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Experimental investigation on flush end-plate bolted composite connection in fire
Journal of Constructional Steel Research 76 (2012) 121–132
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Journal of Constructional Steel Research
Experimental investigation on flush end-plate bolted composite connection in fire Jiao-Ting Li b,⁎, Guo-Qiang Li a, b, Guo-Biao Lou a, b, Ling-zhu Chen b a b
State Key Laboratory for Disaster Reduction in Civil Engineering, Shanghai, 200092, PR China College of Civil Engineering, Tongji University, Shanghai, 200092, PR China
a r t i c l e
i n f o
Article history: Received 18 March 2011 Accepted 23 March 2012 Available online 1 May 2012 Keywords: Flush end-plate Fire tests Composite joint Axial force Fire-resistant capability Catenary action Non-linear restraint Design method
a b s t r a c t Three tests at elevated temperatures were carried out to invest the fire-resistant capacity of flush end-plate composite joints. The axial force was considered in two of the three tests simulating fire conditions to investigate its effect on the connection's load carrying ability (one with fire protection and the other without fire protection). Summaries have been given on the failure mechanisms, temperature distribution, loading carrying capacity of the composite joint and the mutual influence between joints and beams at elevated temperatures. Date shows that the failure mode of the flush end-plate joint without stiffener is usually dominated with the yielding of the bottom flange of steel beam near the supports, elements of the composite connection have different rate of temperature increase, and the axial force from restrained composite beam influences the rotational stiffness and moment capacity of joints. This paper also theoretically presents how the interaction of joints and beam developed in fire conditions. A practical simplified method is proposed to calculate the non-linear variable characteristics of composite connection in the analysis of catenary action of beams at elevated temperatures. The proposed method is verified by the experimental investigations. This study offers a feasibility of fire-resisting design and evaluation for the composite beam with semi-rigid connections in the complete temperature range. © 2012 Elsevier Ltd. All rights reserved.
1. Introduction Semi-rigid connections used in steel frames and steel portal frames are mainly bolted and have been proved to be economical, especially the moment capacity of end-plate connections (either flush or extended) could be as high as that of beams. The three key indications of the performance for semi-rigid composite connections are moment resistance, Mu, rotational stiffness, K0, and rotation capacity, θ, as shown in Fig. 1. Fire tests on composite connections at elevated temperatures were conducted in early studies to obtain the temperature–rotation relationship. R.M. Lawon [1] conducted eight fire tests on column-to-beam joints in the types of extended end-plate joints (rigid), flush end-plate joints (semi-rigid) and partial depth end-plate joints (flexible). It was observed that the connections designed as pinned were able to take a certain amount of moment at large deflections in fire. However in frames, where connections are designed as rigid or moment resistible under vertical load in normal conditions, the redistribution of moment from mid-span to the support zone does not occur to the same extent in fire conditions as in normal conditions. One test at ambient temperature and five others at elevated temperatures in the style of end-plate connection were conducted by L.C. Lestones [2]. And temperature–rotation curves under different load levels of moment were derived from test results. Due to
⁎ Corresponding author at: College of Civil Engineering, Tongji University, 1239 Siping Road, Shanghai 200092, PR China. Tel.: + 86 21 6598 5318. E-mail address: [email protected] (J.-T. Li). 0143-974X/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.jcsr.2012.03.022
the usage of thermal insulating material to simulate the concrete slab above the steel beam, the contribution of the reinforcement to the ultimate moment resistance and stiffness of the joint were ignored. G.B. Lou [3] conducted a series of full scale tests to investigate the temperature distribution, structural behavior and failure mechanisms of bare-steel connections. Two configurations of high-strength bolted extended end-plate connections, including beam-to-column connection and beam-to-beam splice connection, were considered. For each configuration three tests were conducted, with one at ambient temperature throughout the entire moment-rotation range, and two transient state tests at different load levels. W.Y. Wang [4] carried out fire tests on full-scale specimens made with H-shaped steel. The failure characteristics and modes of the extended end-plate joint specimens in fire were obtained. Some experiments on elements of the connections under fire were conducted by researchers to get failure characteristics of elements at high temperatures. However, these existing joint experiments haven't considered the influence of the axial force caused by beam expansion under fire. But most of beams in multi-story structures would certainly develop axial force in fire because of their expansion and circumjacent restraints [5], and the axial force would reduce the moment capacity and rotational stiffness of connection considerably and in return these two factors would affect the axial force development in beams. So, experiments in this paper were conducted to investigate the effect of this axial force on the connection's load carrying ability and the beam's deflection. A general method to analyze the behavior of restrained composite beams at elevated temperatures was presented, considering the catenary
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M Mu 0.85Mu K0
Fig. 1. Moment-rotation relationship of semi-rigid connection.
action [6,7] and nonlinear variation of restraints due to the axial force in beams and high temperatures. 2. Experimental investigation 2.1. Objectives of fire tests In total, three fire tests were carried out in the Structure Fire Resistance Laboratory at Tongji University. Test 1, illustrated in Fig. 2 was conducted on a composite beam specimen with end-plated connection without axial restraint. Test 2 and test 3 were conducted on composite beam specimens with end-plated semi-rigid beam-to-column connection as shown in Fig. 3. The test series are primarily designed to investigate the behavior of the composite semi-rigid beam-to-column joints and the restrained composite beams exposed to fire with their mutual interaction, and indirectly validate the moment-rotation relationship of the composite semi-rigid joints with variation of the temperature and axial force in beams. Therefore, the tests were carried out on a typical type of connection subjected to constant hogging moment, constant shear force and variable axial force which would exist and develop in a real structure under fire condition. 2.2. Specimens and test set-up The test set-up of Test 1 is shown in Fig. 2, and that of Test 2 and Test 3 is shown in Fig. 3. In Test 2 and Test 3, the cruciform specimen stretching over the test furnace was axial restrained by the restraint frame which helped to develop axial force at elevated temperatures. Loading jacks, which were fixed to the distribution beam with the
100 200 200
2102
Jack
2.3. Loading Load of the three fire tests were applied on the beams at a distance of 2.498 m from the column centerline outside the furnace to produce
200 114 114 200
Q 235 B H300×300×12×14
12
dimension of H300 mm ×300 mm × 12 mm ×14 mm, reacted against the restraint frame to form a downward equilibrant force to the specimen. The specimen was pinned to the columns of restraint frame so as to transfer shear force only and produce a definite moment to the composite connection. The column base of the restraint frame could freely move in the horizontal direction. Each specimen consisted of two H-shaped steel beams (H300 mm × 150 mm × 8 mm × 12 mm) which were symmetrically connected to the flange of a single steel column (H240 mm × 240 mm × 12 mm × 14 mm) and covered by a composite slab with a trapezoidal deck. Each beam was connected to the column with eight bolts (M20) in 21.5 mm diameter clearance holes. The thickness of the end-plate is 14 mm. The total thickness of the slab was 140 mm, and the effective thickness was 70 mm. The concrete was mixed on the spot, and three coupons were casted at the same time to obtain the strength of the concrete. The cubic compressive strength of concrete after 28 days curing period was an average 28.9 N/mm 2. The upper-layer reinforcing mesh of the slab was made by smooth reinforcement bar with the grid size of 120 mm × 120 mm and lower-layer reinforcing mesh was made by smooth reinforcement bar with the grid size of 200 mm × 200 mm. Rebar with the diameter of 10 mm was placed in the upper layer in the longitudinal direction running through the slab and gave a 1% reinforcement ratio of the concrete slab. Rebar with the diameter of 10 mm was used as the distributional rebar in the upper layer at the space of 120 mm within the span of the beam and 40 mm near the column. In the lower layer, the diameters of rebar in the two directions were both 6 mm. Four headed studs with a diameter of 19 mm and 100 mm in height were welded to the steel beam at each trough of the deck to ensure the composite beam was complete shear connection. The overall dimensions of specimens are shown in Figs. 2 and 3 and the strength of the materials is listed in Table 1. The fire protection material was vermiculite-cement spray. Only the connection and beams of test 2 were protected. The arrangement of displacement gauges to measure the rotation and deflection of connections and beams in tests were similar, as shown in Fig. 4. Additionally, horizontal displacement of the column base of the restraint frame was measured to calculate the axial force caused by the expansion of composite beams in fire. Thermocouples were located at appropriate locations around the composite connection and along the beams as illustrated in Fig. 5.
2102
200 200 100
12 12
12
8 M 20 Gr.10.9
Jack
C 30
8
658
Jack
Steel column Q235B H240×240×12×14
Steel beam Q 235 B H 300×150 ×8×12 Endplate Q 235B 14 ×150 ×300 14 2246
8 M 20 Gr. 8.8
Ø6@120
Ø10@120 Jack
Steel beam Q 235B H 300×150 ×8×12 14
8
2246
658 150 150
150 150
Fig. 2. Specimen and test set-up for Test 1.
J.-T. Li et al. / Journal of Constructional Steel Research 76 (2012) 121–132
100 200 200
2102
200 114 114 200
123
2102
200 200 100
300
Q 235B H300×300×12×14
730
Jack
Steel column Q235B H240×240×12×14
8M20 Gr.10.9
Jack
Restrain frame beam Q235B 2 [28a Restrain frame column Q235B H500×400×12×20
1
3426
Restrain frame column Q235B H500×400×12×20 2400
Restrain frame beam Q235B 2 [28a Concrete slab
50
8M20 Gr.10.9
Sheer stud
Steel beam Q235B H300×150×8×12 Flush endplate 14×150×300 2332
Steel decking
Reinforcement 50
Steel beam Q235B H300×150×8×12 8M20 Gr.8.8
Fig. 3. Specimen and test set-up for Test 2 and Test 3.
a constant moment for connections in fire. Moment and shear forces applied on the composite connections were a little bit lower than the values in practice to ensure a longer observation in fire. Joints of the three fire tests were loaded with a moment of 0.429 times of the ultimate moment at ambient temperature. Moment and shear forces for tests are summarized in Table 2. The specimens were heated uniformly with a circular natural gas flow pattern and the temperature of the air in furnace was controlled in accordance with the standard ISO 834 temperature–time curve.
2.4. Results It was observed that the behavior of the connections followed a similar pattern. With significant local buckling of the bottom flange of steel beams, the load resistance began to decrease rapidly in Test 1, while in Test 2 and Test 3 the composite beams changed from bearing an axial compressive force into a tensile force at large deflection. Failure modes are shown in Fig. 6. Failure of connecting bolts or reinforcement was not observed, despite considerable large deflection developed in the mid-pan of beams. The end-plate, column flange, bolts, reinforcement and shear studs were observed with very little deformation. All the tests were finally terminated due to the limited measurement of jacks.
2.5. Temperature distribution Temperature development of beams, joints and reinforcement in the three fire tests with time was shown in Figs. 7–10. It could be summarized as follows: 1. It was apparent that there was a significant difference between the temperature at the top flange of the beam supporting concrete floors and that at bottom flange. 2. Temperatures of bolts BP3 and BP4 were also greatly lower than that of the bottom flange. The round decreasing sequence of temperature of the joints for the three fire tests could be concluded as BF8 → BW9 → BF6 → CW14 → BW11 → BF5 → CW7 → CW12 → BP4 → BP3 → CW10. 3. The lowest temperature was at the column web, at the point the most adjacent to the concrete floor. That's because a portion of heat were conducted to the outer air by smoke or to the upper column web outside the furnace. The reduction was about 200 °C to 300 °C when the controlling temperature of the bottom flange of beams was reached. 4. Reinforcement in the upper layer of concrete was significantly cooler due to the heat shielding of the slab. There was a phase of temperature suspending when the reinforcement temperature reached 100 °C, because the water vapor took out most heats from the cracks of concrete slab. 2.6. Deflection, axial force and connection moment of fire tests
Table 1 Measured strength of components in tests. Component
Dimension(mm)
Material
Yield strength (N/mm2)
Ultimate tensile strength(N/mm2)
Bolts Shear studs End-plate Steel beam Steel colum
M20 19 × 100 300 × 150 × 14 H300 × 150 × 8 × 12 H240 × 240 × 12 × 14
8.8 – Q235B Q235B Q235B
830 290 250 285 250
900 450 436.7 433.3 436.7
Some of the readings from displacement gauges did not give reliable data for the tests because of interim or permanent failure at the contact point on the surface or of the connecting cables. Beams and joints deflection versus the temperature of the beam bottom flange curves of the three tests are shown in Figs. 11–13. Figs. 14–16 illustrate the comparison of deflection, moment and axial force between fire tests. All the figures could be summarized as follows: 1. In Test 2 and Test 3 it was observed that the axial force, moment of composite joint and deflection showed a great jump when the
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D3-8
D3-3
D3-9
D3-2
D3-7
D-2 D-3 D-4 D-5 D-6
D3-6
D3-5
D3-4
D3-10
D3-1
Fig. 4. Displacement gauges arrangement for Test 2 and Test 3.
high temperature in the fire, the moment of connection, axial force and deflection did not show great differences between Test 2 and Test 3. 4. Appearance of moment peak point was always a little bit later than the axial force peak point, in other words, the maximum moment of the composite connection would reach at the decreasing rang of axial compressive force. After the axial compressive force reached its peak point, deflection at the middle of the beam rapidly increased, the rate of deflectionδvincrement was larger than that of axial force reduction. Therefore the momentMewould necessarily begin to increase to keep the balance of Eq. (1). After that when
temperature approached the range of 500 °C–650 °C, whether the beams were fire protected or not. This indicated that the material strength degradation at the critical temperature range at the bottom flange of beams in connection region was the key parameter in controlling the behavior of the whole structure at elevated temperatures. 2. In Test 2, greater axial force was developed due to a longer fire experience with the fire protection, and concrete slab expanded with steel beam more sufficiently to generate more thermal expansion. 3. Although beams in Test 3 without fire protection developed catenary action earlier than beams in Test 2 because of an earlier
RE1(2)
CO1(2)
CW10 BP3 BP4
BF5
BW6
BW11
BW9
BF13
BF8
h bf /4
CW12
h bw /2
CW7
CW14
B3-1
B3-2
B3-15
Fig. 5. Thermocouples arrangement of composite connection.
B3-16
J.-T. Li et al. / Journal of Constructional Steel Research 76 (2012) 121–132 Table. 2 Summaries of fire tests. Fire Loading protection manner
Test 1 No Test 2 Yes Test 3 No
Test1 average temperature of furnace Test2 average temperature of furnace Test3 average temperature of furnace ISO834
1200 Force at each Moment Shear(kN) Ratio of test jack (kN) (kN·m) moment
Self-balance 51.3 loading Self-balance 53.89 loading Self-balance 53.89 loading
100.5
40.22
0.43
105.5
44.7
0.45
105.5
44.7
0.45
Test1 average temperature of joint Test2 average temperature of joint Test3 average temperature of joint
1000 800
T / oC
Test no.
125
600 400 200
the deflectionδventered the smooth phase of increase, the rate of deflection increment dropped, and the axial force changed into a tensile force and increased. So the moment of the composite connection tended to decline. Me þ F T δv ¼ VL=2
ð1Þ
0
0
20
40
60
80
100
120
140
160
t / min Fig. 7. Average temperature of inside furnace and joint for the three fire tests.
a) Test 1
b) Test 2
c) Test 3
Fig. 6. Failure of specimens.
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a) Temperature distribution of joint.
a) Temperature distribution of joint. 900 800
CW14
700
BF13
500
CW7
BF-6 CW-10
800
400
CW12
T/ oC
T / oC
BF-5 BW-9 CW-14
1000
BF6
BP4
300
400
BF5
200
BP3
100
CW10
0
5
10
15
20
25
30
35
40
45
600
200 50
0
t / min
0
20
40
60
80
100
120
140
160
180
t / min
b) Temperature distribution of beam
b) Temperature distribution of beam and
and reinforcement.
reinforcement.
900 800
1,000
700
900 800
600 Average temperature of furnace B-2 B-15 Average temperature of joint CO1 RE1
500 400 300 200
700 600
T/ oC
T / oC
BP-4 BF-8 CW-12
BW11
600
0
BP-3 CW-7 BW-11
1200
BF8
500 400
100
300
BP-3
BP-4
BF-5
BF-6
0
200
BF-8
BW-9
CW-10
BW-11
100
CW-12
CW-14
0
5
10
15
20
25
30
35
40
45
50
t / min
0
Fig. 8. Temperature distribution of Test 1.
0
20
40
60
80
100
t / min Fig. 9. Temperature distribution of Test 2.
where Me is the moment of the connection, FT is the axial force, defined as negative if the beam was in compression, δv is the deflection at mid-span of the beam, V is the shear force at the end of the beam. 5. The end-plate semi-rigid connection has good ductility which is produced by the plastic bending deformation of the end-plate and the good ductility helps the beam develop the catenary action. So the application of semi-rigid connection could improve the bearing capacity of the beam. 3. Modeling of experiments 3.1. Temperature distribution [8] The connection is composed of different elements, including steel columns, steel beams, bolts, end-plates and a concrete slab. Because different elements had different rate of temperature increase, the temperature distribution was non-uniform through the connection. The simplified method to determine the temperature of different parts of the connection is listed as follows: 1. The average temperature of the column part below the connection region, which was calculated according to the recommendations for the sections exposed to fire in four sides in the EC3: Part 1.2, could be taken as the average temperature of the column part in the connection region for the composite connection with trapezoidal deck, while the temperature of the column part with the first row of bolts should be revised according to Eq. (2) for the
composite connection with solid slab because of the influence of the concrete slab.
T
′
c;bolt1
¼
3T c;bolt1 þ T c;slab;0:02 4
ð2Þ
Where Tc,' bolt1 is the revised temperature of the column part with the first row of bolts; Tc, bolt1 is the temperature of the column part calculated according to the recommendations for the sections exposed to fire in four sides in the EC3: Part 1.2; Tc, slab, 0.02 is the temperature of the concrete 20 mm above the bottom of the slab. 2. The temperature of the bottom flange and web of the beam could be calculated according to the recommendations for the sections exposed to fire in four sides in the EC3: Part 1.2, while the temperature of the top flange of the beam could be calculated according to the recommendations for the sections exposed to fire in three sides in the EC3: Part 1.2. 3. Due to the influence of the steel beam and concrete slab, the temperature of the end-plate should be revised according to Eq. (3). T
′
ep
¼
2T ep þ ηT b 2þη
ð3Þ
Where T′ep is the revised temperature of the end-plate; Tep,Tb is the temperature of the end-plate and steel beam calculated according
J.-T. Li et al. / Journal of Constructional Steel Research 76 (2012) 121–132
a) Temperature distribution of joint.
127
a) Development of joint deflection with the temperature in the bottom flange of the beam.
1,000 900 800
T / oC
700 600 500 400 300
BP-3
BP-4
BF-5
BF-6
200
BF-8
BW-9
CW-10
BW-11
100
CW-12
CW-14
0
0
20
40
60
80
100
t / min
b) Temperature distribution of reinforcement.
b) Development of beam deflection with the temperature
450
in the bottom flange of the beam.
CO1
400
CO2
350
RE2
T / oC
300 250 200 150 100 50 0
0
20
40
60
80
100
t / min Fig. 10. Temperature distribution of Test 3. Fig. 11. Deformation of the joint and beam in Test 1.
to the recommendations for the sections exposed to fire in four sides in the EC3: Part 1.2 respectively; η is the coefficient, which could be taken as 1.5 deduced from the test result. 4. The temperature of the concrete at the location of the reinforcement could be taken as the temperature of the reinforcement. The temperature of the concrete in the solid slab could be obtained according to Table 3, while that in the composite slab with trapezoidal deck could be calculated by Eq. (4). In addition, the temperature of the concrete located in the concave if the slab should be taken as the reinforcement temperature. "
2 1 t t exp 0:05 þ 0:135 −0:005 −d 8 20 20 2 # t t : : 0:007 þ 0:0145 −0:0005 20 20
Tc ¼ T0 þ
ð4Þ
6 expð−w2 =w4 Þ−1 d × 1þ 10H
Where Tc is the concrete temperature; T0 is the initial temperature; t is the time; d is the distance above the slab bottom; ω2,ω4 is the width of the top and bottom of the trough respectively; H is the total height of the slab.
3.2. Equilibrium equation Fig. 17 shows the composite beams' loading mechanism and equilibrium of specimens in Test 2 and Test 3. Beams were symmetrically loaded. The axial restraint stiffness of the end axial restraint, Ka, was assumed to be a constant due to the temperature of the restrained frame keeps at ambient temperature. And Ka was taken as 83.4 KN/mm, calculated referring to Ref. [9]. FT was the axial force developed in the composite beam. Me was the moment of the specimen at the middle span. The equilibrium equation is: Me þ F T δv ¼ VL=2
ð5Þ
Deflection δv at the middle span could be expressed in two parts: δv ¼ δm þ δT
ð6Þ
where δm is the maximum mechanical deflection at the middle span of the beam due to the load and δT is the maximum thermal bowing deflection under certain temperature distribution of the composite beam. The shear force V is previously defined in the test. Parameters in Eq. (5) will be discussed below.
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a) Development of joint deflection with the temperature
a) Development of joint deflection with the temperature
in the bottom flange of the beam.
in the bottom flange of the beam.
b) Development of beam deflection with the temperature
b) Development of joint deflection with the temperature
in the bottom flange of the beam.
in the bottom flange of the beam.
Fig. 12. Deformation of the joint and beam in Test 2.
Fig. 13. Deformation of the joint and beam in Test 3.
steel at high temperature and αcT is that of concrete. hc is the height of concrete slab and hs is the height of steel beam. Then:
3.3. Deflection δv According to Refs. [7–9], the total composite beam deflection profile could be described as z(x) = zm(x) + zT(x), zm(x) is mechanical deflection profile and zT(x) is the thermal bowing deflection profile. Thus, for the mid-point loaded beam with axial restraints at ends but no rotational restraints, zm(x) and zT(x) could be expressed as below: 8 2δ > < mx L zm ¼ > : 2δm ðL−xÞ L
0 ≤ x ≤ L=2 L=2 ≤ x ≤ L
2 zT ðxÞ ¼ α d ðα sT T b –α cT T t Þ x –Lx =ðhc þ hs Þ
δv ¼ δm þ δT
¼ δm –α d ðα sT T b –α cT T t Þ L2 = 4 =ðhc þ hs Þ
ð7Þ
ð8Þ
In which αd is equal to 1 when the beam is simply supported, otherwise it is 0 when the beam is supported with full rotational restraints at the ends. αsT is the coefficient of thermal expansion of
Fig. 14. Deflection comparison of the three fire tests.
ð9Þ
J.-T. Li et al. / Journal of Constructional Steel Research 76 (2012) 121–132
129
Table 3 Temperature of concrete at the solid slab (°C). d(mm) 90 min
Normal concrete Light concrete
10
20
30
40
50
790 720
650 580
540 460
430 360
370 280
where K is the synthesized axial stiffness of composite beams with end restraints: 1 2 1 ¼ þ K K a K bT
ð13Þ
The axial stiffness KbT of composite beams is defined as: Fig. 15. Moment comparison between Test 2 and Test 3.
3.4. Axial force FT
K bT ¼
EsT As þ EcT Ac when the beam is in compression L
ð14Þ
K bT ¼
EsT As þ EreT Are when beam is in tension L
ð15Þ
Axial force FT is determined by the shortening of the composite beam due to lateral deflection δhm and thermal expansion δhT. δhm could be calculated from the composite beam deflection profile z(x) at certain temperature distribution and load. δhT could be obtained according to the basic thermodynamics formula Δl = αTL. So, expression of the total change of beam's length δh [10] is:
In which EsT, EcT, and EreT are the elastic modulus of the steel beam, concrete and reinforcement respectively. As, Ac, and Are are the area of the steel beam section, concrete slab and total reinforcement respectively.
δh ¼ δhm −δhT ! 2 1=2 dz ¼ − ∫L0 1 þ dx−L −αΔTL dx 0 1 LkT 2 sin B 2δ EsT As α sT T s þ EcT Ac α cT T c 2 C C ¼ mþB L @1− Lk AL− L E A þE A
Moment of the composite joint at middle span of the specimens could be obtained using the suggested method in the companion paper [10] once the rotation of middle composite joint was known. The rotation of joints could be determined from the deflection profile if the δm was given. So the key work of the application of Eq. (5) is to give a reasonable value of δm to keep the balance of the equation.
T
sT
s
cT
ð10Þ
3.5. Mid-span moment Me
c
2
3.6. Analysis procedure and prediction of experiments
where kT is defined as: α T −α cT T t kT ¼ α d sT b hc þ hs
ð11Þ
Here defining δh is positive when the beam is in tension, and negative when the beam is in compression. Then the axial force FT of the composite beam is given by: F T ¼ Kδh
ð12Þ
The analysis procedure of how the composite beam develops catenary action in the tests was illustrated in Fig. 18. The predicted moment of composite joints and axial force of composite beams for the three test specimens were obtained and shown in Figs. 19–21. It could be observed that the theoretical models result and the experimental result were in a good agreement with acceptable accuracy. The unavailable real stress–strain relationship of materials at elevated temperatures in the fire tests would certainly produce a discrepancy between theory and test. Fortunately, the difference of the flange failure temperatures between tests and result obtained with the proposed theoretical method was negligible. 3.7. Summaries From the experimental and theoretical investigation, characteristics of calculated parameters of composite joints and beams in the entire heating range could be summarized as follows:
Fig. 16. Axial force comparison between Test 2 and Test 3.
1. In the earlier phase, expanding in the composite beam was dominating; the axial force in the beam increased quickly with a small quantity of increase in the deflection and the moment resistance of the composite joint was invariable. The bottom flange of the beam at a relatively low temperature could offer sufficient strength and stiffness to avoid buckling under the combination action of axial force and moment at the joint, so the moment resistance of the joint could keep its previous value. Shape parameter n, which defines the shape of moment-rotation relationship at high temperatures, was an important factor. From the comparison between predicted results and experimental data, it was suggested
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V F
Ka
z 0
F/2
FT
Ka
δv
Me
Kr
FT L/2
L
x
V Fig. 17. Beam loading and equilibrium diagrams for tests.
under low temperature could make great contribution to the moment resistance of the joint as the temperature increased further. 2. In the jumping phase, the deflection at mid-span of specimens increased quickly. The axial compressive force began to decrease and then changed into tension sharply due to the instant decline in the rotational stiffness of the end restraint and the quickly decreased
that the expressions of the shape parameter [10] gave a good performance. The neutral axis in the composite joint which defined the ultimate moment resistance combined with axial force moved from the steel beam section towards the concrete slab. It indicated that internal force redistribution had taken place in the joint at elevated temperatures and the reinforcement in the concrete slab
Start Time t i Confirm temperature distribution
Obtain material property in high temperature
Assume deflection
Confirm
vi
Confirm
by Eq . (5)
Confirm rotation
mi
hi
by Eq . (6)
Obtain FTi by Eq. (8)
ri=2 vi /L
Obtain Mui and Ki0 of composite joint under the influence FTi using Table (2) and Eq .(4) in part 1
Obtain Mei of joint using Eq .(9) and Eq.(10) in part 1
Reduce
mi
>0
FTi
vi
+Mei-VL/2=0
<0
Increase
Yes Go into the next step ti+1 tmax Yes No End Fig. 18. Flow chart for analysis of catenary action of beams with nonlinear restraints.
mi
J.-T. Li et al. / Journal of Constructional Steel Research 76 (2012) 121–132
131
a) Deflection of beam.
Fig. 19. Comparison of predicted and experimental results of deflection of specimens in Test 1.
b) Moment in beam-to-column connection. strength of steel material especially at the bottom flange of the beam where local yielding would happen under the combined action of the restrained thermal expansion and hogging bending moment. Staggered raise of the moment resistance of the composite joint had its inevitability to keep the whole structure to be stable. Considering the axial force-bending moment relationship of the composite joint, it is reasonable to reduce axial force for a relative high moment resistance. But with the incessant increasing temperature, the moment resistance would quickly drop with the increasing axial tensile force. So at this stage, when the proposed method was used to calculate the joint moment, the moment value was controlled directly by the axial force in the beam, and the influence of the shape parameter was not so great as that in the first stage. The strength of the reinforcement in the shield of concrete slab at elevated temperatures undertook sufficient axial tensile force for the moment resistance of the composite joint. 3. At the stage of catenary action of the beam, the axial tensile force and deflection increased gently and the bending moment of the joint kept declining. Because the composite joint could be considered as entering into a plastic status at this stage under the combined action of axial force and bending moment, the influence of the shape parameter could be ignored and the ultimate moment of the joint recommended in the companion paper [10] under the axial force FT action at temperature T could be directly used as moment resistance. The plastic neutral axis slowly moved towards the reinforcement.
c) Axial force in the beam.
4. Conclusions Studies on connections and beams at elevated temperatures are carried out respectively in the conventional research and design methods, while the interaction of each other has not been well investigated in a whole structural analysis. In fact, if their interaction were considered in a structural analysis, the members would behave completely different. So, tests conducted in this paper investigated the temperature distribution, load carrying capacity, failure mode and deformation trait of composite connections in fire. And restrained beams were also included in search of the mutual interaction between joints and beams within a frame structure. The proposed method is to present how the composite joint behaves under the influence of the axial force and great rotation at elevated temperatures, and to explain how the non-linear end restraint of the joint was considered in the general analytical method of catenary action. It offers feasibility for the fire resistant design and evaluation of the whole structure for the entire temperature range. The proposed method is validated by comparing the
Fig. 20. Comparison of predicted and experimental results of specimens in Test 2.
model predications with the experiment results. The main conclusions of the paper may be drawn as: 1. At elevated temperatures, the failure mode of the flush end-plate composite joint without stiffeners is usually dominated by the yielding of the bottom flange of the steel beam near the supports, either in unrestrained or restrained beams. 2. Protection in Test 2 just slowed the rate of temperature increase and allowed the concrete slab and steel beam to have a more even
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a) Deflection of beam. 4.
5.
6.
b) Moment in beam-to-column connection.
7.
8.
c) Axial force in the beam.
result, much more precision could be obtained in practical analysis if temperature differences were taken into account instead of using average temperature. The axial force influences the rotational stiffness and moment capacity of the joint. And the non-linear characteristics of the joint determine the deflection and axial force development of the restrained beam. The joint in Test 1 with the beam unrestrained, would lose its moment capacity once the bottom flange of the beam yielded, while in Test 2 and Test 3, the moment resistance of the composite joints could maintain for a longer time in fire. Furthermore, the moment resistance had temporary increase in Test 2 and Test 3 and the whole structure showed good ductility. The reinforcement at low temperature also contributed to the high moment resistance of the connection. So connection research with the connection integrated in the structure is an actual and comprehensive manner to obtain the response of the connection. The deflections of Test 2 with fire protection and Test 3 without fire protection both exceeded the maximum allowable value of span/20, and the structure was still able to keep its stability. The beam, with fire protection, would also tend to develop catenary action earlier if the protection of the bottom flange of the beam in the connection crack and break off. So if the surrounding structure could offer enough axial restraint and support large deflection of composite beam, some beams without fire protection or partial protection are practical. The end-plate semi-rigid connection has good ductility to help the beam develop the catenary action, so the application of semi-rigid connection could improve the bearing capacity of the beam. Further research in the temperature cooling phase should be done. From the record of the experiments in the cooling phase, it was suggested that the deflection and axial force of beams kept increasing. That is a dangerous signal for the connection with limited moment and axial force resistance and surrounding structure with limited deflection allowance. As a result, it is necessary to promote further research on the whole structure in full temperature range.
Acknowledgments The study reported in this paper is financially by the Natural Science Foundation of China by the projects 50738005 and 51120185001. The support is gratefully acknowledged. References
Fig. 21. Comparison of predicted and experimental results of specimens in Test 3.
temperature distribution. The failure mode of specimens in Test 2 and Test 3 were almost the same. There was no obvious difference in the axial force of the beam or the moment resistance of the composite joint. The deflection at mid-span began to increase quickly at the temperature of 600 °C. 3. Because elements of the connection had different rate of temperature increase, especially after the fireproofing material broke off, failure was always controlled by the elements with higher temperature. As a
[1] Lawson RM. Behavior of steel beam-to-column connections in fire. Struct Eng 1990;68:263–71. [2] Leston-Jones LC, Burgess IW, Lennon T, Plank RJ. Elevated-temperature momentrotation tests on steelwork connections. Proc Inst Civ Eng Struct Build 1997;122: 410–9. [3] G.B. Lou. Behavior and design of extended endplate moment connections with highstrength bolts in fire. Doctor's Degree thesis. Tongji University; 2005(in Chinese). [4] Wang WY, Li GQ, Dong YL. Experimental study and spring-component modeling of extended end-plate joints in fire. J Constr Steel Res 2007;63:1127–37. [5] Newman GM, Robinson JT, Bailey CG. Fire safety design: a new approach to multistorey steel-framed buildings. SCI; 2000. p. 288. [6] Yin YZ, Wang YC. A numerical study of large deflection behavior of restrained steel beams at elevated temperature. Journal of Constructional Steel Research 2004;60(7):1029–47. [7] Yin YZ, Wang YC. Analysis of catenary action in steel beams using a simplified hand calculation method, Part 1: theory and validation for uniform temperature distribution. Journal of Constructional Steel Research 2005;61:183–211. [8] J.T. Li. Behavior and design of beam-to-column flush end-plate composite connection in fire. Doctor's Degree thesis. Tongji University; 2009(in Chinese). [9] Y.Z. Wang. Behavior and design of composite beam in fire with considering global structural effect. Doctor's Degree thesis. Tongji University; 2006(in Chinese). [10] G.Q. Li, L.Z. Chen, J.T. Li, G.B. Lou. Modeling of flush end-plate bolted composite connection in fire considering axial force effect, J Constr Steel Res, accepted for publication.
Contents lists available at SciVerse ScienceDirect
Journal of Constructional Steel Research
Experimental investigation on flush end-plate bolted composite connection in fire Jiao-Ting Li b,⁎, Guo-Qiang Li a, b, Guo-Biao Lou a, b, Ling-zhu Chen b a b
State Key Laboratory for Disaster Reduction in Civil Engineering, Shanghai, 200092, PR China College of Civil Engineering, Tongji University, Shanghai, 200092, PR China
a r t i c l e
i n f o
Article history: Received 18 March 2011 Accepted 23 March 2012 Available online 1 May 2012 Keywords: Flush end-plate Fire tests Composite joint Axial force Fire-resistant capability Catenary action Non-linear restraint Design method
a b s t r a c t Three tests at elevated temperatures were carried out to invest the fire-resistant capacity of flush end-plate composite joints. The axial force was considered in two of the three tests simulating fire conditions to investigate its effect on the connection's load carrying ability (one with fire protection and the other without fire protection). Summaries have been given on the failure mechanisms, temperature distribution, loading carrying capacity of the composite joint and the mutual influence between joints and beams at elevated temperatures. Date shows that the failure mode of the flush end-plate joint without stiffener is usually dominated with the yielding of the bottom flange of steel beam near the supports, elements of the composite connection have different rate of temperature increase, and the axial force from restrained composite beam influences the rotational stiffness and moment capacity of joints. This paper also theoretically presents how the interaction of joints and beam developed in fire conditions. A practical simplified method is proposed to calculate the non-linear variable characteristics of composite connection in the analysis of catenary action of beams at elevated temperatures. The proposed method is verified by the experimental investigations. This study offers a feasibility of fire-resisting design and evaluation for the composite beam with semi-rigid connections in the complete temperature range. © 2012 Elsevier Ltd. All rights reserved.
1. Introduction Semi-rigid connections used in steel frames and steel portal frames are mainly bolted and have been proved to be economical, especially the moment capacity of end-plate connections (either flush or extended) could be as high as that of beams. The three key indications of the performance for semi-rigid composite connections are moment resistance, Mu, rotational stiffness, K0, and rotation capacity, θ, as shown in Fig. 1. Fire tests on composite connections at elevated temperatures were conducted in early studies to obtain the temperature–rotation relationship. R.M. Lawon [1] conducted eight fire tests on column-to-beam joints in the types of extended end-plate joints (rigid), flush end-plate joints (semi-rigid) and partial depth end-plate joints (flexible). It was observed that the connections designed as pinned were able to take a certain amount of moment at large deflections in fire. However in frames, where connections are designed as rigid or moment resistible under vertical load in normal conditions, the redistribution of moment from mid-span to the support zone does not occur to the same extent in fire conditions as in normal conditions. One test at ambient temperature and five others at elevated temperatures in the style of end-plate connection were conducted by L.C. Lestones [2]. And temperature–rotation curves under different load levels of moment were derived from test results. Due to
⁎ Corresponding author at: College of Civil Engineering, Tongji University, 1239 Siping Road, Shanghai 200092, PR China. Tel.: + 86 21 6598 5318. E-mail address: [email protected] (J.-T. Li). 0143-974X/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.jcsr.2012.03.022
the usage of thermal insulating material to simulate the concrete slab above the steel beam, the contribution of the reinforcement to the ultimate moment resistance and stiffness of the joint were ignored. G.B. Lou [3] conducted a series of full scale tests to investigate the temperature distribution, structural behavior and failure mechanisms of bare-steel connections. Two configurations of high-strength bolted extended end-plate connections, including beam-to-column connection and beam-to-beam splice connection, were considered. For each configuration three tests were conducted, with one at ambient temperature throughout the entire moment-rotation range, and two transient state tests at different load levels. W.Y. Wang [4] carried out fire tests on full-scale specimens made with H-shaped steel. The failure characteristics and modes of the extended end-plate joint specimens in fire were obtained. Some experiments on elements of the connections under fire were conducted by researchers to get failure characteristics of elements at high temperatures. However, these existing joint experiments haven't considered the influence of the axial force caused by beam expansion under fire. But most of beams in multi-story structures would certainly develop axial force in fire because of their expansion and circumjacent restraints [5], and the axial force would reduce the moment capacity and rotational stiffness of connection considerably and in return these two factors would affect the axial force development in beams. So, experiments in this paper were conducted to investigate the effect of this axial force on the connection's load carrying ability and the beam's deflection. A general method to analyze the behavior of restrained composite beams at elevated temperatures was presented, considering the catenary
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M Mu 0.85Mu K0
Fig. 1. Moment-rotation relationship of semi-rigid connection.
action [6,7] and nonlinear variation of restraints due to the axial force in beams and high temperatures. 2. Experimental investigation 2.1. Objectives of fire tests In total, three fire tests were carried out in the Structure Fire Resistance Laboratory at Tongji University. Test 1, illustrated in Fig. 2 was conducted on a composite beam specimen with end-plated connection without axial restraint. Test 2 and test 3 were conducted on composite beam specimens with end-plated semi-rigid beam-to-column connection as shown in Fig. 3. The test series are primarily designed to investigate the behavior of the composite semi-rigid beam-to-column joints and the restrained composite beams exposed to fire with their mutual interaction, and indirectly validate the moment-rotation relationship of the composite semi-rigid joints with variation of the temperature and axial force in beams. Therefore, the tests were carried out on a typical type of connection subjected to constant hogging moment, constant shear force and variable axial force which would exist and develop in a real structure under fire condition. 2.2. Specimens and test set-up The test set-up of Test 1 is shown in Fig. 2, and that of Test 2 and Test 3 is shown in Fig. 3. In Test 2 and Test 3, the cruciform specimen stretching over the test furnace was axial restrained by the restraint frame which helped to develop axial force at elevated temperatures. Loading jacks, which were fixed to the distribution beam with the
100 200 200
2102
Jack
2.3. Loading Load of the three fire tests were applied on the beams at a distance of 2.498 m from the column centerline outside the furnace to produce
200 114 114 200
Q 235 B H300×300×12×14
12
dimension of H300 mm ×300 mm × 12 mm ×14 mm, reacted against the restraint frame to form a downward equilibrant force to the specimen. The specimen was pinned to the columns of restraint frame so as to transfer shear force only and produce a definite moment to the composite connection. The column base of the restraint frame could freely move in the horizontal direction. Each specimen consisted of two H-shaped steel beams (H300 mm × 150 mm × 8 mm × 12 mm) which were symmetrically connected to the flange of a single steel column (H240 mm × 240 mm × 12 mm × 14 mm) and covered by a composite slab with a trapezoidal deck. Each beam was connected to the column with eight bolts (M20) in 21.5 mm diameter clearance holes. The thickness of the end-plate is 14 mm. The total thickness of the slab was 140 mm, and the effective thickness was 70 mm. The concrete was mixed on the spot, and three coupons were casted at the same time to obtain the strength of the concrete. The cubic compressive strength of concrete after 28 days curing period was an average 28.9 N/mm 2. The upper-layer reinforcing mesh of the slab was made by smooth reinforcement bar with the grid size of 120 mm × 120 mm and lower-layer reinforcing mesh was made by smooth reinforcement bar with the grid size of 200 mm × 200 mm. Rebar with the diameter of 10 mm was placed in the upper layer in the longitudinal direction running through the slab and gave a 1% reinforcement ratio of the concrete slab. Rebar with the diameter of 10 mm was used as the distributional rebar in the upper layer at the space of 120 mm within the span of the beam and 40 mm near the column. In the lower layer, the diameters of rebar in the two directions were both 6 mm. Four headed studs with a diameter of 19 mm and 100 mm in height were welded to the steel beam at each trough of the deck to ensure the composite beam was complete shear connection. The overall dimensions of specimens are shown in Figs. 2 and 3 and the strength of the materials is listed in Table 1. The fire protection material was vermiculite-cement spray. Only the connection and beams of test 2 were protected. The arrangement of displacement gauges to measure the rotation and deflection of connections and beams in tests were similar, as shown in Fig. 4. Additionally, horizontal displacement of the column base of the restraint frame was measured to calculate the axial force caused by the expansion of composite beams in fire. Thermocouples were located at appropriate locations around the composite connection and along the beams as illustrated in Fig. 5.
2102
200 200 100
12 12
12
8 M 20 Gr.10.9
Jack
C 30
8
658
Jack
Steel column Q235B H240×240×12×14
Steel beam Q 235 B H 300×150 ×8×12 Endplate Q 235B 14 ×150 ×300 14 2246
8 M 20 Gr. 8.8
Ø6@120
Ø10@120 Jack
Steel beam Q 235B H 300×150 ×8×12 14
8
2246
658 150 150
150 150
Fig. 2. Specimen and test set-up for Test 1.
J.-T. Li et al. / Journal of Constructional Steel Research 76 (2012) 121–132
100 200 200
2102
200 114 114 200
123
2102
200 200 100
300
Q 235B H300×300×12×14
730
Jack
Steel column Q235B H240×240×12×14
8M20 Gr.10.9
Jack
Restrain frame beam Q235B 2 [28a Restrain frame column Q235B H500×400×12×20
1
3426
Restrain frame column Q235B H500×400×12×20 2400
Restrain frame beam Q235B 2 [28a Concrete slab
50
8M20 Gr.10.9
Sheer stud
Steel beam Q235B H300×150×8×12 Flush endplate 14×150×300 2332
Steel decking
Reinforcement 50
Steel beam Q235B H300×150×8×12 8M20 Gr.8.8
Fig. 3. Specimen and test set-up for Test 2 and Test 3.
a constant moment for connections in fire. Moment and shear forces applied on the composite connections were a little bit lower than the values in practice to ensure a longer observation in fire. Joints of the three fire tests were loaded with a moment of 0.429 times of the ultimate moment at ambient temperature. Moment and shear forces for tests are summarized in Table 2. The specimens were heated uniformly with a circular natural gas flow pattern and the temperature of the air in furnace was controlled in accordance with the standard ISO 834 temperature–time curve.
2.4. Results It was observed that the behavior of the connections followed a similar pattern. With significant local buckling of the bottom flange of steel beams, the load resistance began to decrease rapidly in Test 1, while in Test 2 and Test 3 the composite beams changed from bearing an axial compressive force into a tensile force at large deflection. Failure modes are shown in Fig. 6. Failure of connecting bolts or reinforcement was not observed, despite considerable large deflection developed in the mid-pan of beams. The end-plate, column flange, bolts, reinforcement and shear studs were observed with very little deformation. All the tests were finally terminated due to the limited measurement of jacks.
2.5. Temperature distribution Temperature development of beams, joints and reinforcement in the three fire tests with time was shown in Figs. 7–10. It could be summarized as follows: 1. It was apparent that there was a significant difference between the temperature at the top flange of the beam supporting concrete floors and that at bottom flange. 2. Temperatures of bolts BP3 and BP4 were also greatly lower than that of the bottom flange. The round decreasing sequence of temperature of the joints for the three fire tests could be concluded as BF8 → BW9 → BF6 → CW14 → BW11 → BF5 → CW7 → CW12 → BP4 → BP3 → CW10. 3. The lowest temperature was at the column web, at the point the most adjacent to the concrete floor. That's because a portion of heat were conducted to the outer air by smoke or to the upper column web outside the furnace. The reduction was about 200 °C to 300 °C when the controlling temperature of the bottom flange of beams was reached. 4. Reinforcement in the upper layer of concrete was significantly cooler due to the heat shielding of the slab. There was a phase of temperature suspending when the reinforcement temperature reached 100 °C, because the water vapor took out most heats from the cracks of concrete slab. 2.6. Deflection, axial force and connection moment of fire tests
Table 1 Measured strength of components in tests. Component
Dimension(mm)
Material
Yield strength (N/mm2)
Ultimate tensile strength(N/mm2)
Bolts Shear studs End-plate Steel beam Steel colum
M20 19 × 100 300 × 150 × 14 H300 × 150 × 8 × 12 H240 × 240 × 12 × 14
8.8 – Q235B Q235B Q235B
830 290 250 285 250
900 450 436.7 433.3 436.7
Some of the readings from displacement gauges did not give reliable data for the tests because of interim or permanent failure at the contact point on the surface or of the connecting cables. Beams and joints deflection versus the temperature of the beam bottom flange curves of the three tests are shown in Figs. 11–13. Figs. 14–16 illustrate the comparison of deflection, moment and axial force between fire tests. All the figures could be summarized as follows: 1. In Test 2 and Test 3 it was observed that the axial force, moment of composite joint and deflection showed a great jump when the
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D3-8
D3-3
D3-9
D3-2
D3-7
D-2 D-3 D-4 D-5 D-6
D3-6
D3-5
D3-4
D3-10
D3-1
Fig. 4. Displacement gauges arrangement for Test 2 and Test 3.
high temperature in the fire, the moment of connection, axial force and deflection did not show great differences between Test 2 and Test 3. 4. Appearance of moment peak point was always a little bit later than the axial force peak point, in other words, the maximum moment of the composite connection would reach at the decreasing rang of axial compressive force. After the axial compressive force reached its peak point, deflection at the middle of the beam rapidly increased, the rate of deflectionδvincrement was larger than that of axial force reduction. Therefore the momentMewould necessarily begin to increase to keep the balance of Eq. (1). After that when
temperature approached the range of 500 °C–650 °C, whether the beams were fire protected or not. This indicated that the material strength degradation at the critical temperature range at the bottom flange of beams in connection region was the key parameter in controlling the behavior of the whole structure at elevated temperatures. 2. In Test 2, greater axial force was developed due to a longer fire experience with the fire protection, and concrete slab expanded with steel beam more sufficiently to generate more thermal expansion. 3. Although beams in Test 3 without fire protection developed catenary action earlier than beams in Test 2 because of an earlier
RE1(2)
CO1(2)
CW10 BP3 BP4
BF5
BW6
BW11
BW9
BF13
BF8
h bf /4
CW12
h bw /2
CW7
CW14
B3-1
B3-2
B3-15
Fig. 5. Thermocouples arrangement of composite connection.
B3-16
J.-T. Li et al. / Journal of Constructional Steel Research 76 (2012) 121–132 Table. 2 Summaries of fire tests. Fire Loading protection manner
Test 1 No Test 2 Yes Test 3 No
Test1 average temperature of furnace Test2 average temperature of furnace Test3 average temperature of furnace ISO834
1200 Force at each Moment Shear(kN) Ratio of test jack (kN) (kN·m) moment
Self-balance 51.3 loading Self-balance 53.89 loading Self-balance 53.89 loading
100.5
40.22
0.43
105.5
44.7
0.45
105.5
44.7
0.45
Test1 average temperature of joint Test2 average temperature of joint Test3 average temperature of joint
1000 800
T / oC
Test no.
125
600 400 200
the deflectionδventered the smooth phase of increase, the rate of deflection increment dropped, and the axial force changed into a tensile force and increased. So the moment of the composite connection tended to decline. Me þ F T δv ¼ VL=2
ð1Þ
0
0
20
40
60
80
100
120
140
160
t / min Fig. 7. Average temperature of inside furnace and joint for the three fire tests.
a) Test 1
b) Test 2
c) Test 3
Fig. 6. Failure of specimens.
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a) Temperature distribution of joint.
a) Temperature distribution of joint. 900 800
CW14
700
BF13
500
CW7
BF-6 CW-10
800
400
CW12
T/ oC
T / oC
BF-5 BW-9 CW-14
1000
BF6
BP4
300
400
BF5
200
BP3
100
CW10
0
5
10
15
20
25
30
35
40
45
600
200 50
0
t / min
0
20
40
60
80
100
120
140
160
180
t / min
b) Temperature distribution of beam
b) Temperature distribution of beam and
and reinforcement.
reinforcement.
900 800
1,000
700
900 800
600 Average temperature of furnace B-2 B-15 Average temperature of joint CO1 RE1
500 400 300 200
700 600
T/ oC
T / oC
BP-4 BF-8 CW-12
BW11
600
0
BP-3 CW-7 BW-11
1200
BF8
500 400
100
300
BP-3
BP-4
BF-5
BF-6
0
200
BF-8
BW-9
CW-10
BW-11
100
CW-12
CW-14
0
5
10
15
20
25
30
35
40
45
50
t / min
0
Fig. 8. Temperature distribution of Test 1.
0
20
40
60
80
100
t / min Fig. 9. Temperature distribution of Test 2.
where Me is the moment of the connection, FT is the axial force, defined as negative if the beam was in compression, δv is the deflection at mid-span of the beam, V is the shear force at the end of the beam. 5. The end-plate semi-rigid connection has good ductility which is produced by the plastic bending deformation of the end-plate and the good ductility helps the beam develop the catenary action. So the application of semi-rigid connection could improve the bearing capacity of the beam. 3. Modeling of experiments 3.1. Temperature distribution [8] The connection is composed of different elements, including steel columns, steel beams, bolts, end-plates and a concrete slab. Because different elements had different rate of temperature increase, the temperature distribution was non-uniform through the connection. The simplified method to determine the temperature of different parts of the connection is listed as follows: 1. The average temperature of the column part below the connection region, which was calculated according to the recommendations for the sections exposed to fire in four sides in the EC3: Part 1.2, could be taken as the average temperature of the column part in the connection region for the composite connection with trapezoidal deck, while the temperature of the column part with the first row of bolts should be revised according to Eq. (2) for the
composite connection with solid slab because of the influence of the concrete slab.
T
′
c;bolt1
¼
3T c;bolt1 þ T c;slab;0:02 4
ð2Þ
Where Tc,' bolt1 is the revised temperature of the column part with the first row of bolts; Tc, bolt1 is the temperature of the column part calculated according to the recommendations for the sections exposed to fire in four sides in the EC3: Part 1.2; Tc, slab, 0.02 is the temperature of the concrete 20 mm above the bottom of the slab. 2. The temperature of the bottom flange and web of the beam could be calculated according to the recommendations for the sections exposed to fire in four sides in the EC3: Part 1.2, while the temperature of the top flange of the beam could be calculated according to the recommendations for the sections exposed to fire in three sides in the EC3: Part 1.2. 3. Due to the influence of the steel beam and concrete slab, the temperature of the end-plate should be revised according to Eq. (3). T
′
ep
¼
2T ep þ ηT b 2þη
ð3Þ
Where T′ep is the revised temperature of the end-plate; Tep,Tb is the temperature of the end-plate and steel beam calculated according
J.-T. Li et al. / Journal of Constructional Steel Research 76 (2012) 121–132
a) Temperature distribution of joint.
127
a) Development of joint deflection with the temperature in the bottom flange of the beam.
1,000 900 800
T / oC
700 600 500 400 300
BP-3
BP-4
BF-5
BF-6
200
BF-8
BW-9
CW-10
BW-11
100
CW-12
CW-14
0
0
20
40
60
80
100
t / min
b) Temperature distribution of reinforcement.
b) Development of beam deflection with the temperature
450
in the bottom flange of the beam.
CO1
400
CO2
350
RE2
T / oC
300 250 200 150 100 50 0
0
20
40
60
80
100
t / min Fig. 10. Temperature distribution of Test 3. Fig. 11. Deformation of the joint and beam in Test 1.
to the recommendations for the sections exposed to fire in four sides in the EC3: Part 1.2 respectively; η is the coefficient, which could be taken as 1.5 deduced from the test result. 4. The temperature of the concrete at the location of the reinforcement could be taken as the temperature of the reinforcement. The temperature of the concrete in the solid slab could be obtained according to Table 3, while that in the composite slab with trapezoidal deck could be calculated by Eq. (4). In addition, the temperature of the concrete located in the concave if the slab should be taken as the reinforcement temperature. "
2 1 t t exp 0:05 þ 0:135 −0:005 −d 8 20 20 2 # t t : : 0:007 þ 0:0145 −0:0005 20 20
Tc ¼ T0 þ
ð4Þ
6 expð−w2 =w4 Þ−1 d × 1þ 10H
Where Tc is the concrete temperature; T0 is the initial temperature; t is the time; d is the distance above the slab bottom; ω2,ω4 is the width of the top and bottom of the trough respectively; H is the total height of the slab.
3.2. Equilibrium equation Fig. 17 shows the composite beams' loading mechanism and equilibrium of specimens in Test 2 and Test 3. Beams were symmetrically loaded. The axial restraint stiffness of the end axial restraint, Ka, was assumed to be a constant due to the temperature of the restrained frame keeps at ambient temperature. And Ka was taken as 83.4 KN/mm, calculated referring to Ref. [9]. FT was the axial force developed in the composite beam. Me was the moment of the specimen at the middle span. The equilibrium equation is: Me þ F T δv ¼ VL=2
ð5Þ
Deflection δv at the middle span could be expressed in two parts: δv ¼ δm þ δT
ð6Þ
where δm is the maximum mechanical deflection at the middle span of the beam due to the load and δT is the maximum thermal bowing deflection under certain temperature distribution of the composite beam. The shear force V is previously defined in the test. Parameters in Eq. (5) will be discussed below.
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a) Development of joint deflection with the temperature
a) Development of joint deflection with the temperature
in the bottom flange of the beam.
in the bottom flange of the beam.
b) Development of beam deflection with the temperature
b) Development of joint deflection with the temperature
in the bottom flange of the beam.
in the bottom flange of the beam.
Fig. 12. Deformation of the joint and beam in Test 2.
Fig. 13. Deformation of the joint and beam in Test 3.
steel at high temperature and αcT is that of concrete. hc is the height of concrete slab and hs is the height of steel beam. Then:
3.3. Deflection δv According to Refs. [7–9], the total composite beam deflection profile could be described as z(x) = zm(x) + zT(x), zm(x) is mechanical deflection profile and zT(x) is the thermal bowing deflection profile. Thus, for the mid-point loaded beam with axial restraints at ends but no rotational restraints, zm(x) and zT(x) could be expressed as below: 8 2δ > < mx L zm ¼ > : 2δm ðL−xÞ L
0 ≤ x ≤ L=2 L=2 ≤ x ≤ L
2 zT ðxÞ ¼ α d ðα sT T b –α cT T t Þ x –Lx =ðhc þ hs Þ
δv ¼ δm þ δT
¼ δm –α d ðα sT T b –α cT T t Þ L2 = 4 =ðhc þ hs Þ
ð7Þ
ð8Þ
In which αd is equal to 1 when the beam is simply supported, otherwise it is 0 when the beam is supported with full rotational restraints at the ends. αsT is the coefficient of thermal expansion of
Fig. 14. Deflection comparison of the three fire tests.
ð9Þ
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129
Table 3 Temperature of concrete at the solid slab (°C). d(mm) 90 min
Normal concrete Light concrete
10
20
30
40
50
790 720
650 580
540 460
430 360
370 280
where K is the synthesized axial stiffness of composite beams with end restraints: 1 2 1 ¼ þ K K a K bT
ð13Þ
The axial stiffness KbT of composite beams is defined as: Fig. 15. Moment comparison between Test 2 and Test 3.
3.4. Axial force FT
K bT ¼
EsT As þ EcT Ac when the beam is in compression L
ð14Þ
K bT ¼
EsT As þ EreT Are when beam is in tension L
ð15Þ
Axial force FT is determined by the shortening of the composite beam due to lateral deflection δhm and thermal expansion δhT. δhm could be calculated from the composite beam deflection profile z(x) at certain temperature distribution and load. δhT could be obtained according to the basic thermodynamics formula Δl = αTL. So, expression of the total change of beam's length δh [10] is:
In which EsT, EcT, and EreT are the elastic modulus of the steel beam, concrete and reinforcement respectively. As, Ac, and Are are the area of the steel beam section, concrete slab and total reinforcement respectively.
δh ¼ δhm −δhT ! 2 1=2 dz ¼ − ∫L0 1 þ dx−L −αΔTL dx 0 1 LkT 2 sin B 2δ EsT As α sT T s þ EcT Ac α cT T c 2 C C ¼ mþB L @1− Lk AL− L E A þE A
Moment of the composite joint at middle span of the specimens could be obtained using the suggested method in the companion paper [10] once the rotation of middle composite joint was known. The rotation of joints could be determined from the deflection profile if the δm was given. So the key work of the application of Eq. (5) is to give a reasonable value of δm to keep the balance of the equation.
T
sT
s
cT
ð10Þ
3.5. Mid-span moment Me
c
2
3.6. Analysis procedure and prediction of experiments
where kT is defined as: α T −α cT T t kT ¼ α d sT b hc þ hs
ð11Þ
Here defining δh is positive when the beam is in tension, and negative when the beam is in compression. Then the axial force FT of the composite beam is given by: F T ¼ Kδh
ð12Þ
The analysis procedure of how the composite beam develops catenary action in the tests was illustrated in Fig. 18. The predicted moment of composite joints and axial force of composite beams for the three test specimens were obtained and shown in Figs. 19–21. It could be observed that the theoretical models result and the experimental result were in a good agreement with acceptable accuracy. The unavailable real stress–strain relationship of materials at elevated temperatures in the fire tests would certainly produce a discrepancy between theory and test. Fortunately, the difference of the flange failure temperatures between tests and result obtained with the proposed theoretical method was negligible. 3.7. Summaries From the experimental and theoretical investigation, characteristics of calculated parameters of composite joints and beams in the entire heating range could be summarized as follows:
Fig. 16. Axial force comparison between Test 2 and Test 3.
1. In the earlier phase, expanding in the composite beam was dominating; the axial force in the beam increased quickly with a small quantity of increase in the deflection and the moment resistance of the composite joint was invariable. The bottom flange of the beam at a relatively low temperature could offer sufficient strength and stiffness to avoid buckling under the combination action of axial force and moment at the joint, so the moment resistance of the joint could keep its previous value. Shape parameter n, which defines the shape of moment-rotation relationship at high temperatures, was an important factor. From the comparison between predicted results and experimental data, it was suggested
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V F
Ka
z 0
F/2
FT
Ka
δv
Me
Kr
FT L/2
L
x
V Fig. 17. Beam loading and equilibrium diagrams for tests.
under low temperature could make great contribution to the moment resistance of the joint as the temperature increased further. 2. In the jumping phase, the deflection at mid-span of specimens increased quickly. The axial compressive force began to decrease and then changed into tension sharply due to the instant decline in the rotational stiffness of the end restraint and the quickly decreased
that the expressions of the shape parameter [10] gave a good performance. The neutral axis in the composite joint which defined the ultimate moment resistance combined with axial force moved from the steel beam section towards the concrete slab. It indicated that internal force redistribution had taken place in the joint at elevated temperatures and the reinforcement in the concrete slab
Start Time t i Confirm temperature distribution
Obtain material property in high temperature
Assume deflection
Confirm
vi
Confirm
by Eq . (5)
Confirm rotation
mi
hi
by Eq . (6)
Obtain FTi by Eq. (8)
ri=2 vi /L
Obtain Mui and Ki0 of composite joint under the influence FTi using Table (2) and Eq .(4) in part 1
Obtain Mei of joint using Eq .(9) and Eq.(10) in part 1
Reduce
mi
>0
FTi
vi
+Mei-VL/2=0
<0
Increase
Yes Go into the next step ti+1 tmax Yes No End Fig. 18. Flow chart for analysis of catenary action of beams with nonlinear restraints.
mi
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131
a) Deflection of beam.
Fig. 19. Comparison of predicted and experimental results of deflection of specimens in Test 1.
b) Moment in beam-to-column connection. strength of steel material especially at the bottom flange of the beam where local yielding would happen under the combined action of the restrained thermal expansion and hogging bending moment. Staggered raise of the moment resistance of the composite joint had its inevitability to keep the whole structure to be stable. Considering the axial force-bending moment relationship of the composite joint, it is reasonable to reduce axial force for a relative high moment resistance. But with the incessant increasing temperature, the moment resistance would quickly drop with the increasing axial tensile force. So at this stage, when the proposed method was used to calculate the joint moment, the moment value was controlled directly by the axial force in the beam, and the influence of the shape parameter was not so great as that in the first stage. The strength of the reinforcement in the shield of concrete slab at elevated temperatures undertook sufficient axial tensile force for the moment resistance of the composite joint. 3. At the stage of catenary action of the beam, the axial tensile force and deflection increased gently and the bending moment of the joint kept declining. Because the composite joint could be considered as entering into a plastic status at this stage under the combined action of axial force and bending moment, the influence of the shape parameter could be ignored and the ultimate moment of the joint recommended in the companion paper [10] under the axial force FT action at temperature T could be directly used as moment resistance. The plastic neutral axis slowly moved towards the reinforcement.
c) Axial force in the beam.
4. Conclusions Studies on connections and beams at elevated temperatures are carried out respectively in the conventional research and design methods, while the interaction of each other has not been well investigated in a whole structural analysis. In fact, if their interaction were considered in a structural analysis, the members would behave completely different. So, tests conducted in this paper investigated the temperature distribution, load carrying capacity, failure mode and deformation trait of composite connections in fire. And restrained beams were also included in search of the mutual interaction between joints and beams within a frame structure. The proposed method is to present how the composite joint behaves under the influence of the axial force and great rotation at elevated temperatures, and to explain how the non-linear end restraint of the joint was considered in the general analytical method of catenary action. It offers feasibility for the fire resistant design and evaluation of the whole structure for the entire temperature range. The proposed method is validated by comparing the
Fig. 20. Comparison of predicted and experimental results of specimens in Test 2.
model predications with the experiment results. The main conclusions of the paper may be drawn as: 1. At elevated temperatures, the failure mode of the flush end-plate composite joint without stiffeners is usually dominated by the yielding of the bottom flange of the steel beam near the supports, either in unrestrained or restrained beams. 2. Protection in Test 2 just slowed the rate of temperature increase and allowed the concrete slab and steel beam to have a more even
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a) Deflection of beam. 4.
5.
6.
b) Moment in beam-to-column connection.
7.
8.
c) Axial force in the beam.
result, much more precision could be obtained in practical analysis if temperature differences were taken into account instead of using average temperature. The axial force influences the rotational stiffness and moment capacity of the joint. And the non-linear characteristics of the joint determine the deflection and axial force development of the restrained beam. The joint in Test 1 with the beam unrestrained, would lose its moment capacity once the bottom flange of the beam yielded, while in Test 2 and Test 3, the moment resistance of the composite joints could maintain for a longer time in fire. Furthermore, the moment resistance had temporary increase in Test 2 and Test 3 and the whole structure showed good ductility. The reinforcement at low temperature also contributed to the high moment resistance of the connection. So connection research with the connection integrated in the structure is an actual and comprehensive manner to obtain the response of the connection. The deflections of Test 2 with fire protection and Test 3 without fire protection both exceeded the maximum allowable value of span/20, and the structure was still able to keep its stability. The beam, with fire protection, would also tend to develop catenary action earlier if the protection of the bottom flange of the beam in the connection crack and break off. So if the surrounding structure could offer enough axial restraint and support large deflection of composite beam, some beams without fire protection or partial protection are practical. The end-plate semi-rigid connection has good ductility to help the beam develop the catenary action, so the application of semi-rigid connection could improve the bearing capacity of the beam. Further research in the temperature cooling phase should be done. From the record of the experiments in the cooling phase, it was suggested that the deflection and axial force of beams kept increasing. That is a dangerous signal for the connection with limited moment and axial force resistance and surrounding structure with limited deflection allowance. As a result, it is necessary to promote further research on the whole structure in full temperature range.
Acknowledgments The study reported in this paper is financially by the Natural Science Foundation of China by the projects 50738005 and 51120185001. The support is gratefully acknowledged. References
Fig. 21. Comparison of predicted and experimental results of specimens in Test 3.
temperature distribution. The failure mode of specimens in Test 2 and Test 3 were almost the same. There was no obvious difference in the axial force of the beam or the moment resistance of the composite joint. The deflection at mid-span began to increase quickly at the temperature of 600 °C. 3. Because elements of the connection had different rate of temperature increase, especially after the fireproofing material broke off, failure was always controlled by the elements with higher temperature. As a
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