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A practical approach for fire resistance design of extended end-plate joints
Journal of Constructional Steel Research 64 (2008) 1456–1462 www.elsevier.com/locate/jcsr
A practical approach for fire resistance design of extended end-plate joints Wei-Yong Wang a,∗ , Guo-Qiang Li a,b , Yu-li Dong c a College of Civil Engineering, Tongji University, No. 1239 Siping Road, Shanghai, 200092, People’s Republic of China b State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University, No. 1239, Siping Road, Shanghai, 200092, People’s Republic of China c College of Civil Engineering, Harbin Institute of Technology, Harbin, 150091, People’s Republic of China
Received 29 March 2007; accepted 9 January 2008
Abstract Although beam-to-column joints are known to have a very significant effect on the behaviour of steel frames in the event of fire, no specific approach for evaluating the behaviour of extended end-plate joints in fire has been proposed. In this paper, on the basis of the current Chinese Code for Design of Steel Structures [Chinese code for design of steel structures. 2002] and Technical Code on Fire Safety of Steel Building Structures [Chinese Technical code on fire safety of steel building structure. CECS, 2006], analysis is presented on the load-bearing capacity of extended end-plate joints in fire, by taking the mechanical properties of steel at elevated temperature into account. A practical approach for fire-resistance calculation and assessment of the joints is proposed, based on the load-bearing capacity of the components of joints at elevated temperatures including the bolt, extended end-plate, column flange and panel zone. Employing the practical approach, the critical temperatures of two extended end-plate joints are predicted. By comparison with the results measured from the tests, the effectiveness of this practical approach is verified. c 2008 Elsevier Ltd. All rights reserved.
Keywords: Extended end-plate joint; Practical approach; Fire resistance; Column flange; Panel zone
1. Introduction Beam-to-column joints have been found to be of great significance in influencing the structural behaviour of frameworks at ambient and elevated temperatures. Observations from fullscale fire tests and from damage to steel frame structures due to real fires [1,2] confirm that joints have a considerable effect on the survival time of structural members in fire due to their ability to distribute forces. Fire is a disaster that frequently happens in buildings. Since steel structures are widely used in buildings and sensitive to fire, much research has focused on studying the influence of high temperature on the behaviour of steel structures. In recent years, considerable research work has been conducted to understand the performance of steel beam-tocolumn joints at ambient temperature at both experimental and analytical modelling levels. Experimental tests have been carried out on a wide variety of joints either in isolation or as part of complete steel-framed structures in order to understand their behaviour. A number of fire tests on steel joints ∗ Corresponding author. Tel.: +86 21 65985318; fax: +86 21 65983431.
E-mail address: [email protected] (W.-Y. Wang). c 2008 Elsevier Ltd. All rights reserved. 0143-974X/$ - see front matter doi:10.1016/j.jcsr.2008.01.008
were conducted by CTICM [3] with the primary purpose of investigating the performance of high strength bolts at elevated temperatures. In addition, tests to study the behaviour of beamto-column joints at elevated temperatures were carried out by British Steel [4], Lawson [5] and Leston-Jones [6]. An experiment study was performed on four full-scale extend endplate joints in fire and a spring-component modelling was presented to predict the rotation of the joints in fire by Wei-yong Wang et al. [7]. These tests provide useful data for theoretical study. However, up to now, there is little literature covering the fire resistance design of steel beam-to-column joints including EC3: Part1.2 [8] and Chinese Technical Code on Fire safety of Steel Building Structures [9]. This paper is mainly concerned with the fire resistance design of extended end-plate joints, commonly used in steel frames. A practical approach is proposed on fire resistance design of extended end-plate joints made with H-shaped steel, based on the current Chinese Code for Design of Steel Structures [10] and Technical Code on Fire Safety of Steel Building Structures [9]. The mechanical properties of steel for the joints and high-strength bolts at elevated temperatures are introduced. A joint is supposed to be divided into a number of basic components with known load capacities, such as the high strength bolt, column flange,
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column web and end-plate. By assembling the contributions of individual components which represent various parts of the joint as a set of elements, the entire critical temperature of the joint may be determined. The critical temperature of a joint is defined as the temperature at which the load bearing capacity of the joint is reduced and not enough to compensate the action of the loads applied on the joint. What is new in this paper is that a practical approach is presented to check and assess the extended end-plate joints in fire, which can be used for fireresistant design of extended end-plate joints. 2. Mechanical properties of steel at elevated temperatures Materials which are commonly used to fabricate steel beamto-column joints in China include structural steel of Q235 or Q345 for plate and hot-rolled H-shaped sections, and Grade 8.8 or 10.9 for high strength bolts with ultimate tensile strengths respectively over 800 and 1000 N/mm2 . When a steel extended end-plate joint is exposed to fire, the temperature of the joint will be increased to a high level. At elevated temperatures, the elastic modulus and yield strength of steel will be reduced. Although lots of recommendations may be found in the literature for various standard of steel, the following expressions are recommended for determining the reduction of the elastic modulus and yielding strength of steel, according to Chinese standard [9], at elevated temperatures. For steel plate and hot-rolled sections 7Ts − 4780 ET 20 ◦ C ≤ Ts ≤ 600 ◦ C = E 6Ts − 4760 (1) ET 1000 − Ts = 600 ◦ C ≤ Ts ≤ 1000 ◦ C E 6Ts − 2800 f yT = 1.0 20 ◦ C ≤ Ts ≤ 300 ◦ C f y f yT = 1.24 × 10−8 T 3 − 2.096 × 10−5 T 2 s s fy (2) −3 ◦ ◦ +9.228 × 10 T − 0.2168 300 C < T < 800 C s s f yT = 0.5 − Ts 800 ◦ C ≤ Ts ≤ 1000 ◦ C fy 2000 for steel bolts [11], the ultimate strength at elevated temperature is determined by f ubT = −2 × 10−6 × Tb2 + 7 × 10−5 × Tb + 1.0473 f ub 20 ◦ C ≤ Tb ≤ 700 ◦ C
(3)
where E is the elastic modulus of steel at ambient temperature; E T the elastic modulus of steel at a given temperature; Ts the temperature of steel in centigrade; f y the yield strength of steel at ambient temperature; f yT the yield strength of steel at a given temperature; f ub the ultimate strength of the bolt at ambient temperature; f ubT the ultimate strength of the bolt at a given temperature; and Tb is the temperature of the bolts. The decrease of the yield strength and elastic modulus of structural steel and the ultimate strength of high strength bolts with elevated temperatures is presented in Fig. 1.
Fig. 1. Yield strength and elastic modulus of structural steel and high strength bolts at elevated temperatures.
Fig. 2. Configuration of extend end-plate joint.
3. Approach for determining the temperature of the joints in fire If fire attacks a steel building, the steel members including the joints will be heated up. On the basis of thermal conductivity theory, the temperature of the joints may be determined. The temperature of the components consisting of an extended end plate joint may be different, when the joint is exposed to fire. The components mainly include the extended end-plate and the column zone at the joint (see Fig. 2). It is assumed that the temperature of the joints is approximatively equal to the average temperature of column and beam. The temperature of the column and beam exposed to fire Ts (t) can be obtained by [9]: Ts (t + 1t) =
B [Tg (t) − Ts (t)]1t + Ts (t) cs ρs
(4)
where Tg (t) is the temperature of the fire varying with time; cs is specific heat of steel; ρs is density of steel; 1t is the time increment; and B is the general heat transfer coefficient. The general heat transfer coefficient, B, can be obtained by the following equation: for the case without fire protection B = (αc + αr )
F V
(5)
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and for the case with non-intumescent fire protection 1
B= 1+
ci ρi di Fi 2cs ρs V
λi Fi di V
The shear capacity of high strength bolt at elevated temperatures can be predicted by: (6)
where αc is the convection heat transfer coefficient; αr is the emission heat transfer coefficient and determined by " # Tg + 273 4 Ts + 273 4 2.041 αr = − (7) Tg − Ts 100 100 F is the area per length of column or beam exposed to fire; V is the volume per length of column or beam; ci is the specific heat of fire protection material; ρi is the density of fire protection material; di is the thickness of fire protection material; λi is the equivalent heat conductivity of fire protection; Fi is the interior area pre length of fire protection of column or beam. 4. Check of fire resistance of extended end-plate joints Similar to the load capacity check at ambient temperature, the fire resistance of an extended end-plate joint at elevated temperatures due to fire can be checked in three aspects, including fire resistance of high strength bolts in tension and shear; fire resistance of extended end-plate and column flange in flexure; and fire resistance of panel zone. The limit state of fire resistance of the joint is defined for each of the following cases; (a) (b) (c) (d) (e) (f)
High strength bolt yields in tension; High strength bolt yields in shear; End-plate yields in flexure; Column flange yields in flexure; Panel zone yielding in shear; The rotation of the joint reaches 0.05 radians and increases rapidly.
4.1. High strength bolts of the joint in fire It is assumed that the high strength bolt rotates around the shape center of all the bolts for the joint. Load capacity of the bolt in tension and shear is considered at ambient temperature. Similarly, at elevated temperatures, the tension and shear bearing capacity of one bolt can be obtained by the consideration of influence of temperature on the mechanical properties of the bolts. The capacity of high strength bolt at elevated temperatures in tension can be predicted by the following expression: πd02 × 0.46 f ubT (8) 4 where d0 is the effective diameter of the bolt shaft. The capacity of the bolt at elevated temperatures can then be checked by: NtbT =
M yi Ntbi = P 2 ≤ NtbT yi
πd 2 × 0.3 f ubT (10) 4 where d is diameter of bolt shaft. The capacity of the groupware of the bolts at elevated temperatures in shear can be checked by: X b Q≤ NvT (11) b NvT =
where Q is shear force of the joint. A check of the bolt subjected to a combined tension and shear at elevated temperature can be made with the following expression: v ! !2 u u Nb 2 Ntbi t v + ≤1 (12) b NvT NtbT Q ≤ d min(tep , tc f ) × 0.92 f yT (13) n where n is the number of bolts; tep is the thickness of the endplate; tc f is the thickness of the column flange. Nvb =
4.2. Extended end-plate of the joints in fire The stiffeners in the column web can increase the fire resistance of bolts significantly [7]. It is assumed that the joint is stiffened to avoid the bulking of the column web when considering the fire resistance design. Based on the ultimate moment capacity of the extended endplate of the joint at normal temperature in literature [12], the ultimate moment capacity of the extended end-plate at elevated temperatures can be expressed as " # 1.2 h b − tb f 2bep 2 + (h b − tb f ) (14) MuepT = f yT tep dc − tb f gc − tbw where the symbols of dc and gc can be seen from Fig. 2; h b is the depth of the beam; tb f is the thickness of the beam flange; tbw is the thickness of the beam web; and bep is the width of the end-plate. The fire resistance check of the extended end-plate can then be made with: M ≤ MuepT .
(15)
4.3. Column flange of the joint in fire The ultimate moment capacity of the column flange of the joint at elevated temperature can be obtained by the following two expressions [7]:
(9)
Muc f T 1 =
where M is moment of the joint; yi is distance from the bolt to shape center of bolts.
Muc f T 2 =
(1 + η)be f f c f tc2f (h b − tb f ) f yT 2m c (γ be f f c f tc2f f yT + 3πd02 n c f ybT )(h b − tb f ) 3(m c + n c )
(16) (17)
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where, η = 1 − bdeph , be f f c f = min{4π m c , 2πm c + dc , 8m c + 2.5n c , 4m c + 1.25n c + dc }; γ is a magnifying coefficient with steel strain hardening under consideration; m c is the distance from the center of the bolt hole to the column web; n c is the distance from the center of the bolt hole to the nearest edge of column flange. The fire resistance check of the column flange at elevated temperature can be found by M ≤ min(Muc f T 1 , Muc f T 2 ).
(18)
4.4. Panel zone of the joint in fire The fire resistance check of the panel zone of the joint in fire can be found by τ=
M ≤ 0.77 f yT Vp
(19)
where V p = h b h c tcw ; h c is the depth of the column; tcw is the thickness of the column web.
of the spring simulating the extended end-plate and the column flange at elevated temperature may be determined by [7]: K epT =
48E T h i 3 Z ep 1 − q 3aep − 4aep
(24)
Kc f T =
48E T i h 1 − q 3ac f − 4ac3f
(25)
Zc f
where m ep is the distance from the center of the bolt hole in the upside to the upper surface of beam flange; n ep is distance from the center of the bolt hole in the upside to the upper edge of end-plate; lc f = 2(m c + n c );
aep1 =
4.5. Rotation of the joints in fire The rotation of the joints in fire can be predicted by a component model, considering any steel beam-to-column joint as a set of individual components. A beam-to-column joint using the extended end-plate connection can be divided into four major zones (i.e. flexure, tension, shear and compression zone). Each zone of the joint can be further divided into a number of components, each of which is simply a nonlinear spring, possessing its own strength and stiffness in flexure, tension, compression or shear, and will be reduced with elevation of the temperatures. The global rotational stiffness of the joint K I T can be determined for any moment at any given temperature based on the assembled stiffness of all components as KIT =
(h b − tb f )2 1 Kc f T
+
1 K epT
+
1
.
(20)
K cwvT
With the spring model, the ultimate moment of the joint can be estimated using the following expression: M pT = F pT h b − tb f (21) F pT = min Fu,bT , Fu,epT , Fu,c f T , Fu,cwvT . (22) After obtaining the stiffness and ultimate load of each component, the moment-rotation relation may be obtained from the following equation [7]: −(K I T − K pT + CθT )θT M = M pT 1 − exp M pT + K pT θT
(23)
where, K pT can be expressed as 0.02 K I T , Quan Jing [13] recommended a value of C equal to zero. From classical simple beam-deflection theory, with the properties of steel at elevated temperature, the initial stiffness
n ep ; lep
aep =
Z ep = Ic f =
ac f 1 =
3 aep aep − ; 8 6 3 lep
Iep
;
lep = 2(m ep + n ep );
q=
ac3f ac f − ; 8 6 2 aep
aep2 =
2
ac f 2 = −
3 2aep
3
Z c f ac f 2 + Z ep ac f 1 +
1 be f f c f tc3f ; 12
Iep =
lb0 Ab0
nc ; lc f
ac2f
2ac3f
2
−
Zc f =
;
Z c f aep1 + Z ep aep2
ac f =
3 lc3f Ic f
; ;
;
1 3 bep tep . 12
When calculating the shear stiffness of the column web at elevated temperatures, the column web can be seen as a short column subjected to a shear force which is transferred from the beam flange. For a short column, the deformation caused by moment is far less than shear force, so the shear stiffness of the column web at elevated temperature may be expressed as [7]: K cwvT =
E T h c tcw 2(h b − tb f )(1 + µ)
(26)
where µ is Poisson’s ratio for steel. The ultimate load capacity of the high strength bolt at elevated temperature can be determined with: Fu,bT =
4 f ubT Abo γb
(27)
πd 2
where Abo = 4 0 . Considering the reduced failure strength with elevated temperatures, according to Eqs. (14) and (21), the ultimate load capacity of the extended end-plate may be evaluated using the following expression: " # 1.2 h b − tb f 2bep 2 FuepT = f yT tep + . (28) dc − tb f gc − tbw The ultimate load capacity of the column flange may be given as [7]: Fu,c f T = min{Fu,c f 1T , Fu,c f 2T }
(29)
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Table 1 Predicted and measured results of specimens Specimen Predicted temperature of the components (◦ C)
S-1 S-2
High strength bolts
Extended end-plate
Column flange
Panel zone
Joint rotation
572 572
513 624
551 551
545 569
550 555
Predicted critical temperature of joint (◦ C)
Predicted fire resistance of the joints (min)
Measured critical temperature of joint (◦ C)
Measured fire resistance of the joints (min)
513 551
20 21.5
545 569
24 22
where Fu,c f 1T = Fu,c f 2T =
(1 + η) be f f c f t 2f f yT
, 2m c γ be f f c f tc2f f yT + 12BuT n c 3 (m c + n c )
,
BuT = πdo2 f ubT /4. The ultimate shear capacity of the column web may be written as f yT Fu,cwvT = √ Avc 3
(30) Fig. 3. Details of specimens.
where Avc = Ac − 2bc f tc f + (tcw + 2rc ) tc f ; Ac is area of the column section; rc is column root radius. The fire resistance check of rotation of the joint in fire may be determined by: θT ≤ 0.05
(31)
5. Critical temperature of the joints in fire Obviously, the load-bearing capacity of the joints is reduced with temperature elevation. The critical temperature of the joints is that at which the load-bearing capacity of the joints is not enough to support their action and the joints fail. The critical temperature of the joints can be obtained according to the previous fire resistance check formulas for various joint components. According to the required fire resistance duration of the joint, and temperature-time curve of fire, the maximum temperature of the bare joint can be obtained through Eq. (4). If the critical temperature of the joints is less than the maximum temperature of the joints caused by fire, the joints should be protected. The thickness of fire protection material is determined by requiring the maximum temperature of the joints protected be less than the critical temperature of the joints. 6. Experimental verification In order to validate the approach proposed in this paper for predicting the fire resistance of extended end-plate joints, two experimental studies are carried out on two full scale specimens of the joints made with H shaped steel with grade Q235 and size H 244 × 175 × 7 × 11 and H 175 × 125 × 6 × 9. The critical temperature and fire resistance of the specimens
were recorded in the experiment. The yield strength of bolt at normal temperature is 940 MPa and the diameter of the bolts is 20 mm. The depth of the end-plate is 12 mm for specimen 1 and 16 mm for specimen 2. The configuration and size of the joint specimens is shown in Figs. 2 and 3. For more detailed information about the experiment refer to another published paper [7]. The shearing force and moment applied on the specimens are 30 kN and 37.5 kN m respectively. The critical temperature of the specimens can be predicted by employing the approach presented above following the procedure below: Firstly, the critical temperature of the bolts in tension can be predicted by employing the Eqs. (8) and (9), similarly, the critical temperature of the bolts in shear can be obtained by Eqs. (10) and (11). The critical temperature of the bolts in combined tension and shear can be calculated by Eqs. (12) and (13). Secondly, the critical temperature of the end-plate and the column flange in flexure can be predicted by Eqs. (14)–(18) respectively. Thirdly, the critical temperature of the panel zone in shear can be calculated by Eq. (19). Fourthly, the rotationtemperature relationship of the joint can be plotted employing the Eq. (23), then the critical temperature of the joint rotation is determined by the rotation of the joint reaches 0.05 radium. Finally, the critical temperature of the joints is determined by finding the minimum value of the temperature of all the joint components. The rotation-temperature curve of joint in the experiment and the predicted result are plotted in Fig. 4. From Fig. 4, the critical temperature of rotation of the joints in fire can be obtained when the rotation reaches 0.05 radians. The results predicted and measured from experiment are listed in Table 1.
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Fig. 4. Recorded and predicted rotation of joint at elevated temperature of specimens.
7. Conclusion A practical approach is proposed for predicting the fire resistance and assessment of extended end-plate joints. Mechanical properties are introduced at elevated temperatures to predict the decrease of the yield strength and the elastic modulus of steel and bolt. The load bearing capacities of the joints can be predicted by analyzing the joint components, including high strength bolts, the end-plate, the flange of column and the panel zone. The maximum temperature of the joint with and without fire protection and the critical temperature of the joints can be obtained by the approach presented in this paper. By comparing the predicted results with experimental measurement, it is verified that the approach proposed can be employed for the evaluation the critical temperature of extended end-plate joint with an acceptable degree of accuracy.
(a) S-1.
References
(b) S-2. Fig. 5. Deformation of specimens.
The deformation of the two specimens after failure is shown in Fig. 5. It can be seen clearly that flexure deformation of the extended end-plate and the column flange has significantly taken place, and that shear deformation has occurred in the panel zone. A significant gap has appeared between the column flange and the end-plate around the top flange of the beam, especially for specimen 2.
[1] Al-Jabri KS, Lennon T, Burgess IW, Plank RJ. Behaviour of steel and composite beam-column joints in fire. Journal of Constructional Steel Research 1998;46(1–3):308–9. [2] Al-Jabri KS, Lennon T, Burgess IW, Plank RJ. The performance of frame joints in fire. ACTA Polytech 1999;39(5):65–75. [3] Kruppa J. Resistance on feu des assemblage par boulous. CTICM report. Document no. 1013-1, Centre Technique Industrial de la Construction Metallique. France: St. Remy Chevzuese; 1976 [English translation available entitled Fire resistance of joints with high strength bolts]. [4] The performance of beam/column/beam joints in the BS 5950: Part 8 fire test. Reports T/RS/1380/33/82D and T/RS/1380/34/82D, Rotherham: British Steel (Swindon labs); 1982. [5] Lawson RM. Behaviour of steel beam-to-column connections in fire. Structure Engineering 1990;68(14):263–71. [6] Leston-Jones LC. The influence of semi-rigid connections on the performance of steel framed structures in fire. Ph.D. thesis. University of Sheffield; 1997. [7] Wang W-Y, Li G-Q, Dong Y-L. Experimental study and springcomponent modelling of extended end-plate joints in fire. Journal of Constructional Steel Research 2007;63(8):1127–37. [8] Eurocode 3. Design of steel structures, Part 1.2: General rules structural fire design, prEN-1993-1-2. European Committee for Standardisation (CEN); 2003. [9] Chinese Technical code on fire safety of steel building structure. CECS, 2006.
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[10] Chinese code for design of steel structures. 2002. [11] Li G-Q, Jiang S-C, Yin Y-Z, Chen K, Li M-F. Experimental studies on the properties of constructional steel at elevated temperatures. Journal of Structural Engineering 2003;129(12):1717–21. [12] Zheng BX. Performance and design method study of light weight steel
joint of portal frame. Master’s degree thesis. Wuhan University of Technology; 2003. [13] Quan Jing. The relationship between moment and rotation of extended end-plate joint of Steel frame. Master’s Degree thesis. Tongji University; 2004.
A practical approach for fire resistance design of extended end-plate joints Wei-Yong Wang a,∗ , Guo-Qiang Li a,b , Yu-li Dong c a College of Civil Engineering, Tongji University, No. 1239 Siping Road, Shanghai, 200092, People’s Republic of China b State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University, No. 1239, Siping Road, Shanghai, 200092, People’s Republic of China c College of Civil Engineering, Harbin Institute of Technology, Harbin, 150091, People’s Republic of China
Received 29 March 2007; accepted 9 January 2008
Abstract Although beam-to-column joints are known to have a very significant effect on the behaviour of steel frames in the event of fire, no specific approach for evaluating the behaviour of extended end-plate joints in fire has been proposed. In this paper, on the basis of the current Chinese Code for Design of Steel Structures [Chinese code for design of steel structures. 2002] and Technical Code on Fire Safety of Steel Building Structures [Chinese Technical code on fire safety of steel building structure. CECS, 2006], analysis is presented on the load-bearing capacity of extended end-plate joints in fire, by taking the mechanical properties of steel at elevated temperature into account. A practical approach for fire-resistance calculation and assessment of the joints is proposed, based on the load-bearing capacity of the components of joints at elevated temperatures including the bolt, extended end-plate, column flange and panel zone. Employing the practical approach, the critical temperatures of two extended end-plate joints are predicted. By comparison with the results measured from the tests, the effectiveness of this practical approach is verified. c 2008 Elsevier Ltd. All rights reserved.
Keywords: Extended end-plate joint; Practical approach; Fire resistance; Column flange; Panel zone
1. Introduction Beam-to-column joints have been found to be of great significance in influencing the structural behaviour of frameworks at ambient and elevated temperatures. Observations from fullscale fire tests and from damage to steel frame structures due to real fires [1,2] confirm that joints have a considerable effect on the survival time of structural members in fire due to their ability to distribute forces. Fire is a disaster that frequently happens in buildings. Since steel structures are widely used in buildings and sensitive to fire, much research has focused on studying the influence of high temperature on the behaviour of steel structures. In recent years, considerable research work has been conducted to understand the performance of steel beam-tocolumn joints at ambient temperature at both experimental and analytical modelling levels. Experimental tests have been carried out on a wide variety of joints either in isolation or as part of complete steel-framed structures in order to understand their behaviour. A number of fire tests on steel joints ∗ Corresponding author. Tel.: +86 21 65985318; fax: +86 21 65983431.
E-mail address: [email protected] (W.-Y. Wang). c 2008 Elsevier Ltd. All rights reserved. 0143-974X/$ - see front matter doi:10.1016/j.jcsr.2008.01.008
were conducted by CTICM [3] with the primary purpose of investigating the performance of high strength bolts at elevated temperatures. In addition, tests to study the behaviour of beamto-column joints at elevated temperatures were carried out by British Steel [4], Lawson [5] and Leston-Jones [6]. An experiment study was performed on four full-scale extend endplate joints in fire and a spring-component modelling was presented to predict the rotation of the joints in fire by Wei-yong Wang et al. [7]. These tests provide useful data for theoretical study. However, up to now, there is little literature covering the fire resistance design of steel beam-to-column joints including EC3: Part1.2 [8] and Chinese Technical Code on Fire safety of Steel Building Structures [9]. This paper is mainly concerned with the fire resistance design of extended end-plate joints, commonly used in steel frames. A practical approach is proposed on fire resistance design of extended end-plate joints made with H-shaped steel, based on the current Chinese Code for Design of Steel Structures [10] and Technical Code on Fire Safety of Steel Building Structures [9]. The mechanical properties of steel for the joints and high-strength bolts at elevated temperatures are introduced. A joint is supposed to be divided into a number of basic components with known load capacities, such as the high strength bolt, column flange,
W.-Y. Wang et al. / Journal of Constructional Steel Research 64 (2008) 1456–1462
1457
column web and end-plate. By assembling the contributions of individual components which represent various parts of the joint as a set of elements, the entire critical temperature of the joint may be determined. The critical temperature of a joint is defined as the temperature at which the load bearing capacity of the joint is reduced and not enough to compensate the action of the loads applied on the joint. What is new in this paper is that a practical approach is presented to check and assess the extended end-plate joints in fire, which can be used for fireresistant design of extended end-plate joints. 2. Mechanical properties of steel at elevated temperatures Materials which are commonly used to fabricate steel beamto-column joints in China include structural steel of Q235 or Q345 for plate and hot-rolled H-shaped sections, and Grade 8.8 or 10.9 for high strength bolts with ultimate tensile strengths respectively over 800 and 1000 N/mm2 . When a steel extended end-plate joint is exposed to fire, the temperature of the joint will be increased to a high level. At elevated temperatures, the elastic modulus and yield strength of steel will be reduced. Although lots of recommendations may be found in the literature for various standard of steel, the following expressions are recommended for determining the reduction of the elastic modulus and yielding strength of steel, according to Chinese standard [9], at elevated temperatures. For steel plate and hot-rolled sections 7Ts − 4780 ET 20 ◦ C ≤ Ts ≤ 600 ◦ C = E 6Ts − 4760 (1) ET 1000 − Ts = 600 ◦ C ≤ Ts ≤ 1000 ◦ C E 6Ts − 2800 f yT = 1.0 20 ◦ C ≤ Ts ≤ 300 ◦ C f y f yT = 1.24 × 10−8 T 3 − 2.096 × 10−5 T 2 s s fy (2) −3 ◦ ◦ +9.228 × 10 T − 0.2168 300 C < T < 800 C s s f yT = 0.5 − Ts 800 ◦ C ≤ Ts ≤ 1000 ◦ C fy 2000 for steel bolts [11], the ultimate strength at elevated temperature is determined by f ubT = −2 × 10−6 × Tb2 + 7 × 10−5 × Tb + 1.0473 f ub 20 ◦ C ≤ Tb ≤ 700 ◦ C
(3)
where E is the elastic modulus of steel at ambient temperature; E T the elastic modulus of steel at a given temperature; Ts the temperature of steel in centigrade; f y the yield strength of steel at ambient temperature; f yT the yield strength of steel at a given temperature; f ub the ultimate strength of the bolt at ambient temperature; f ubT the ultimate strength of the bolt at a given temperature; and Tb is the temperature of the bolts. The decrease of the yield strength and elastic modulus of structural steel and the ultimate strength of high strength bolts with elevated temperatures is presented in Fig. 1.
Fig. 1. Yield strength and elastic modulus of structural steel and high strength bolts at elevated temperatures.
Fig. 2. Configuration of extend end-plate joint.
3. Approach for determining the temperature of the joints in fire If fire attacks a steel building, the steel members including the joints will be heated up. On the basis of thermal conductivity theory, the temperature of the joints may be determined. The temperature of the components consisting of an extended end plate joint may be different, when the joint is exposed to fire. The components mainly include the extended end-plate and the column zone at the joint (see Fig. 2). It is assumed that the temperature of the joints is approximatively equal to the average temperature of column and beam. The temperature of the column and beam exposed to fire Ts (t) can be obtained by [9]: Ts (t + 1t) =
B [Tg (t) − Ts (t)]1t + Ts (t) cs ρs
(4)
where Tg (t) is the temperature of the fire varying with time; cs is specific heat of steel; ρs is density of steel; 1t is the time increment; and B is the general heat transfer coefficient. The general heat transfer coefficient, B, can be obtained by the following equation: for the case without fire protection B = (αc + αr )
F V
(5)
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and for the case with non-intumescent fire protection 1
B= 1+
ci ρi di Fi 2cs ρs V
λi Fi di V
The shear capacity of high strength bolt at elevated temperatures can be predicted by: (6)
where αc is the convection heat transfer coefficient; αr is the emission heat transfer coefficient and determined by " # Tg + 273 4 Ts + 273 4 2.041 αr = − (7) Tg − Ts 100 100 F is the area per length of column or beam exposed to fire; V is the volume per length of column or beam; ci is the specific heat of fire protection material; ρi is the density of fire protection material; di is the thickness of fire protection material; λi is the equivalent heat conductivity of fire protection; Fi is the interior area pre length of fire protection of column or beam. 4. Check of fire resistance of extended end-plate joints Similar to the load capacity check at ambient temperature, the fire resistance of an extended end-plate joint at elevated temperatures due to fire can be checked in three aspects, including fire resistance of high strength bolts in tension and shear; fire resistance of extended end-plate and column flange in flexure; and fire resistance of panel zone. The limit state of fire resistance of the joint is defined for each of the following cases; (a) (b) (c) (d) (e) (f)
High strength bolt yields in tension; High strength bolt yields in shear; End-plate yields in flexure; Column flange yields in flexure; Panel zone yielding in shear; The rotation of the joint reaches 0.05 radians and increases rapidly.
4.1. High strength bolts of the joint in fire It is assumed that the high strength bolt rotates around the shape center of all the bolts for the joint. Load capacity of the bolt in tension and shear is considered at ambient temperature. Similarly, at elevated temperatures, the tension and shear bearing capacity of one bolt can be obtained by the consideration of influence of temperature on the mechanical properties of the bolts. The capacity of high strength bolt at elevated temperatures in tension can be predicted by the following expression: πd02 × 0.46 f ubT (8) 4 where d0 is the effective diameter of the bolt shaft. The capacity of the bolt at elevated temperatures can then be checked by: NtbT =
M yi Ntbi = P 2 ≤ NtbT yi
πd 2 × 0.3 f ubT (10) 4 where d is diameter of bolt shaft. The capacity of the groupware of the bolts at elevated temperatures in shear can be checked by: X b Q≤ NvT (11) b NvT =
where Q is shear force of the joint. A check of the bolt subjected to a combined tension and shear at elevated temperature can be made with the following expression: v ! !2 u u Nb 2 Ntbi t v + ≤1 (12) b NvT NtbT Q ≤ d min(tep , tc f ) × 0.92 f yT (13) n where n is the number of bolts; tep is the thickness of the endplate; tc f is the thickness of the column flange. Nvb =
4.2. Extended end-plate of the joints in fire The stiffeners in the column web can increase the fire resistance of bolts significantly [7]. It is assumed that the joint is stiffened to avoid the bulking of the column web when considering the fire resistance design. Based on the ultimate moment capacity of the extended endplate of the joint at normal temperature in literature [12], the ultimate moment capacity of the extended end-plate at elevated temperatures can be expressed as " # 1.2 h b − tb f 2bep 2 + (h b − tb f ) (14) MuepT = f yT tep dc − tb f gc − tbw where the symbols of dc and gc can be seen from Fig. 2; h b is the depth of the beam; tb f is the thickness of the beam flange; tbw is the thickness of the beam web; and bep is the width of the end-plate. The fire resistance check of the extended end-plate can then be made with: M ≤ MuepT .
(15)
4.3. Column flange of the joint in fire The ultimate moment capacity of the column flange of the joint at elevated temperature can be obtained by the following two expressions [7]:
(9)
Muc f T 1 =
where M is moment of the joint; yi is distance from the bolt to shape center of bolts.
Muc f T 2 =
(1 + η)be f f c f tc2f (h b − tb f ) f yT 2m c (γ be f f c f tc2f f yT + 3πd02 n c f ybT )(h b − tb f ) 3(m c + n c )
(16) (17)
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where, η = 1 − bdeph , be f f c f = min{4π m c , 2πm c + dc , 8m c + 2.5n c , 4m c + 1.25n c + dc }; γ is a magnifying coefficient with steel strain hardening under consideration; m c is the distance from the center of the bolt hole to the column web; n c is the distance from the center of the bolt hole to the nearest edge of column flange. The fire resistance check of the column flange at elevated temperature can be found by M ≤ min(Muc f T 1 , Muc f T 2 ).
(18)
4.4. Panel zone of the joint in fire The fire resistance check of the panel zone of the joint in fire can be found by τ=
M ≤ 0.77 f yT Vp
(19)
where V p = h b h c tcw ; h c is the depth of the column; tcw is the thickness of the column web.
of the spring simulating the extended end-plate and the column flange at elevated temperature may be determined by [7]: K epT =
48E T h i 3 Z ep 1 − q 3aep − 4aep
(24)
Kc f T =
48E T i h 1 − q 3ac f − 4ac3f
(25)
Zc f
where m ep is the distance from the center of the bolt hole in the upside to the upper surface of beam flange; n ep is distance from the center of the bolt hole in the upside to the upper edge of end-plate; lc f = 2(m c + n c );
aep1 =
4.5. Rotation of the joints in fire The rotation of the joints in fire can be predicted by a component model, considering any steel beam-to-column joint as a set of individual components. A beam-to-column joint using the extended end-plate connection can be divided into four major zones (i.e. flexure, tension, shear and compression zone). Each zone of the joint can be further divided into a number of components, each of which is simply a nonlinear spring, possessing its own strength and stiffness in flexure, tension, compression or shear, and will be reduced with elevation of the temperatures. The global rotational stiffness of the joint K I T can be determined for any moment at any given temperature based on the assembled stiffness of all components as KIT =
(h b − tb f )2 1 Kc f T
+
1 K epT
+
1
.
(20)
K cwvT
With the spring model, the ultimate moment of the joint can be estimated using the following expression: M pT = F pT h b − tb f (21) F pT = min Fu,bT , Fu,epT , Fu,c f T , Fu,cwvT . (22) After obtaining the stiffness and ultimate load of each component, the moment-rotation relation may be obtained from the following equation [7]: −(K I T − K pT + CθT )θT M = M pT 1 − exp M pT + K pT θT
(23)
where, K pT can be expressed as 0.02 K I T , Quan Jing [13] recommended a value of C equal to zero. From classical simple beam-deflection theory, with the properties of steel at elevated temperature, the initial stiffness
n ep ; lep
aep =
Z ep = Ic f =
ac f 1 =
3 aep aep − ; 8 6 3 lep
Iep
;
lep = 2(m ep + n ep );
q=
ac3f ac f − ; 8 6 2 aep
aep2 =
2
ac f 2 = −
3 2aep
3
Z c f ac f 2 + Z ep ac f 1 +
1 be f f c f tc3f ; 12
Iep =
lb0 Ab0
nc ; lc f
ac2f
2ac3f
2
−
Zc f =
;
Z c f aep1 + Z ep aep2
ac f =
3 lc3f Ic f
; ;
;
1 3 bep tep . 12
When calculating the shear stiffness of the column web at elevated temperatures, the column web can be seen as a short column subjected to a shear force which is transferred from the beam flange. For a short column, the deformation caused by moment is far less than shear force, so the shear stiffness of the column web at elevated temperature may be expressed as [7]: K cwvT =
E T h c tcw 2(h b − tb f )(1 + µ)
(26)
where µ is Poisson’s ratio for steel. The ultimate load capacity of the high strength bolt at elevated temperature can be determined with: Fu,bT =
4 f ubT Abo γb
(27)
πd 2
where Abo = 4 0 . Considering the reduced failure strength with elevated temperatures, according to Eqs. (14) and (21), the ultimate load capacity of the extended end-plate may be evaluated using the following expression: " # 1.2 h b − tb f 2bep 2 FuepT = f yT tep + . (28) dc − tb f gc − tbw The ultimate load capacity of the column flange may be given as [7]: Fu,c f T = min{Fu,c f 1T , Fu,c f 2T }
(29)
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Table 1 Predicted and measured results of specimens Specimen Predicted temperature of the components (◦ C)
S-1 S-2
High strength bolts
Extended end-plate
Column flange
Panel zone
Joint rotation
572 572
513 624
551 551
545 569
550 555
Predicted critical temperature of joint (◦ C)
Predicted fire resistance of the joints (min)
Measured critical temperature of joint (◦ C)
Measured fire resistance of the joints (min)
513 551
20 21.5
545 569
24 22
where Fu,c f 1T = Fu,c f 2T =
(1 + η) be f f c f t 2f f yT
, 2m c γ be f f c f tc2f f yT + 12BuT n c 3 (m c + n c )
,
BuT = πdo2 f ubT /4. The ultimate shear capacity of the column web may be written as f yT Fu,cwvT = √ Avc 3
(30) Fig. 3. Details of specimens.
where Avc = Ac − 2bc f tc f + (tcw + 2rc ) tc f ; Ac is area of the column section; rc is column root radius. The fire resistance check of rotation of the joint in fire may be determined by: θT ≤ 0.05
(31)
5. Critical temperature of the joints in fire Obviously, the load-bearing capacity of the joints is reduced with temperature elevation. The critical temperature of the joints is that at which the load-bearing capacity of the joints is not enough to support their action and the joints fail. The critical temperature of the joints can be obtained according to the previous fire resistance check formulas for various joint components. According to the required fire resistance duration of the joint, and temperature-time curve of fire, the maximum temperature of the bare joint can be obtained through Eq. (4). If the critical temperature of the joints is less than the maximum temperature of the joints caused by fire, the joints should be protected. The thickness of fire protection material is determined by requiring the maximum temperature of the joints protected be less than the critical temperature of the joints. 6. Experimental verification In order to validate the approach proposed in this paper for predicting the fire resistance of extended end-plate joints, two experimental studies are carried out on two full scale specimens of the joints made with H shaped steel with grade Q235 and size H 244 × 175 × 7 × 11 and H 175 × 125 × 6 × 9. The critical temperature and fire resistance of the specimens
were recorded in the experiment. The yield strength of bolt at normal temperature is 940 MPa and the diameter of the bolts is 20 mm. The depth of the end-plate is 12 mm for specimen 1 and 16 mm for specimen 2. The configuration and size of the joint specimens is shown in Figs. 2 and 3. For more detailed information about the experiment refer to another published paper [7]. The shearing force and moment applied on the specimens are 30 kN and 37.5 kN m respectively. The critical temperature of the specimens can be predicted by employing the approach presented above following the procedure below: Firstly, the critical temperature of the bolts in tension can be predicted by employing the Eqs. (8) and (9), similarly, the critical temperature of the bolts in shear can be obtained by Eqs. (10) and (11). The critical temperature of the bolts in combined tension and shear can be calculated by Eqs. (12) and (13). Secondly, the critical temperature of the end-plate and the column flange in flexure can be predicted by Eqs. (14)–(18) respectively. Thirdly, the critical temperature of the panel zone in shear can be calculated by Eq. (19). Fourthly, the rotationtemperature relationship of the joint can be plotted employing the Eq. (23), then the critical temperature of the joint rotation is determined by the rotation of the joint reaches 0.05 radium. Finally, the critical temperature of the joints is determined by finding the minimum value of the temperature of all the joint components. The rotation-temperature curve of joint in the experiment and the predicted result are plotted in Fig. 4. From Fig. 4, the critical temperature of rotation of the joints in fire can be obtained when the rotation reaches 0.05 radians. The results predicted and measured from experiment are listed in Table 1.
W.-Y. Wang et al. / Journal of Constructional Steel Research 64 (2008) 1456–1462
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Fig. 4. Recorded and predicted rotation of joint at elevated temperature of specimens.
7. Conclusion A practical approach is proposed for predicting the fire resistance and assessment of extended end-plate joints. Mechanical properties are introduced at elevated temperatures to predict the decrease of the yield strength and the elastic modulus of steel and bolt. The load bearing capacities of the joints can be predicted by analyzing the joint components, including high strength bolts, the end-plate, the flange of column and the panel zone. The maximum temperature of the joint with and without fire protection and the critical temperature of the joints can be obtained by the approach presented in this paper. By comparing the predicted results with experimental measurement, it is verified that the approach proposed can be employed for the evaluation the critical temperature of extended end-plate joint with an acceptable degree of accuracy.
(a) S-1.
References
(b) S-2. Fig. 5. Deformation of specimens.
The deformation of the two specimens after failure is shown in Fig. 5. It can be seen clearly that flexure deformation of the extended end-plate and the column flange has significantly taken place, and that shear deformation has occurred in the panel zone. A significant gap has appeared between the column flange and the end-plate around the top flange of the beam, especially for specimen 2.
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[10] Chinese code for design of steel structures. 2002. [11] Li G-Q, Jiang S-C, Yin Y-Z, Chen K, Li M-F. Experimental studies on the properties of constructional steel at elevated temperatures. Journal of Structural Engineering 2003;129(12):1717–21. [12] Zheng BX. Performance and design method study of light weight steel
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