameters representing the stiffness and strength are degraded with increasing temperatures. Comparison of the results from the model with existing test data generated good results especially in the elastic zone. Also, the predicted degradation of the connection stiffness and capacity compares well with the experimental results. 2004 Elsevier Ltd. All rights reserved. Keywords: Flexible end-plate; Stiffness; Strength; Temperature; Fire; Component-based model; Composite
1. Introduction Laboratory tests 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. Component-based models started to attract researchers due to their relative simplicity and their ability to model the whole connection behaviour to an acceptable degree of accuracy. Due the improved understanding of the behaviour of connection’s elements at ambient temperature, EC3: Annex J [1] suggested a method for the design of connections at ambient temperature using component model. This method is based on dividing the connection into its basic elements of known mechanical properties. By assembling the contributions of individual components which represent the connection as a set of rigid and deformable elements, the entire behaviour of the connection may be determined. However, elevated temperature component-based models are scarce due to the lack of experimental data *
Tel.: +968-515-335; fax: +968-513-416. E-mail address: [email protected] (K.S. Al-Jabri).
0263-8223/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruct.2004.04.040
that describes the connection behaviour. If such simplified models are developed which has the capability of representing the connection response to an acceptable degree of accuracy, this of course will lead to better understanding of the high performance of steel structures in fire with fraction of testing costs and time. Consequently this will be beneficial in improving the current design codes in which the behaviour of steel structures in fire is inadequately addressed. This paper presents the results from a proposed component model developed to predict the behaviour of flexible end-plate composite connections at elevated temperature.
2. Behaviour of flexible end-plate connections Flexible (partial depth) end-plates are classified as ‘pinned’ connections with the end-plate partially welded to the beam web (Fig. 1). They possess higher flexibility and larger rotational capacity than those connections, which are classified as ‘semi-rigid’. Flexible end-plate connections are widely used in the construction of braced multi-storey steel framed buildings due to the ease of fabrication and assemblage and speed of erection. One of the main characteristics of a flexible end-plate is that the response has two stages:
216
K.S. Al-Jabri / Composite Structures 66 (2004) 215–221
Nomenclature Ar Db Dc Er Ert
fyrt h hb hr hr k Kb Kbt Kc Kcc Kcct
cross-sectional area of the reinforcing bar depth of the steel beam column depth elastic modulus of reinforcement modulus of elasticity of the reinforcement (mesh and reinforcement bars), at a given temperature; yield strength of the reinforcement at a given temperature distance from the beam slab interface to the centre of rotation; distance between centroid of top row of bolts and centre of rotation; distance between the centroid of reinforcement and centre of rotation; distance from the reinforcement to the centre of rotation secant stiffness of one shear stud axial spring stiffness of bolt bolt stiffness at a given temperature stiffness of the bare-steel connection initial stiffness of the composite connection at ambient temperature rotational stiffness of the composite connection for a given temperature;
φ
M conn
Kr Krpt Krt Ks Kst lr M N tb z
a / lr
column flange stiffness at a given temperature column web stiffness at a given temperature end-plate stiffness at given temperature equivalent single stiffness of all components in tension zone at a given temperature axial spring stiffness of reinforcement strain hardening stiffness of the reinforcement at a given temperature, stiffness of the spring representing the reinforcement for a given temperature axial spring stiffness of shear stud stiffness of the spring representing shear connection for a given temperature assumed length of reinforcement (23.8 mm). applied bending moment number of active shear studs temperature of the bolt distance from the centre of rotation to the centreline equivalent spring in the tension zone increase factor (@2) rotation of the composite connection the strain hardening coefficient for the reinforcement ( ¼ 0.05)
bearing the rotation is assumed to take place at the centre-line of the bottom flange as shown in Fig. 1, resulting in an enhanced stiffness and capacity. Due to lack of elevated temperature experimental data for the second stage, only the first stage is accounted for in the model. However, a simple modification of the model is possible to accommodate this response once test data becomes available.
3. The proposed composite model
Centre of Rotation
(a)
Kcft Kcwt Kept Keqt
(b)
Fig. 1. Behaviour of flexible end-plate connection. (a) Before contact and (b) after contact.
stage one: the unobstructed rotation of the connection; stage two: the beam lower flange bears against the column with further rotation. Prior to contact, the connection is assumed to rotate about the lower edge of the end-plate, whilst after
Composite construction has become popular in multi-storey structures in the last two decades, due to its increased structural efficiency allowing the use of lighter sections which leads to cost saving when compared with bare-steel construction. Similarly the performance of bare-steel beam-to-column connections is significantly improved by incorporating a composite slab. A nominal steel mesh is used to control the development of cracks as well as providing resistance to any applied tensile forces. Shear studs are used to ensure that the composite slab and the bare-steel section act compositely. The composite slab, in fire, act as insulation to the top part of the connection, shear studs and reinforcing mesh,
K.S. Al-Jabri / Composite Structures 66 (2004) 215–221
reducing their temperature and thus enhancing the inherent fire resistance of the connection. The principle of component models is based on dividing the connection into its basic elements. These elements are idealised as springs with known mechanical characteristics of strength and stiffness. The composite connection is divided into parts: the bare-steel connection and the composite slab. Bare-steel connection components are simulated by individual springs at each bolt row representing the stiffnesses of the components which are assumed to follow a pre-defined force-displacement relationship. For simplicity, an equivalent single spring stiffness at a given temperature, Keqt is used to represent the stiffness of all components in the tension zone in accordance with EC3: Annex J [1] whilst the compression zone is defined by a separate spring, Kcwt . The tension zone comprises bolt stiffness ðKbt Þ, end-plate stiffness ðKept Þ and column flange stiffness (Kcft ) while column web stiffness ðKcwt Þ represents the connection component in the compression zone. The global rotational stiffness of the bare-steel connection is determined by assembling the stiffnesses in the tension and compression zones to form an equivalent single spring. In the composite model additional springs are incorporated to represent the composite slab components such as reinforcing mesh and shear studs. An idealised representation of the component model of the composite connection is shown in Fig. 2. The elevated temperature component model representing the bare-steel flexible end-plate connections is described in detail elsewhere [2]. The connection characteristics of the composite connection may be assessed by taking into consideration the bare-steel section, reinforcement and shear studs. Therefore, the rotation, of the composite connection, /, at any given moment, M may be expressed as /¼
M Kcc
ð1Þ
where, Kcc is the initial stiffness of the composite connection at ambient temperature.
A number of authors have proposed a simple form of equations in order to predict initial stiffness of the connection at ambient temperature. Aribert and Lachal [3] developed a simple equation for calculating the initial stiffness suitable for flush end-plate composite connections based on eight tests. This may be defined as Kcc ¼ Kc þ
Krt
δ rt δs Kst
Ptt,1
Ktt,1
δ t,1 hr
Ptt,2
Ktt,2
Mconn
δt,2 h1 h2
Pcwt
Kcwt
Fig. 2. Idealised representation of composite connection component model.
Db Dc a þ 2Er Ar hr Nkhb
ð2Þ
where, Kc is the stiffness of the corresponding bare-steel connection, Er is the elastic modulus of reinforcement, Ar is the cross-sectional area of the reinforcing bar, hr is the distance from the reinforcement to the centre of rotation, N is the number of active shear studs, Db is the depth of the steel beam, Dc is the column depth, k is the secant stiffness of one shear stud and a is the increase factor (@2). Anderson and Najafi [4] proposed a model relating rotation and moment using the following expression: /¼
M Kr Ks hr h 2 þ Kb hb Kr þ Ks
ð3Þ
where, h is the distance from the beam slab interface to the centre of rotation, hb is the distance between centroid of top row of bolts and centre of rotation and Kr , Ks and Kb are the axial spring stiffness of the reinforcement, shear stud and bolt respectively. Ren and Crisinel [5] developed a relation between the moment and rotation for composite flush end-plate connections which can be used to predict the initial stiffness of the connection. The derivation of the model assumed that the moment capacity of a connection is the sum of the reinforcement and the bare-steel capacity. The method considers the deformation of the column web due to the compression at the level of the beam bottom flange. The model may be expressed as M hr
/¼ 1 Kr
Prt
217
ð4Þ
þ K1s þ K1c
A more generalised stiffness model has been proposed by Ahmed and Nethercot [6] to predict the initial stiffness for flush end-plate composite connections. The initial stiffness of the connection may be expressed as 1 1 1 1 1 1 2 hhr þ þ þ þhb hb ðhþhr Þ Kb Kcw Kr Ks Kcw Kcw Kcc ¼ 1 1 1 1 1 1 þ þ þ 2 Kr Ks Kcw Kb Kcw Kcw ð5Þ The form of model proposed by Anderson and Najafi [4] has been adopted in the elevated temperature flexible composite connection model. The model has been
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modified to consider the effect of elevated temperatures and to maintain consistency with the bare-steel component model. The stiffness of the composite connection may be obtained by adding the stiffness of the bare-steel connection to that of the reinforcement and shear studs. Therefore, the stiffness of the composite connection may be expressed as follows: 1 Krt Kst hr h 1 Kcct ¼ ðKeqt þ Kcwt Þ z2 þ ð6Þ Krt þ Kst where, Kcct , Krt , and Kst are the rotational stiffness of the composite connection, reinforcement and shear studs for a given temperature and z is the distance from the centre of rotation to the centreline equivalent spring in the tension zone. By introducing temperature-dependent parameters that have the capability of predicting the response of additional components required for composite action, it is possible to follow the entire moment-rotation characteristics in a tri-linear form. The model also requires suitable representations of the composite slab elements such as reinforcement and shear studs. 3.1. Behaviour of reinforcing bars In the model proposed, it is assumed that the concrete has negligible tensile strength, and that the reinforcement resists the internal tensile forces generated in the connection under load. A number of authors [3–6] have suggested that the reinforcement obeys Hooke’s law. Hence, the stiffness of the reinforcement, Krt , at a given temperature is expressed as Ert Ar Krt ¼ lr
ð7Þ
All studs in the hogging moment region should be considered when calculating the stiffness of the shear studs. If the connection has more studs than are required for full interaction the actual number of studs required for full interaction should be utilised. Results from push out tests [7–10] show that the elastic stiffness of shear studs is in the range of 110–350 kN/mm. Therefore an approximate value of 200 kN/mm is adopted to represent the stiffness of the shear studs in the current model.
4. Degradation of connection characteristics at elevated temperature The degradation of stiffness and strength of the connection components was based on the degradation of structural steel at elevated temperature according to EC3: Part 1.2 [11] as shown in Table 1. However, the degradation of bolt stiffness and capacity is based on recommendations presented by Kirby and Preston [12] based on experimental tests using the following expressions: For tb 6 300 C
ð9Þ
where, Krpt is the strain hardening stiffness of the reinforcement at a given temperature and lr is the strain hardening coefficient for the reinforcement ( ¼ 0.05).
ð11aÞ
For tb < 300 C 6 680 C SFR ¼ 1:0 ðtb 300Þ 2:128 103
ð11bÞ
Table 1 Degradation of connection stiffness and strength at elevated temperature Steel temperature, (C)
ð8Þ
where, fyrt is the yield strength of the reinforcement at a given temperature. A reduced stiffness is assumed in the strain hardening zone following the onset of yielding, which may expressed as Krpt ¼ lr Krt
3.2. Stiffness of the shear studs
SFR ¼ 1:0
where, Ert is modulus of elasticity of the reinforcement (mesh and reinforcement bars), at a given temperature and lr is the assumed length of reinforcement (23.8 mm). It is anticipated that the reinforcement will behave elastically until the onset of plasticity. Thus, the force, Frpt that causes yielding in the reinforcement, at a given temperature, may be expressed as: Frpt ¼ fyrt Ar
The force in the reinforcement for a give rotation may be expressed as Krt Kst h / ð10Þ Frt ¼ Krt þ Kst
200 100 200 300 400 500 600 700 800 900 1000 1100 1200
Reduction factors for yield stress, fy and Young’s modulus, Ea , at temperature, ha ky;h ¼ fy;h =fy
kE;h ¼ Ea;h =Ea
1.000 1.000 0.926 0.848 0.775 0.618 0.357 0.169 0.087 0.060 0.040 0.020 0.000
1.000 1.000 0.900 0.800 0.700 0.600 0.310 0.130 0.09 0.0675 0.0450 0.0225 0.000
K.S. Al-Jabri / Composite Structures 66 (2004) 215–221
For tb < 680 C 6 1000 C SFR ¼ 0:17 ðtb 680Þ 5:13 10
4
ð11cÞ
where, tb is the temperature of the bolt and SFR is strength retention factor of the bolt.
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selected based on tensile coupon tests conducted on structural steel specimens [2]. However, the bolts were assumed to have yield and ultimate stresses of 480 and 600 MPa, respectively. Geometrical properties of the steel sections were based on nominal values. The temperature profile across the connection depth was based on experimental observations [2].
5. Connection geometry and material properties In order to illustrate the behaviour of steel composite connections under fire loading, a cruciform bolted flexible end-plate composite connection tested by Al-Jabri [2] was selected. This major axis connection configuration consists of two 356 · 171UB51 beams connected to a 254 · 254UC89 column by 8 mm thick flush end-plates and eight M20 bolts. The form of the composite slab was namely PMF COMFLOR C70 decking with 130 mm overall slab depth using lightweight concrete of Grade C35 with A142 mesh reinforcement. The length of continuous slab across the connection was 1400 mm and its width was 1200 mm. The length of the slab was enough to allow two 100 mm by 19 mm shear studs at 300 mm centres on each cantilever beam. The composite connection detail is shown in Fig. 3. The elevated temperature tests were performed under anisothermal conditions, the levels of applied bending moment being based on the moment capacity of the connection obtained from experimental test at ambient temperature. The moment capacity of the connection was 102 kNm. Four tests were conducted at loading levels of: 34, 46, 62 and 82 kNm representing 0.32, 0.46, 0.59 and 0.78 of moment capacity of the connection. Two load cases were modeled at loading levels of 34 and 46 kNm which represent the behaviour of the connection in the first stage of rotation. The yield and ultimate stresses of the connection components were taken as 426 and 573 MPa, respectively while a value of 197 kN/mm2 was adopted for the Young’s modulus of structural steel. The yield and ultimate stress values of reinforcing mesh were taken as 487 and 553 MPa, respectively. These values were
6. Validation of the model The connection response predicted by the model is compared with experimental test data at both ambient and elevated temperatures. The rate of degradation of the connection’s stiffness and strength for connection is also compared with the numerical prediction. Five tests were carried out, four at elevated temperature and one at ambient temperature. Two elevated temperature tests were conducted within the first stage of the connection response and used in the validation of the model. Results from the ambient temperature test are compared with the predicted response from the model as shown in Fig. 4. The stiffness of the connection remains constant up to a moment of approximately 45 kNm, after which curved knee response appears in the moment-rotation response due to the yielding of the reinforcement and failure of the composite slab. This is followed by response which is represented by flat plateau due to the significant end-plate deformation until the beam bears against the column at a rotation of approximately 65 mrad. It can be seen from the plotted results that the predicted elastic response of the connection compares closely with the experimental results suggesting that the proposed model is capable of predicting the initial stiffness of the connection accurately. However, the model predicts a more flexible response in the plastification zone up to approximately 15 mrad, beyond which the predicted response becomes stiffer. This difference, in the strain hardening zone, is probably due to the actual Moment (kNm) 80
100x19mm(dia.) shear stud
254x254x89UC(50)
A142 reinforcing mesh 130
70 40 60
100
25
8
700 356x171x51UB(50)
Light weight concrete C35
PMF COMFLOR C70 profiled deck
60
260
60 40
70 60 50 40 30 20 Test Component Model
10
6mm FW to beam web
0
71
All holes 22mm dia. for M20 Grade 8.8 bolts
90 150
Fig. 3. Composite connection detail.
0
10
20
30
40
50
Rotation (Millirads)
Fig. 4. Comparison of predicted ambient temperature response with test results for flexible end-plate composite connection.
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variation in the material properties as well as lack of data defining the connection components responses in the plastification zone. Despite the slight variation in the response, the model can predict the connection response to a reasonable accuracy. It may be anticipated that the reinforcement and shear studs would remain at a relatively low temperature due to the protection provided by the concrete. It is therefore assumed that this temperature is 20% of the beam bottom flange temperature. The analysis was repeated using the experimental temperature profiles to investigate the ability of the model to predict the performance of the composite connection at elevated temperature. The experimental and predicted rate of degradation of connection’s stiffness and capacity are compared in Figs. 5 and 6. It may be seen from Fig. 5(a)
Stiffness Retention Factor 1
(a) Stiffness
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2
Experimental Results Predicted Degradation
0.1 0 0
100 200 300 400 500 600 700 800 Temperature (˚C)
Strength Retention Factor 1
(b) Capacity
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2
Experimental Results
0.1
Predicted Degradation
0 0
100 200 300 400 500 600 700 800 Temperature (˚C)
Fig. 5. Degradation of composite connection’s (a) stiffness at elevated temperature and (b) strength at elevated temperature.
Beam Flange Temperature (˚C) 700
34 kNm
600
46 kNm
500 400 300 200
Experimental Results Component Model
100 0 0
10
20
30
40
50
60
70 80
Rotation (Millirads)
Fig. 6. Comparison of predicted elevated temperature response with composite connection test results.
that there is close agreement between the predicted rate of degradation of stiffness and that observed experimentally. This demonstrates that the degradation of connection stiffness is primarily controlled by the degradation of the reinforcement in the tension zone since in the first stage of response the exposed column web in the compression zone has little influence on stiffness degradation. Considering connection capacity, it may be seen from Fig. 5(b) that there is a reasonable correlation between the predicted and experimental data, with the proposed model predicting a greater degradation rate than the recorded at intermediate temperatures. This difference is more pronounced at low failure temperatures where the connection is exposed to high levels of loading. This is probably due to the fact that the degradation of capacity adopted in the model was based on a strain level of 0.5% which underestimates the actual rate of degradation of connection capacity. Unfortunately experimental data was not available for temperatures below 480 C, as a result of the levels of moment utilised in testing. The applicability of the model to predict the connection response at elevated temperature is investigated against two elevated temperature tests conducted within the first stage of response. These tests were conducted at moments of approximately 34 and 46 kNm respectively. Experimental results are compared with those obtained from the proposed component model as shown in Fig. 6 based on experimental material properties and temperature profiles. It may be seen that the proposed component model provides a reasonable prediction of the initial stiffness and capacity of the connection for both tests. However, for the first elevated temperature test (i.e. 34 kNm), the model slightly underestimates the yield capacity of the connection at high temperatures, whilst it provides a close prediction of initial stiffness. However, this variation may be attributable to a reversal in the connection rotation in the first test at temperatures between 300 and 500 C due to thermal bowing. The current model does not account for this.
K.S. Al-Jabri / Composite Structures 66 (2004) 215–221
7. Conclusions A simplified component model was presented for modelling the elevated temperature response of flexible end-plate composite connections. Connections were modelled by assembling the contributions of individual components. Tri-linear modelling was adopted, with the separation of the connection into its main components allowing the use of any chosen temperature profile. The main parameters describing stiffness and capacity of the elements were degraded with increasing temperatures. The predicted response of the connection was compared with the response observed from experimental tests. Results showed that there a good agreement between the predicted and the experimental response at low levels of loading. This agreement was more noticeable in the elastic zone. However, at high levels of loading and in the plastic region the model underestimates to some extent the connection response. This may be attributed to the lack of experimental data that describes the connection behaviour in the strain hardening region. The rate of degradation of stiffness and strength was closely predicted by the model for both connections. 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. References [1] EC3: Design of steel structures Part 1.1: Revised Annex J joints and building frames (draft) document CEN/TC250/SC3 N419E. European Committee for Standardisation. 1994.
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[2] Al-Jabri KS. The behaviour of steel and composite beamto-column connections in Fire. Ph.D. Thesis. Department of Civil and Structural Engineering, University of Sheffield, UK. 1999. [3] Aribert JM, Lachel A. Experimental investigation of composite connections in global interpretation. Proc COST C1 conf on semirigid joints. Strasbourg, France. 1992, pp. 158–169. [4] Anderson D, Najafi AA. Performance of composite connections: major axis end-plate joints. J Construct Steel Res 1994;31(1):31– 57. [5] Ren P, Crisinel M. Prediction method for moment-rotation behaviour of composite beam to steel column connection. In: Bjorhovde R, et al. editors, Connections in steel structures III: behaviour, strength and design, Proc 3rd int workshop, Trento University, Italy, 1995, pp. 33–46. [6] Ahmed B, Nethercot D. A prediction of initial stiffness and available rotation capacity of major axis composite flush end-plate connections. J Construct Steel Res 1997;41(1):31–60. [7] Chapman JC. Experiments on composite beams. The Struct Eng 1964;42(11):369–83. [8] Mottram JT, Johnson RP. Push tests on studs welded through profiled steel sheeting. Struct Engr 1990;68(10):187–93. [9] Lloyd RM, Wright HD. Shear connection between composite slabs and steel beams. J Construct Steel Res 1990;15:255– 85. [10] Mistakidis ES, Thomopolos KT, Avdelas A, Panagiotopoulos PD. Analysis of Composite Beams with Shear Connectors Allowing for Softening. in: Kounadis, editor, Steel StructuresEurosteel ’95. Rotterdam: Balkema; 1995, p. 73–80. [11] EC3: Design of steel structures, part 1.1: Revised Annex J joints and building frames., (draft). Document CEN/TC250/ SC3 N419E. European Committee for Standardisation. 1994. [12] Kirby BR, Preston RR. High temperature properties of hot rolled structural steels for use in fire engineering design studies. Fire Safety J 1988;13:27–37.