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Experiments of Class 4 open section beams at elevated temperature
Thin-Walled Structures 98 (2016) 2–18
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Experiments of Class 4 open section beams at elevated temperature Martin Prachar a,n, Jan Hricak a, Michal Jandera a,n, Frantisek Wald a, Bin Zhao b a b
Faculty of Civil Engineering, Czech Technical University in Prague, Thakurova 7, Praha, Czech Republic CTICM, Centre Technique Industriel de la Construction Métallique, Saint-Aubin, France
art ic l e i nf o
a b s t r a c t
Available online 15 May 2015
At elevated temperature, behaviour of Class 1 to 3 open cross-section beams have been investigated experimentally and numerically, whereas for slender Class 4 sections only few experimental data have been collected. Due to the economic assumptions of members with Class 4 cross section and general validity of the existing design rules, further investigation is desired. This paper presents tests and numerical simulation of welded slender (Class 4) I-section beams at elevated temperature. The design of the test set-up, as well as progress of the experiments is presented. Detailed information about the geometrical data, measured geometrical imperfections, temperature, load and actual mechanical properties were collected. The tests were subsequently used for a FE model validation. The described research allows better understanding to the fire behaviour of steel members of Class 4 crosssection beams. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Slender section Elevated temperature Lateral torsional buckling Tapered beam
1. Introduction The area of research in slender cross-sections in case of fire is very important as only little investigation was made and structural fire design became an inseparable part of structural design. The correctness of the design is essential regarding safety of the structure as well as its economy, concerning also possible additional fire protection costs. Therefore, well representing design models, which simulate the actual behaviour of the structures exposed to fire, are crucial as a base of such design formulas. Steel members with thin-walled cross-sections are commonly used in buildings due to its lightness and long span capacity. The design principles of Class 4 sections are very specific and usually more difficult than for stocky sections. Despite the current EC3 contains a number of simple rules for design of Class 4 crosssections at elevated temperature, based on recent numerical simulations they were found to be not accurate [1]. Through refining these rules, a significant material savings could be achieved which would lead to higher competitiveness of the steel structures. However, the lack of numerical and experimental data have been collected until now, which may serve as a base to such changes. The structural steel members of slender cross-sections (Class 4 section according to EC3 1.1 [2]) subjected to bending are
n
Corresponding authors. E-mail addresses: [email protected] (M. Prachar), [email protected] (J. Hricak), [email protected] (M. Jandera), [email protected] (F. Wald), [email protected] (B. Zhao). http://dx.doi.org/10.1016/j.tws.2015.04.025 0263-8231/& 2015 Elsevier Ltd. All rights reserved.
characterized by having the possibility of failure by both local and global buckling modes. The local buckling mode occurs due to the compression of thin plates in the section (see Fig. 1a). Therefore, the section resistance is significantly affected by deformations of the area in compression. The lateral torsional buckling (global buckling mode for members in bending) is an instability induced by the compressed flange of unrestrained open section beams subjected to bending around the major axis as shown in Fig. 1b. The actual bending resistance is reduced by this effect compared to simple bending (section) resistance. The effect of local buckling may be considered in the structural design by using the effective areas of plate elements in compression for Class 4 sections by effective sectional properties (effective cross section method) or using stress limits for plates (reduced stress method). The reduction factor ρ depending on the plate slenderness λp is used in both of these two methods. In the first method, the effective cross-section method, the reduction factor reduces cross-section area Ac (resp. the section modulus). The effective area of the compression zone Ac;eff should be obtained from (1) as a result of effective (reduced) widths of the plates: Ac;eff ¼ ρAc
ð1Þ
In the second method, the reduced stress method, the reduction factor reduces the maximum allowed stress, where the components of the stress field ðσ x;Ed ; σ z;Ed ; τEd Þ in the ultimate limit state are considered as acting together. This method does not take into account the second-order effect in the possible shift of the neutral axis position. The advantage of this method is the possibility to use gross cross section properties for calculation, resulting in lower computational cost as it isn’t necessary to
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Fig. 1. Buckling mode shapes: (a) local buckling (left); (b) lateral-torsional buckling (right).
determine effective section properties. One (general) possibility of the verification formula is given by (2), others are given by EC3 1.5 [3]:
σ x;Ed ρx f y =γ M1
!2 þ
σ z;Ed ρz f y =γ M1
!2
σ x;Ed ρx f y =γ M1
!
!
σ z;Ed τEd þ3 ρz f y =γ M1 χ w f y =γ M1
!2 r
ρ2
ð2Þ As described above, the reduction factor depends on the plate slenderness. According to EC3 1.5 [3], the plate slenderness λp is given by Eq. (3). sffiffiffiffiffiffiffi vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u fy fy b=t b u qffiffiffiffiffiffiffi pffiffiffiffiffi ¼ pffiffiffiffiffi ¼t λp ¼ ð3Þ ¼ kσ π 2 E t 2 E σ cr ε kσ 28:4 t k 0:95 σ fy 12ð1 ν2 Þ b where σ cr is the elastic critical plate buckling stress, kσ is the buckling factor, t is the thickness of the plate, b is the appropriate width, ε is a factor depending on f y and E (f y and E to be expressed in N=mm2 ) sffiffiffiffiffiffiffiffiffi 235 ε¼ ð4Þ fy Both highlight values in Eq. (3) depends on temperature. It brings additional term, which reflects degradation of material properties, see Eq. (5): sffiffiffiffiffiffiffiffisffiffiffiffiffi kE;θ E ky;θ f y
ð5Þ
The cross-section classification is therefore different at fire situation than at normal temperature. According to EC3 1.2 [4], for the purpose of these simplified rules, the cross-sections may be classified as for normal temperature design with a reduced value
Fig. 2. Ratio of material properties reduction as a function of temperature.
3
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for ε as given by Eq. (6): " #0:5 235 εθ ¼ 0:85 fy
ð6Þ
where the reduction coefficient 0.85 represents the effect of the degradation of material properties regardless temperature and material. The correct relationship for ε taking into account influence of different temperature can be written as (7): sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi" #0:5 kE;θ 235 εθ ¼ ð7Þ ky;θ or kp0:2θ f y Compared to the real dependence of reduced material properties on temperature, apparently the simple reduction by 0.85 is sufficient and mostly safe approximation, see Fig. 2a). The Informative Annex E of EC3 1.2 [4] recommends using different value of yield strength for Class 4 section (0.2% proof strength for Class 4 instead of 2.0% total strain for stockier Class 1 to 3 sections). The effective cross-section characteristics should be calculated according the EC3 1.5 [3] (resp. EC3 1.3 [5]). This means the effective section is based on the material properties at 20 1C. The actual relationship for ε depending on temperature is shown in Fig. 2b). Determination of the bending resistance for members subjected to lateral torsional buckling of Classes 1 to 3 cross sections at elevated temperature is based on the same principles as the design at room temperature according to EC3 1.1 [2]. However, it differs in using one imperfection factor only for all types of crosssections. The procedure may be used for Class 4 sections as well, however with restriction for the maximum critical temperature and different reduction for the yield strength (Annex E). For web-tapered beams, a limited design procedure is given in the informative Annex BB of the standard EC3 1.1 [2] applicable for the room temperature only. The additional procedure is the clause
Fig. 3. Scheme of tested beam.
6.3.4 (General Method) given in EC3 1.1 [2]. The suitability of this approach for Class 1 to 3 cross-section and ambient temperature was verified in [6]. The resistance of the non-uniform members according to the General Method was analysed and compared with numerical results and the procedures of clauses 6.3.1 to 6.3.3 of EC3 1.1 [2]. For elevated temperature, the General method was validated for selected stocky sections by Couto et al. [7]. EC3 1.5, Annex B [3], gives another possible approach for non-uniform members. It considers the effect of both plate (local) and lateral torsional buckling (global) by one reduction factor. In case of member subjected to the lateral torsional buckling, the reduction factor used should be the minimum of the reduction factor ρ given by EC3 1.5 [3] in clause B1 (used for the reduction due to the local buckling) and χ LT —the reduction for lateral torsional buckling according to EC3 1.1. 6.3.2 [2]. This in fact leads to the method in clause 6.3.2., but with neglecting the local buckling effect by considering the elastic section modulus for slender beams. Resistance of non-uniform members at room temperature was also published by Marques et al. [8] or using Merchant-Rankine procedure by Braham and Hanikenne [9]. The possibility of using any of the above described rules for lateral-torsional buckling in case of fire has not been investigated yet. In the framework of the RFCS project FIDESC4—Fire Design of Steel Members with Welded or Hot-rolled Class 4 Cross-sections, several simple supported beams, submitted to four-point bending were tested to study the pure bending and the lateral torsional buckling at different temperatures.
2. Description of the experiments In the described research of slender sections at elevated temperature, four tests were carried out to study the simple bending (section resistance) and three tests for beams subjected to lateral torsional buckling. First, a preliminary numerical model for calibration of experiments was made using FE software ABAQUS [10]. In order to achieve local or global failure mode as main failure mode, different boundary condition and load distributions were modelled. Based on the numerical model development and laboratory conditions, appropriate cross-sections and procedures were chosen.
Table 1 Tested sections—simple bending. Test number
Dimensions [mm]
Classification
Test 1 (450 1C) and Test 2 (650 1C)
h ¼ 680 b ¼ 250
Web—Class 4 λp ¼ 1:44 Flange—Class 4 λp ¼ 0:66
tf ¼ 12 tw ¼ 4
Test 3 (450 1C) and Test 4 (650 1C)
h ¼ 846 b ¼ 300 tf ¼ 8 tw ¼ 5
NOTE
Classification—according to EN 1993-1-2 Plate slenderness—according to EN 1993-1-2 Annex E
Web—Class 4 λp ¼ 1:45 Flange—Class 4 λp ¼ 1:18
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Fig. 4. Tested beams: 1 to 7.
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Table 2 Tested sections—lateral torsional buckling. Test number Test 5 (450 1C)
Dimensions [mm] h ¼460 b¼ 150 tf ¼5 tw ¼ 4
Test 6 (450 1C)
h ¼460 b¼ 150
hA ¼460 hB ¼ 620
Non-dimensional slenderness
Web—Class 4
λLT ¼ 0:92 λLT;θ ¼ 0:88
λp ¼ 1:01 Flange—Class 4 λp ¼ 0:69
tf ¼7 tw ¼ 4
Test 7 Tapered beam (650 1C)
Classification Web—Class 4 λp ¼ 1:07 Flange—Class 4 λp ¼ 0:96
End—section A-B
λLT ¼ 0:91 λLT;θ ¼ 0:86
Web—Class 4 λpðAÞ ¼ 1:07 λpðBÞ ¼ 1:52 Flange—Class 4 λpðA;BÞ ¼ 0:96
b¼ 150 tf ¼7 tw ¼ 4
Fig. 5. Simple bending test setup (upper) and lateral torsional buckling test setup (lower).
A simply supported beam with two equal concentrated point loads applied symmetrically was chosen for the test, see Fig. 3. The central part of the beam (between the point loads) subjected to uniform bending moment was the only heated part. The temperature affects the plate slenderness as described above and shown in
Fig. 2b. The two temperatures selected for the tests were decided to represent the most significant change of the slenderness for the same section. These were namely 450 1C and 650 1C. Seven tests vary in the cross-sections, length of the middle and side span and temperature. Table 1 present the used
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Fig. 6. Lateral restraints.
Fig. 7. Simple bending test supports: (a) pinned; (b) roller.
cross-sections, which were fabricated by one side fillet welding. Fig. 4 summarises the tested beams dimensions and used steel plates S1–S7 for which the material properties are given later (Table 5). In case of the simple bending, two cross-sections of constant height were tested for each temperature. In these tests, the lateral movement of the beam was prevented at small distances so the failure mode was not affected by lateral torsional buckling. The length of the middle part was approximately 1500 mm (after heating). Each section was tested at temperatures 450 1C and 650 1C. The other three tests were designed to fail with major contribution of lateral torsional buckling and the lateral restrains were at larger distances. Two of the tests were performed on beams of constant section height. One test was made on a tapered beam where the height of the web varied linearly from one end to another. The length of the middle part (between the load points) of the beams was approximately 2800 mm (after heating). Free rotation and transverse deflection was allowed between load points. The section rotation was also allowed at the supports. The temperature for each section is detailed in Tables 1 and 2.
Fig. 8. Lateral restraints at the end of the tested beams (simple bending and LTB).
All tests were controlled by displacement (vertical deflection) which was estimated as 4.5 mm per minute for simple bending tests. Final deflection at midspan was 70 mm. For beams subjected
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Fig. 9. Lateral torsional buckling test supports: (a) pinned; (b) roller.
Fig. 10. Manual measurement.
Fig. 11. Simple bending tests—points of the measurement (the web and the upper flange).
to lateral torsional buckling, deformation increase was estimated as 3.5 mm per minute and the final deflection was 50 mm. The load was introduced via a distributing beam at the edges of the heated part (middle span). The load was applied by means of one hydraulic jack of 650 kN capacity. All the tests were performed on steady state, it means that the beams were first heated and then the load was applied until failure. The additional test equipment was designed as universal for the experiments. It respected boundary conditions based on the numerical analyses and is described below. Test setup for both types of the tests is illustrated in Fig. 5. It consisted of lateral restraints, supports and the load distributing beam. At the location of the load application (at the edge of the heated part), the top and the bottom flange were laterally restrained by two vertical CHS 80 5.6 supported transversally by diagonal members. Bolts above and below the tested profile section interconnected these two vertical profiles. The lateral restraints are depicted in Fig. 6. For all tests, the beams were supported at the ends under the lower flange. In the case of simple bending tests, both supports were pinned (free rotation in the direction of the strong axis). One of the supports was designed as a rolling bearing (set of horizontal rods) and allowed free horizontal displacement in the longitudinal direction (beam axis—roller). Other displacements and rotations were restricted, see Fig. 7. The restriction of lateral displacement and lateral rotation was ensured by couple of vertical profiles (UPE 100), see Fig. 8. The horizontal rectification of the vertical profiles was allowed to fit to both tested section widths. In the case of the lateral torsional buckling tests, the end supports were considered just by one point support. It was made using a high-resistance steel sphere bearing placed between two steel plates. Both end supports allowed free torsion of the end cross-section around the sphere bearing. One restrained the displacement in all directions (pinned). The second allowed also free horizontal displacement in the direction along the beam axis (roller). The prevented transverse displacement in at the supports was found to have very little effect on the beam resistance and was much easier to reach in the test. Fig. 9 shows both pinned and roller supports of the beam.
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Fig. 12. Lateral torsional buckling tests—points of the measurement (the web and the upper flange).
Fig. 13. Distribution of the imperfection amplitude along the beam—Test 1.
2.1. Measurement of the initial geometric imperfections Before the experiment, after placing the beam on the support, the initial geometry of the specimens was established using the two methods, namely manual measurements and laser scanning. The first method—manual measurement consists of amplitude measurement for global and local imperfection. Amplitude of global imperfection was measured as a deviation from a string spanned between the stiffeners (load application points). For measurements of local imperfection amplitude, a special device set with a centesimal displacement meter was used, see Fig. 10. The length of device set was chosen according to the half sine wave length corresponding to the local buckling shape for each beam calculated in ABAQUS. The investigation was made in compression zone of the beams only. Figs. 11 and 12 show the position of the measurements. The local imperfection amplitudes of the web and flange for beam test 1 to 4 are in Figs. 13–16 and in Figs. 17 and 18 for the beam test 5 to 7. For these, the side of the flange with higher imperfection amplitude is shown. Table 3
Fig. 14. Distribution of the imperfection amplitude along the beam—Test 2.
summarises the maximum amplitude of the local and global imperfection along each beam. The second method of imperfection measurement (see Fig. 19) was the laser scanning method. It is still comparatively new technology (first instrument were used about 15 years ago) and it is very effective for measuring of complex surface topography. Therefore, it was used as control method to measure the global and local initial imperfections. All tested beams were scanned before testing. Scanning resolution was set to average grid 5 5 mm on the beam surface. The result were plotted as set of longitudinal and transverse sections trough the tested beams, which adequately describes each beams geometrical properties. Eight standpoints were used to reach maximum covering of the beam surface. It took about 5 min to carry out one standpoint. Surphaser 25HSX with IR_X configuration (the second most accurate configuration) was used in all cases. It is the most accurate polar laser scanning system on the market. The most important specification of the scanner are: measurement speed up to 1.2 million points per second, field of view panoramic, accuracy
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Table 3 Local and global geometric imperfection amplitudes. Test number
Test Test Test Test Test Test Test
1 2 3 4 5 6 7
Imperfection amplitude [mm] Local-web
Local-flange
Global
4.77 1.34 2.36 1.60 7.36 5.8 7.59
1.20 1.98 1.92 0.67 2.27 0.69 2.13
– – – – 2.5 1.5 1.5
2.2. Heating of specimens
Fig. 15. Distribution of the imperfection amplitude along the beam—Test 3.
Fig. 16. Distribution of the imperfection amplitude along the beam—Test 4.
better than 0.5 mm (absolute) at 5 m, noise 0.1 mm at 3 m, measurement range 0.4–30 m. Scanner 3D data from eight standpoints was transformed to unique coordinate system using spherical control points in the Leica Cyclone software. Then, the beam part from point cloud was cut out and 3D model in the form of triangular mesh was created in the software Geomagic Studio, see Fig. 20. The last step was generation of cross and horizontal sections in 5 cm intervals see Fig. 21. Detailed information about scanning of these beams can be found in [11]. In comparison of both methods, laser scanning and manual measurement, found the imperfection amplitudes very similar, see Fig. 22.
There is not much experimental work on the behaviour of Class 4 beams at elevated temperature, but similar experiments, using the same type of heating equipment, were made on the lateral-torsional buckling of Class 1 section beams in 2003 [12] and in 2005 [13]. For the described tests, Mannings 70 kV A heat power units with 6 channels were used to heat the specimens, see Fig. 23. This unit provides a 60 V supply for powering various types of low voltage heating elements. It consists of an air natural 3 phase transformer, switching is by contactors. The output channels are controlled by means of energy regulators and the temperature controllers. Each channel has its own auto/manual switch so any combination of channels can be operated either auto or manual. Cable connection of 70 kV A consists of 6 triple cable sets and 4-way splitter cables can accommodate total of 24 flexible ceramic heating pads attached. Maximum connected load for the 70 kV A unit is 64.8 kW. In order to be able to heat two different beams of the experimental tests, universal size of the ceramic pads was used: 305 165 mm. Ceramic heating elements are constructed from nickel-chrome core wire and nickel cold tail wire, which is electrically insulated by interlocking high grade sintered alumina ceramic beads. The construction allows the heating element to be flexible and provides high heat transfer efficiency. The heating pads are able to reach a maximum temperature of 1200 1C, working temperature capability is 1050 1C at a heating rate 10 1C/min. In the first step, the pads were put on the rod rack in order to maintain the position of the heating elements on the web. On the bottom flange, the pads were fixed with steel wire. On the top flange, the pads were fixed with adhesive tape only. They were placed on the outer surface of the flanges. For the web, they were attached from one side only, where the side was alternated along the beam length (Fig. 24). Two types of material were used for the beams insulation. First, the space between the flanges and the outer surface of the flanges was insulated by standard mineral wool (ROCKWOOL Airrock HD). The wool was fixed on the beam with steel wires. Second, the middle span was wrapped by super wool insulation material, see Fig. 25. Seventeen thermocouples were used for the temperature measurement. Eleven of them were placed in the middle span and six were placed in the side spans for monitoring of the temperature in not-heated section. For lateral torsional buckling test, where the middle span was longer, twenty thermocouples were used in the middle span and four in the side spans. The thermocouples were distributed on the beam according to the position of ceramic pads, as shown and numbered in Fig. 24. Beam temperatures were recorded from the beginning of heating to the end of the experiment. The average measured temperatures during the loading can be found in Table 4 for each part of the beam separately. The temperature of the bottom flange was lower
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Fig. 17. Local imperfection amplitude along the web—lateral torsional buckling Test 5 to 7.
Fig. 18. Local imperfection amplitude along the upper flange—lateral torsional buckling Test 5 to 7.
Fig. 19. Laser scanner.
Fig. 20. Beam triangular mesh model.
as result of worse contact between beam and ceramic pads. The sets of four heating pads were controlled by one thermocouple. The displacements were measured by potentiometers. For the simple bending test, two potentiometers were used for measurement of the vertical displacement in the locations of load application and one at the mid span. For the lateral torsional bending test,
two potentiometers were place in the locations of load application, as in the previous case. Vertical (VD) and horizontal (HD) deflection of the bottom flange centre and section rotation (R) of the beam at mid-span were calculated from measurement of four potentiometers. Two measured vertical deflection and two horizontal one for two points of the section (see Fig. 26).
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Fig. 21. Cross and horizontal beam sections.
Table 4 Temperature during the tests. Test number
Fig. 22. Comparison between manual measurement and laser scanning for web of beam.
Test Test Test Test Test Test Test
1 2 3 4 5 6 7
Average temperature [1C] Upper flange
Bottom flange
Web
444 654 481 661 457 481 624
469 636 425 631 354 369 416
458 649 431 641 444 443 567
3. Numerical analyses and its comparison with experiments
Fig. 23. Mannings heat power units.
2.3. Material properties For possible model validation, material properties for each part of the welded section were measured at ambient temperature and at elevated temperature, namely 450 1C and 650 1C. The tensile coupon tests were carried out in accordance with EN ISO 6892-1 [14] to determine the basic engineering stress-strain response of the material. The measured values of yield strength for each plate as were define in Fig. 4 and temperature are presented in Table 5.
The tests were replicated by means of the finite element method program ABAQUS [10]. The ABAQUS code is general software and allows a complete solution for a large range of problems, including the analysis of structures under fire. Static calculation was used in this case. The same models as for preliminary numerical simulation were used. The beam was meshed using quadrilateral conventional shell elements (namely type S4). Conventional shell elements discretize a body by defining the geometry at a reference surface. In this case the thickness is defined through the section property definition. Conventional shell elements have 3 displacement and 3 rotational degrees of freedom per node. Element type S4 is a fully integrated, generalpurpose, finite-membrane-strain shell element. The element has four integration points per element. All experimental data have been used for validation of the numerical model. Both local and global (if any) geometrical imperfections were introduced into the geometrically and materially nonlinear analysis. The material law was defined by elastic–plastic nonlinear stress–strain diagram, where enough data points were used. The true material stress–strain relationship was calculated from the static engineering strass–strain curves obtained from the coupon tests at room temperature. The reductions of material properties as well as the material nonlinearity were taken from the EC3 1.2 [4] as only two levels of elevated temperature were tested and mostly confirmed the established reduction factors. The measured average temperatures from each heated part of the beams were introduced to the model. Adjacent parts of the beam and stiffeners were modelled as in room temperature (20 1C).
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Fig. 24. Layout of flexible ceramic pads and thermocouples (numbered).
Fig. 25. Isolation of the beam.
The numerical models were loaded by displacements. The steel thermal expansion was not modelled directly, but the middle spans were set as 1500 mm resp. 2800 mm (expected length after the thermal expansion). The measured values of the steel mechanical properties (yield strength and modulus of elasticity) and the measured temperatures were adopted in the models. All experimental data were used for the numerical model validation. Generally, the residual stresses have a negligible influence on the sectional resistance [15] at elevated temperature. For beams subjected to lateral torsional buckling, the influence was found to be notable. It was more than 4% decrease of the resistance for the tested beams if generalised residual stress patterns (published also
in [15]) were used. However, the residual stresses were not measured for the tested beams and newer investigated for the specific fabrication method (one side fillet weld) which is believed to lead to a lower stress levels due to the lower heat input by welding. No residual stresses were therefore considered in the validation. 3.1. Simple bending tests For each model of the beam, web was formed by 200 elements along the length and by 16 elements along the height of the crosssection. Upper and lower flanges were modelled by 6 elements
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across the width of the cross-section. The structural mesh and boundary conditions are shown in Fig. 27. The mesh coarseness was established by a sensitivity study. Initial imperfections were modelled by the actual measured imperfections of the beams. The individual curves describing the shape imperfections (see from Figs.13–16) were replaced by a sinusoidal function for simplification with the maximum amplitude taken from Table 3. In the next table and figures, the results obtained in the fire tests are compared to the results obtained by the numerical simulations. The load corresponds to the total force imposed on the two load application points. The shown displacement corresponds to the vertical displacement at the bottom flange at mid
span. Failure mode of the tests and the numerical model is also compared in the figures (Figs. 28 and 29). They show the deformed shape of the central heated part of the beam for Test 1 and Test 2, Figs. 30 and 31 for Test 3 and Test 4. Comparison of load– deflection curves are depicted in Figs. 32 and 33.
3.2. Lateral torsional buckling tests A similar mesh geometry was used as for the previous model. But 20 elements for web height and 4 elements per 100 mm of the beam length were used. The mesh and boundary conditions are shown in Fig. 34. Initial global and local geometric imperfections were included to the model by means of the elastic buckling eigenmodes. Two imperfection shapes were considered: the beam first local buckling mode and first global buckling mode (LTB) shapes, see Fig. 35. The imperfection amplitudes were based on the initial geometry measurements. In test below, the experimental results are compared with the numerical results. Figs. 36–38 show the beams after tests (Test 5 to 7). As can be observed from Fig. 39, the obtained failure shapes were very close to numerical prediction. Comparison of load– deflection curves are in Fig. 40.
Fig. 26. Measurement of vertical displacement (VD), horizontal displacement (HD) and section rotation (R) at beam midspan.
Table 5 Steel plates yield strength (S355). Part
S1
S2
S3
S4
S5
S6
Upper yield stress ReH [MPa] Lower yield stress ReL [MPa] Yield stress R0.2 at 450 1C [MPa] Yield stress R2.0 at 450 1C [MPa] Yield stress R0.2 at 650 1C [MPa] Yield stress R2.0 at 650 1C [MPa]
430 424 349 399 125 126
394 392 260 310 76 84
388 384 271 328 109 118
376 361 – – – –
385 435 260 318 98 108
435 408 272 330 – –
Fig. 28. Failure mode—Test 1, (a) numerical simulation; (b) experiment.
Fig. 27. Loading and boundary conditions for the simple bending test model.
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Fig. 29. Failure mode—Test 2, (a) numerical simulation; (b) experiment.
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Fig. 31. Failure mode—Test 4, (a) numerical simulation; (b) experiment.
Fig. 30. Failure mode—Test 3, (a) numerical simulation; (b) experiment. Fig. 32. Load–deflection diagram for Test 1 (left) and 2 (right).
4. Discussion of the results Numerical simulations exhibit similar behaviour as the beams during the experiment. As seen in Table 6 and Fig. 41, the difference between the resistance calculated by ABAQUS and obtained from the test is less than 3% for the simple bending test. Whereas the results obtained for the beams subjected to the lateral torsional buckling shows bigger difference (15% in average). This demonstrates the difficulties of lateral torsional buckling tests, which are highlighted by the elevated temperature. A problem with lateral restraints occurred during Test 5. The experimental curve of load displacement relationship is not smooth and the force is unnaturally increasing, see Fig. 40. Besides
that, the experimentally obtained initial stiffness is different from the numerical curves mainly in Test 5 and 7. Overall the approximations are reasonable considering the nature of the different parameters involved in the presented tests, as for instance the heating process. The numerical model was able to predict the behaviour (load capacity and failure mode) of beams observed in the tests.
5. Conclusions The paper presents experiments and numerical modelling of seven steel beams at elevated temperature. All beams were of
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Fig. 36. Test 5—beam after the test.
Fig. 33. Load-deflection diagram for Test 3 and 4.
Fig. 34. Loading and boundary conditions for the lateral torsional buckling test model.
Fig. 37. Test 6—beam after the test.
Fig. 38. Test 7—beam after the test.
Fig. 35. Beams buckling modes shape: (a) local; (b) global.
slender Class 4 open I-section fabricated by welding. Four beams were tested by simple bending and additional three with influence of the lateral torsional buckling. The elevated temperature was induced by heat power units and the tests were carried out in
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Fig. 39. Failure mode carried by: (a) ABAQUS analysis; (b) experiment.
Fig. 40. Load–displacement diagram for the lateral torsional buckling tests: experimental and numerical.
Table 6 Summary of tests results vs. numerical results. Test Cross-section hw x t w bf x t f
1 2 3 4 5 6 7
656 4 250 12 656 4 250 12 830 5 300 8 830 5 300 8 450 4 150 5 446 4 150 7 (610–450) 4–150 5
Load capacity [kN] Difference between the experiment and FEM [%] Experiment FEM 637.82 230.61 484.68 201.22 134.59 189.05 70.96
640.52 0.42 236.99 2.69 498.01 2.68 195.91 2.64 107.2 25.56 151.84 24.05 74.11 4.25 Fig. 41. Comparison of test results with numerical results.
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standard laboratory conditions. For all tests, the necessary characteristics were measured. Namely the initial geometric imperfections and material properties at both room and elevated temperature. The results of the numerical models were compared to the tests and found reasonably close, especially for the simple bending tests. Therefore the numerical model may be used for possible calculation of beam load-capacity or further parametric study.
Acknowledgement The presented research was supported by the RFCS research project FIDESC4 - Fire Design of Steel Members (Grant Agreement Number: RFSR-CT-2011-00030) with Welded or Hot-rolled Class 4 Cross-sections. References [1] Renaud, C, Zhao B. Investigation of simple calculation method in EN 1993-1-2 for buckling of hot rolled Class 4 steel members exposed to fire. In: Structures in fire: proceedings of the fourth international conference, Aveiro, Portugal; 2006, pp. 199–211. [2] CEN European Committee for Standardisation, EN 1993-1-1. Eurocode 3— design of steel structures. Part 1–1, General rules and rules for buildings, CEN Brussels; 2005. [3] CEN European Committee for Standardisation, EN 1993-1-5, Eurocode 3, design of steel structures—Part 1–5: Plated structural elements, Brussels, Belgium; 2005.
[4] CEN European Committee for Standardisation, EN 1993-1-2, Eurocode 3-design of steel structures-Part 1–2: general rules structural fire design; 2005. [5] CEN European Committee for Standardisation, EN 1993-1-3, Eurocode 3 – design of steel structures – Part 1–3: general rules – supplementary rules for cold-formed members and sheeting; 2006. [6] Marques, L, Simões da Silva, L Rebelo, C. Application of the general method for the evaluation of the stability resistance of non-uniform members. In: Proceedings of ICASS, Hong Kong, 16–18 December; 2009. [7] Couto, C, Vila Real, PMM Ferreira, J Lopes, N. Numerical validation of the General Method for structural fire design of web-tapered beams. In: EUROSTEEL 2014—seventh European conference on steel and composite structures, Naples, Italy, September; 2014. [8] Marques L, Simões da Silva L, Greiner R, Rebelo C, Taras A. Development of a consistent design procedure for lateral-torsional buckling of tapered beams. J Construct Steel Res 2013;89:213–35. [9] Braham M, Hanikenne D. Lateral buckling of web tapered beams: an original design method confronted with a computer simulation. J Construct Steel Res 1993;27:23–36. [10] Hibbitt, Karlsson & Sorensen, ABAQUS: Analysis user’s manual, Volumes I–IV, version 6.10, Inc., Providence, R.I, USA, 2010. [11] Kremen, T, Koska, B. Determination of the initial shape and the deformation of the steel beams with high accuracy during the stress tests using laser scanning technology. In: Thirteenth international multidisciplinary scientific geoconference and EXPO, Albena; Bulgaria; 2013, pp. 601–608. [12] Vila Real PMM, Piloto PAG, Franssen JM. A new proposal of a simple model for the lateral-torsional buckling of unrestrained steel I-beams in case of fire: experimental and numerical validation. J Construct Steel Res 2003;59:179–99. [13] Mesquita L, Piloto P, Vaz M, Vila Real P. Experimental and numerical research on the critical temperature of laterally unrestrained steel I beams. J Construct Steel Res 2005;61:1435–46. [14] EN ISO 6892-1, International Standard, Metallic materials – tensile testing – Part 1: Method of test at room temperature, Switzerland; 2009. [15] Couto C, Vila Real P, Lopes N, Zhao B. Effective width method to account for the local buckling of steel thin plates at elevated temperatures. Thin-Walled Struct 2014;84:134–49.
Contents lists available at ScienceDirect
Thin-Walled Structures journal homepage: www.elsevier.com/locate/tws
Experiments of Class 4 open section beams at elevated temperature Martin Prachar a,n, Jan Hricak a, Michal Jandera a,n, Frantisek Wald a, Bin Zhao b a b
Faculty of Civil Engineering, Czech Technical University in Prague, Thakurova 7, Praha, Czech Republic CTICM, Centre Technique Industriel de la Construction Métallique, Saint-Aubin, France
art ic l e i nf o
a b s t r a c t
Available online 15 May 2015
At elevated temperature, behaviour of Class 1 to 3 open cross-section beams have been investigated experimentally and numerically, whereas for slender Class 4 sections only few experimental data have been collected. Due to the economic assumptions of members with Class 4 cross section and general validity of the existing design rules, further investigation is desired. This paper presents tests and numerical simulation of welded slender (Class 4) I-section beams at elevated temperature. The design of the test set-up, as well as progress of the experiments is presented. Detailed information about the geometrical data, measured geometrical imperfections, temperature, load and actual mechanical properties were collected. The tests were subsequently used for a FE model validation. The described research allows better understanding to the fire behaviour of steel members of Class 4 crosssection beams. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Slender section Elevated temperature Lateral torsional buckling Tapered beam
1. Introduction The area of research in slender cross-sections in case of fire is very important as only little investigation was made and structural fire design became an inseparable part of structural design. The correctness of the design is essential regarding safety of the structure as well as its economy, concerning also possible additional fire protection costs. Therefore, well representing design models, which simulate the actual behaviour of the structures exposed to fire, are crucial as a base of such design formulas. Steel members with thin-walled cross-sections are commonly used in buildings due to its lightness and long span capacity. The design principles of Class 4 sections are very specific and usually more difficult than for stocky sections. Despite the current EC3 contains a number of simple rules for design of Class 4 crosssections at elevated temperature, based on recent numerical simulations they were found to be not accurate [1]. Through refining these rules, a significant material savings could be achieved which would lead to higher competitiveness of the steel structures. However, the lack of numerical and experimental data have been collected until now, which may serve as a base to such changes. The structural steel members of slender cross-sections (Class 4 section according to EC3 1.1 [2]) subjected to bending are
n
Corresponding authors. E-mail addresses: [email protected] (M. Prachar), [email protected] (J. Hricak), [email protected] (M. Jandera), [email protected] (F. Wald), [email protected] (B. Zhao). http://dx.doi.org/10.1016/j.tws.2015.04.025 0263-8231/& 2015 Elsevier Ltd. All rights reserved.
characterized by having the possibility of failure by both local and global buckling modes. The local buckling mode occurs due to the compression of thin plates in the section (see Fig. 1a). Therefore, the section resistance is significantly affected by deformations of the area in compression. The lateral torsional buckling (global buckling mode for members in bending) is an instability induced by the compressed flange of unrestrained open section beams subjected to bending around the major axis as shown in Fig. 1b. The actual bending resistance is reduced by this effect compared to simple bending (section) resistance. The effect of local buckling may be considered in the structural design by using the effective areas of plate elements in compression for Class 4 sections by effective sectional properties (effective cross section method) or using stress limits for plates (reduced stress method). The reduction factor ρ depending on the plate slenderness λp is used in both of these two methods. In the first method, the effective cross-section method, the reduction factor reduces cross-section area Ac (resp. the section modulus). The effective area of the compression zone Ac;eff should be obtained from (1) as a result of effective (reduced) widths of the plates: Ac;eff ¼ ρAc
ð1Þ
In the second method, the reduced stress method, the reduction factor reduces the maximum allowed stress, where the components of the stress field ðσ x;Ed ; σ z;Ed ; τEd Þ in the ultimate limit state are considered as acting together. This method does not take into account the second-order effect in the possible shift of the neutral axis position. The advantage of this method is the possibility to use gross cross section properties for calculation, resulting in lower computational cost as it isn’t necessary to
M. Prachar et al. / Thin-Walled Structures 98 (2016) 2–18
Fig. 1. Buckling mode shapes: (a) local buckling (left); (b) lateral-torsional buckling (right).
determine effective section properties. One (general) possibility of the verification formula is given by (2), others are given by EC3 1.5 [3]:
σ x;Ed ρx f y =γ M1
!2 þ
σ z;Ed ρz f y =γ M1
!2
σ x;Ed ρx f y =γ M1
!
!
σ z;Ed τEd þ3 ρz f y =γ M1 χ w f y =γ M1
!2 r
ρ2
ð2Þ As described above, the reduction factor depends on the plate slenderness. According to EC3 1.5 [3], the plate slenderness λp is given by Eq. (3). sffiffiffiffiffiffiffi vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u fy fy b=t b u qffiffiffiffiffiffiffi pffiffiffiffiffi ¼ pffiffiffiffiffi ¼t λp ¼ ð3Þ ¼ kσ π 2 E t 2 E σ cr ε kσ 28:4 t k 0:95 σ fy 12ð1 ν2 Þ b where σ cr is the elastic critical plate buckling stress, kσ is the buckling factor, t is the thickness of the plate, b is the appropriate width, ε is a factor depending on f y and E (f y and E to be expressed in N=mm2 ) sffiffiffiffiffiffiffiffiffi 235 ε¼ ð4Þ fy Both highlight values in Eq. (3) depends on temperature. It brings additional term, which reflects degradation of material properties, see Eq. (5): sffiffiffiffiffiffiffiffisffiffiffiffiffi kE;θ E ky;θ f y
ð5Þ
The cross-section classification is therefore different at fire situation than at normal temperature. According to EC3 1.2 [4], for the purpose of these simplified rules, the cross-sections may be classified as for normal temperature design with a reduced value
Fig. 2. Ratio of material properties reduction as a function of temperature.
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for ε as given by Eq. (6): " #0:5 235 εθ ¼ 0:85 fy
ð6Þ
where the reduction coefficient 0.85 represents the effect of the degradation of material properties regardless temperature and material. The correct relationship for ε taking into account influence of different temperature can be written as (7): sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi" #0:5 kE;θ 235 εθ ¼ ð7Þ ky;θ or kp0:2θ f y Compared to the real dependence of reduced material properties on temperature, apparently the simple reduction by 0.85 is sufficient and mostly safe approximation, see Fig. 2a). The Informative Annex E of EC3 1.2 [4] recommends using different value of yield strength for Class 4 section (0.2% proof strength for Class 4 instead of 2.0% total strain for stockier Class 1 to 3 sections). The effective cross-section characteristics should be calculated according the EC3 1.5 [3] (resp. EC3 1.3 [5]). This means the effective section is based on the material properties at 20 1C. The actual relationship for ε depending on temperature is shown in Fig. 2b). Determination of the bending resistance for members subjected to lateral torsional buckling of Classes 1 to 3 cross sections at elevated temperature is based on the same principles as the design at room temperature according to EC3 1.1 [2]. However, it differs in using one imperfection factor only for all types of crosssections. The procedure may be used for Class 4 sections as well, however with restriction for the maximum critical temperature and different reduction for the yield strength (Annex E). For web-tapered beams, a limited design procedure is given in the informative Annex BB of the standard EC3 1.1 [2] applicable for the room temperature only. The additional procedure is the clause
Fig. 3. Scheme of tested beam.
6.3.4 (General Method) given in EC3 1.1 [2]. The suitability of this approach for Class 1 to 3 cross-section and ambient temperature was verified in [6]. The resistance of the non-uniform members according to the General Method was analysed and compared with numerical results and the procedures of clauses 6.3.1 to 6.3.3 of EC3 1.1 [2]. For elevated temperature, the General method was validated for selected stocky sections by Couto et al. [7]. EC3 1.5, Annex B [3], gives another possible approach for non-uniform members. It considers the effect of both plate (local) and lateral torsional buckling (global) by one reduction factor. In case of member subjected to the lateral torsional buckling, the reduction factor used should be the minimum of the reduction factor ρ given by EC3 1.5 [3] in clause B1 (used for the reduction due to the local buckling) and χ LT —the reduction for lateral torsional buckling according to EC3 1.1. 6.3.2 [2]. This in fact leads to the method in clause 6.3.2., but with neglecting the local buckling effect by considering the elastic section modulus for slender beams. Resistance of non-uniform members at room temperature was also published by Marques et al. [8] or using Merchant-Rankine procedure by Braham and Hanikenne [9]. The possibility of using any of the above described rules for lateral-torsional buckling in case of fire has not been investigated yet. In the framework of the RFCS project FIDESC4—Fire Design of Steel Members with Welded or Hot-rolled Class 4 Cross-sections, several simple supported beams, submitted to four-point bending were tested to study the pure bending and the lateral torsional buckling at different temperatures.
2. Description of the experiments In the described research of slender sections at elevated temperature, four tests were carried out to study the simple bending (section resistance) and three tests for beams subjected to lateral torsional buckling. First, a preliminary numerical model for calibration of experiments was made using FE software ABAQUS [10]. In order to achieve local or global failure mode as main failure mode, different boundary condition and load distributions were modelled. Based on the numerical model development and laboratory conditions, appropriate cross-sections and procedures were chosen.
Table 1 Tested sections—simple bending. Test number
Dimensions [mm]
Classification
Test 1 (450 1C) and Test 2 (650 1C)
h ¼ 680 b ¼ 250
Web—Class 4 λp ¼ 1:44 Flange—Class 4 λp ¼ 0:66
tf ¼ 12 tw ¼ 4
Test 3 (450 1C) and Test 4 (650 1C)
h ¼ 846 b ¼ 300 tf ¼ 8 tw ¼ 5
NOTE
Classification—according to EN 1993-1-2 Plate slenderness—according to EN 1993-1-2 Annex E
Web—Class 4 λp ¼ 1:45 Flange—Class 4 λp ¼ 1:18
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Fig. 4. Tested beams: 1 to 7.
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Table 2 Tested sections—lateral torsional buckling. Test number Test 5 (450 1C)
Dimensions [mm] h ¼460 b¼ 150 tf ¼5 tw ¼ 4
Test 6 (450 1C)
h ¼460 b¼ 150
hA ¼460 hB ¼ 620
Non-dimensional slenderness
Web—Class 4
λLT ¼ 0:92 λLT;θ ¼ 0:88
λp ¼ 1:01 Flange—Class 4 λp ¼ 0:69
tf ¼7 tw ¼ 4
Test 7 Tapered beam (650 1C)
Classification Web—Class 4 λp ¼ 1:07 Flange—Class 4 λp ¼ 0:96
End—section A-B
λLT ¼ 0:91 λLT;θ ¼ 0:86
Web—Class 4 λpðAÞ ¼ 1:07 λpðBÞ ¼ 1:52 Flange—Class 4 λpðA;BÞ ¼ 0:96
b¼ 150 tf ¼7 tw ¼ 4
Fig. 5. Simple bending test setup (upper) and lateral torsional buckling test setup (lower).
A simply supported beam with two equal concentrated point loads applied symmetrically was chosen for the test, see Fig. 3. The central part of the beam (between the point loads) subjected to uniform bending moment was the only heated part. The temperature affects the plate slenderness as described above and shown in
Fig. 2b. The two temperatures selected for the tests were decided to represent the most significant change of the slenderness for the same section. These were namely 450 1C and 650 1C. Seven tests vary in the cross-sections, length of the middle and side span and temperature. Table 1 present the used
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Fig. 6. Lateral restraints.
Fig. 7. Simple bending test supports: (a) pinned; (b) roller.
cross-sections, which were fabricated by one side fillet welding. Fig. 4 summarises the tested beams dimensions and used steel plates S1–S7 for which the material properties are given later (Table 5). In case of the simple bending, two cross-sections of constant height were tested for each temperature. In these tests, the lateral movement of the beam was prevented at small distances so the failure mode was not affected by lateral torsional buckling. The length of the middle part was approximately 1500 mm (after heating). Each section was tested at temperatures 450 1C and 650 1C. The other three tests were designed to fail with major contribution of lateral torsional buckling and the lateral restrains were at larger distances. Two of the tests were performed on beams of constant section height. One test was made on a tapered beam where the height of the web varied linearly from one end to another. The length of the middle part (between the load points) of the beams was approximately 2800 mm (after heating). Free rotation and transverse deflection was allowed between load points. The section rotation was also allowed at the supports. The temperature for each section is detailed in Tables 1 and 2.
Fig. 8. Lateral restraints at the end of the tested beams (simple bending and LTB).
All tests were controlled by displacement (vertical deflection) which was estimated as 4.5 mm per minute for simple bending tests. Final deflection at midspan was 70 mm. For beams subjected
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Fig. 9. Lateral torsional buckling test supports: (a) pinned; (b) roller.
Fig. 10. Manual measurement.
Fig. 11. Simple bending tests—points of the measurement (the web and the upper flange).
to lateral torsional buckling, deformation increase was estimated as 3.5 mm per minute and the final deflection was 50 mm. The load was introduced via a distributing beam at the edges of the heated part (middle span). The load was applied by means of one hydraulic jack of 650 kN capacity. All the tests were performed on steady state, it means that the beams were first heated and then the load was applied until failure. The additional test equipment was designed as universal for the experiments. It respected boundary conditions based on the numerical analyses and is described below. Test setup for both types of the tests is illustrated in Fig. 5. It consisted of lateral restraints, supports and the load distributing beam. At the location of the load application (at the edge of the heated part), the top and the bottom flange were laterally restrained by two vertical CHS 80 5.6 supported transversally by diagonal members. Bolts above and below the tested profile section interconnected these two vertical profiles. The lateral restraints are depicted in Fig. 6. For all tests, the beams were supported at the ends under the lower flange. In the case of simple bending tests, both supports were pinned (free rotation in the direction of the strong axis). One of the supports was designed as a rolling bearing (set of horizontal rods) and allowed free horizontal displacement in the longitudinal direction (beam axis—roller). Other displacements and rotations were restricted, see Fig. 7. The restriction of lateral displacement and lateral rotation was ensured by couple of vertical profiles (UPE 100), see Fig. 8. The horizontal rectification of the vertical profiles was allowed to fit to both tested section widths. In the case of the lateral torsional buckling tests, the end supports were considered just by one point support. It was made using a high-resistance steel sphere bearing placed between two steel plates. Both end supports allowed free torsion of the end cross-section around the sphere bearing. One restrained the displacement in all directions (pinned). The second allowed also free horizontal displacement in the direction along the beam axis (roller). The prevented transverse displacement in at the supports was found to have very little effect on the beam resistance and was much easier to reach in the test. Fig. 9 shows both pinned and roller supports of the beam.
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Fig. 12. Lateral torsional buckling tests—points of the measurement (the web and the upper flange).
Fig. 13. Distribution of the imperfection amplitude along the beam—Test 1.
2.1. Measurement of the initial geometric imperfections Before the experiment, after placing the beam on the support, the initial geometry of the specimens was established using the two methods, namely manual measurements and laser scanning. The first method—manual measurement consists of amplitude measurement for global and local imperfection. Amplitude of global imperfection was measured as a deviation from a string spanned between the stiffeners (load application points). For measurements of local imperfection amplitude, a special device set with a centesimal displacement meter was used, see Fig. 10. The length of device set was chosen according to the half sine wave length corresponding to the local buckling shape for each beam calculated in ABAQUS. The investigation was made in compression zone of the beams only. Figs. 11 and 12 show the position of the measurements. The local imperfection amplitudes of the web and flange for beam test 1 to 4 are in Figs. 13–16 and in Figs. 17 and 18 for the beam test 5 to 7. For these, the side of the flange with higher imperfection amplitude is shown. Table 3
Fig. 14. Distribution of the imperfection amplitude along the beam—Test 2.
summarises the maximum amplitude of the local and global imperfection along each beam. The second method of imperfection measurement (see Fig. 19) was the laser scanning method. It is still comparatively new technology (first instrument were used about 15 years ago) and it is very effective for measuring of complex surface topography. Therefore, it was used as control method to measure the global and local initial imperfections. All tested beams were scanned before testing. Scanning resolution was set to average grid 5 5 mm on the beam surface. The result were plotted as set of longitudinal and transverse sections trough the tested beams, which adequately describes each beams geometrical properties. Eight standpoints were used to reach maximum covering of the beam surface. It took about 5 min to carry out one standpoint. Surphaser 25HSX with IR_X configuration (the second most accurate configuration) was used in all cases. It is the most accurate polar laser scanning system on the market. The most important specification of the scanner are: measurement speed up to 1.2 million points per second, field of view panoramic, accuracy
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Table 3 Local and global geometric imperfection amplitudes. Test number
Test Test Test Test Test Test Test
1 2 3 4 5 6 7
Imperfection amplitude [mm] Local-web
Local-flange
Global
4.77 1.34 2.36 1.60 7.36 5.8 7.59
1.20 1.98 1.92 0.67 2.27 0.69 2.13
– – – – 2.5 1.5 1.5
2.2. Heating of specimens
Fig. 15. Distribution of the imperfection amplitude along the beam—Test 3.
Fig. 16. Distribution of the imperfection amplitude along the beam—Test 4.
better than 0.5 mm (absolute) at 5 m, noise 0.1 mm at 3 m, measurement range 0.4–30 m. Scanner 3D data from eight standpoints was transformed to unique coordinate system using spherical control points in the Leica Cyclone software. Then, the beam part from point cloud was cut out and 3D model in the form of triangular mesh was created in the software Geomagic Studio, see Fig. 20. The last step was generation of cross and horizontal sections in 5 cm intervals see Fig. 21. Detailed information about scanning of these beams can be found in [11]. In comparison of both methods, laser scanning and manual measurement, found the imperfection amplitudes very similar, see Fig. 22.
There is not much experimental work on the behaviour of Class 4 beams at elevated temperature, but similar experiments, using the same type of heating equipment, were made on the lateral-torsional buckling of Class 1 section beams in 2003 [12] and in 2005 [13]. For the described tests, Mannings 70 kV A heat power units with 6 channels were used to heat the specimens, see Fig. 23. This unit provides a 60 V supply for powering various types of low voltage heating elements. It consists of an air natural 3 phase transformer, switching is by contactors. The output channels are controlled by means of energy regulators and the temperature controllers. Each channel has its own auto/manual switch so any combination of channels can be operated either auto or manual. Cable connection of 70 kV A consists of 6 triple cable sets and 4-way splitter cables can accommodate total of 24 flexible ceramic heating pads attached. Maximum connected load for the 70 kV A unit is 64.8 kW. In order to be able to heat two different beams of the experimental tests, universal size of the ceramic pads was used: 305 165 mm. Ceramic heating elements are constructed from nickel-chrome core wire and nickel cold tail wire, which is electrically insulated by interlocking high grade sintered alumina ceramic beads. The construction allows the heating element to be flexible and provides high heat transfer efficiency. The heating pads are able to reach a maximum temperature of 1200 1C, working temperature capability is 1050 1C at a heating rate 10 1C/min. In the first step, the pads were put on the rod rack in order to maintain the position of the heating elements on the web. On the bottom flange, the pads were fixed with steel wire. On the top flange, the pads were fixed with adhesive tape only. They were placed on the outer surface of the flanges. For the web, they were attached from one side only, where the side was alternated along the beam length (Fig. 24). Two types of material were used for the beams insulation. First, the space between the flanges and the outer surface of the flanges was insulated by standard mineral wool (ROCKWOOL Airrock HD). The wool was fixed on the beam with steel wires. Second, the middle span was wrapped by super wool insulation material, see Fig. 25. Seventeen thermocouples were used for the temperature measurement. Eleven of them were placed in the middle span and six were placed in the side spans for monitoring of the temperature in not-heated section. For lateral torsional buckling test, where the middle span was longer, twenty thermocouples were used in the middle span and four in the side spans. The thermocouples were distributed on the beam according to the position of ceramic pads, as shown and numbered in Fig. 24. Beam temperatures were recorded from the beginning of heating to the end of the experiment. The average measured temperatures during the loading can be found in Table 4 for each part of the beam separately. The temperature of the bottom flange was lower
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Fig. 17. Local imperfection amplitude along the web—lateral torsional buckling Test 5 to 7.
Fig. 18. Local imperfection amplitude along the upper flange—lateral torsional buckling Test 5 to 7.
Fig. 19. Laser scanner.
Fig. 20. Beam triangular mesh model.
as result of worse contact between beam and ceramic pads. The sets of four heating pads were controlled by one thermocouple. The displacements were measured by potentiometers. For the simple bending test, two potentiometers were used for measurement of the vertical displacement in the locations of load application and one at the mid span. For the lateral torsional bending test,
two potentiometers were place in the locations of load application, as in the previous case. Vertical (VD) and horizontal (HD) deflection of the bottom flange centre and section rotation (R) of the beam at mid-span were calculated from measurement of four potentiometers. Two measured vertical deflection and two horizontal one for two points of the section (see Fig. 26).
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Fig. 21. Cross and horizontal beam sections.
Table 4 Temperature during the tests. Test number
Fig. 22. Comparison between manual measurement and laser scanning for web of beam.
Test Test Test Test Test Test Test
1 2 3 4 5 6 7
Average temperature [1C] Upper flange
Bottom flange
Web
444 654 481 661 457 481 624
469 636 425 631 354 369 416
458 649 431 641 444 443 567
3. Numerical analyses and its comparison with experiments
Fig. 23. Mannings heat power units.
2.3. Material properties For possible model validation, material properties for each part of the welded section were measured at ambient temperature and at elevated temperature, namely 450 1C and 650 1C. The tensile coupon tests were carried out in accordance with EN ISO 6892-1 [14] to determine the basic engineering stress-strain response of the material. The measured values of yield strength for each plate as were define in Fig. 4 and temperature are presented in Table 5.
The tests were replicated by means of the finite element method program ABAQUS [10]. The ABAQUS code is general software and allows a complete solution for a large range of problems, including the analysis of structures under fire. Static calculation was used in this case. The same models as for preliminary numerical simulation were used. The beam was meshed using quadrilateral conventional shell elements (namely type S4). Conventional shell elements discretize a body by defining the geometry at a reference surface. In this case the thickness is defined through the section property definition. Conventional shell elements have 3 displacement and 3 rotational degrees of freedom per node. Element type S4 is a fully integrated, generalpurpose, finite-membrane-strain shell element. The element has four integration points per element. All experimental data have been used for validation of the numerical model. Both local and global (if any) geometrical imperfections were introduced into the geometrically and materially nonlinear analysis. The material law was defined by elastic–plastic nonlinear stress–strain diagram, where enough data points were used. The true material stress–strain relationship was calculated from the static engineering strass–strain curves obtained from the coupon tests at room temperature. The reductions of material properties as well as the material nonlinearity were taken from the EC3 1.2 [4] as only two levels of elevated temperature were tested and mostly confirmed the established reduction factors. The measured average temperatures from each heated part of the beams were introduced to the model. Adjacent parts of the beam and stiffeners were modelled as in room temperature (20 1C).
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Fig. 24. Layout of flexible ceramic pads and thermocouples (numbered).
Fig. 25. Isolation of the beam.
The numerical models were loaded by displacements. The steel thermal expansion was not modelled directly, but the middle spans were set as 1500 mm resp. 2800 mm (expected length after the thermal expansion). The measured values of the steel mechanical properties (yield strength and modulus of elasticity) and the measured temperatures were adopted in the models. All experimental data were used for the numerical model validation. Generally, the residual stresses have a negligible influence on the sectional resistance [15] at elevated temperature. For beams subjected to lateral torsional buckling, the influence was found to be notable. It was more than 4% decrease of the resistance for the tested beams if generalised residual stress patterns (published also
in [15]) were used. However, the residual stresses were not measured for the tested beams and newer investigated for the specific fabrication method (one side fillet weld) which is believed to lead to a lower stress levels due to the lower heat input by welding. No residual stresses were therefore considered in the validation. 3.1. Simple bending tests For each model of the beam, web was formed by 200 elements along the length and by 16 elements along the height of the crosssection. Upper and lower flanges were modelled by 6 elements
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across the width of the cross-section. The structural mesh and boundary conditions are shown in Fig. 27. The mesh coarseness was established by a sensitivity study. Initial imperfections were modelled by the actual measured imperfections of the beams. The individual curves describing the shape imperfections (see from Figs.13–16) were replaced by a sinusoidal function for simplification with the maximum amplitude taken from Table 3. In the next table and figures, the results obtained in the fire tests are compared to the results obtained by the numerical simulations. The load corresponds to the total force imposed on the two load application points. The shown displacement corresponds to the vertical displacement at the bottom flange at mid
span. Failure mode of the tests and the numerical model is also compared in the figures (Figs. 28 and 29). They show the deformed shape of the central heated part of the beam for Test 1 and Test 2, Figs. 30 and 31 for Test 3 and Test 4. Comparison of load– deflection curves are depicted in Figs. 32 and 33.
3.2. Lateral torsional buckling tests A similar mesh geometry was used as for the previous model. But 20 elements for web height and 4 elements per 100 mm of the beam length were used. The mesh and boundary conditions are shown in Fig. 34. Initial global and local geometric imperfections were included to the model by means of the elastic buckling eigenmodes. Two imperfection shapes were considered: the beam first local buckling mode and first global buckling mode (LTB) shapes, see Fig. 35. The imperfection amplitudes were based on the initial geometry measurements. In test below, the experimental results are compared with the numerical results. Figs. 36–38 show the beams after tests (Test 5 to 7). As can be observed from Fig. 39, the obtained failure shapes were very close to numerical prediction. Comparison of load– deflection curves are in Fig. 40.
Fig. 26. Measurement of vertical displacement (VD), horizontal displacement (HD) and section rotation (R) at beam midspan.
Table 5 Steel plates yield strength (S355). Part
S1
S2
S3
S4
S5
S6
Upper yield stress ReH [MPa] Lower yield stress ReL [MPa] Yield stress R0.2 at 450 1C [MPa] Yield stress R2.0 at 450 1C [MPa] Yield stress R0.2 at 650 1C [MPa] Yield stress R2.0 at 650 1C [MPa]
430 424 349 399 125 126
394 392 260 310 76 84
388 384 271 328 109 118
376 361 – – – –
385 435 260 318 98 108
435 408 272 330 – –
Fig. 28. Failure mode—Test 1, (a) numerical simulation; (b) experiment.
Fig. 27. Loading and boundary conditions for the simple bending test model.
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Fig. 29. Failure mode—Test 2, (a) numerical simulation; (b) experiment.
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Fig. 31. Failure mode—Test 4, (a) numerical simulation; (b) experiment.
Fig. 30. Failure mode—Test 3, (a) numerical simulation; (b) experiment. Fig. 32. Load–deflection diagram for Test 1 (left) and 2 (right).
4. Discussion of the results Numerical simulations exhibit similar behaviour as the beams during the experiment. As seen in Table 6 and Fig. 41, the difference between the resistance calculated by ABAQUS and obtained from the test is less than 3% for the simple bending test. Whereas the results obtained for the beams subjected to the lateral torsional buckling shows bigger difference (15% in average). This demonstrates the difficulties of lateral torsional buckling tests, which are highlighted by the elevated temperature. A problem with lateral restraints occurred during Test 5. The experimental curve of load displacement relationship is not smooth and the force is unnaturally increasing, see Fig. 40. Besides
that, the experimentally obtained initial stiffness is different from the numerical curves mainly in Test 5 and 7. Overall the approximations are reasonable considering the nature of the different parameters involved in the presented tests, as for instance the heating process. The numerical model was able to predict the behaviour (load capacity and failure mode) of beams observed in the tests.
5. Conclusions The paper presents experiments and numerical modelling of seven steel beams at elevated temperature. All beams were of
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Fig. 36. Test 5—beam after the test.
Fig. 33. Load-deflection diagram for Test 3 and 4.
Fig. 34. Loading and boundary conditions for the lateral torsional buckling test model.
Fig. 37. Test 6—beam after the test.
Fig. 38. Test 7—beam after the test.
Fig. 35. Beams buckling modes shape: (a) local; (b) global.
slender Class 4 open I-section fabricated by welding. Four beams were tested by simple bending and additional three with influence of the lateral torsional buckling. The elevated temperature was induced by heat power units and the tests were carried out in
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Fig. 39. Failure mode carried by: (a) ABAQUS analysis; (b) experiment.
Fig. 40. Load–displacement diagram for the lateral torsional buckling tests: experimental and numerical.
Table 6 Summary of tests results vs. numerical results. Test Cross-section hw x t w bf x t f
1 2 3 4 5 6 7
656 4 250 12 656 4 250 12 830 5 300 8 830 5 300 8 450 4 150 5 446 4 150 7 (610–450) 4–150 5
Load capacity [kN] Difference between the experiment and FEM [%] Experiment FEM 637.82 230.61 484.68 201.22 134.59 189.05 70.96
640.52 0.42 236.99 2.69 498.01 2.68 195.91 2.64 107.2 25.56 151.84 24.05 74.11 4.25 Fig. 41. Comparison of test results with numerical results.
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standard laboratory conditions. For all tests, the necessary characteristics were measured. Namely the initial geometric imperfections and material properties at both room and elevated temperature. The results of the numerical models were compared to the tests and found reasonably close, especially for the simple bending tests. Therefore the numerical model may be used for possible calculation of beam load-capacity or further parametric study.
Acknowledgement The presented research was supported by the RFCS research project FIDESC4 - Fire Design of Steel Members (Grant Agreement Number: RFSR-CT-2011-00030) with Welded or Hot-rolled Class 4 Cross-sections. References [1] Renaud, C, Zhao B. Investigation of simple calculation method in EN 1993-1-2 for buckling of hot rolled Class 4 steel members exposed to fire. In: Structures in fire: proceedings of the fourth international conference, Aveiro, Portugal; 2006, pp. 199–211. [2] CEN European Committee for Standardisation, EN 1993-1-1. Eurocode 3— design of steel structures. Part 1–1, General rules and rules for buildings, CEN Brussels; 2005. [3] CEN European Committee for Standardisation, EN 1993-1-5, Eurocode 3, design of steel structures—Part 1–5: Plated structural elements, Brussels, Belgium; 2005.
[4] CEN European Committee for Standardisation, EN 1993-1-2, Eurocode 3-design of steel structures-Part 1–2: general rules structural fire design; 2005. [5] CEN European Committee for Standardisation, EN 1993-1-3, Eurocode 3 – design of steel structures – Part 1–3: general rules – supplementary rules for cold-formed members and sheeting; 2006. [6] Marques, L, Simões da Silva, L Rebelo, C. Application of the general method for the evaluation of the stability resistance of non-uniform members. In: Proceedings of ICASS, Hong Kong, 16–18 December; 2009. [7] Couto, C, Vila Real, PMM Ferreira, J Lopes, N. Numerical validation of the General Method for structural fire design of web-tapered beams. In: EUROSTEEL 2014—seventh European conference on steel and composite structures, Naples, Italy, September; 2014. [8] Marques L, Simões da Silva L, Greiner R, Rebelo C, Taras A. Development of a consistent design procedure for lateral-torsional buckling of tapered beams. J Construct Steel Res 2013;89:213–35. [9] Braham M, Hanikenne D. Lateral buckling of web tapered beams: an original design method confronted with a computer simulation. J Construct Steel Res 1993;27:23–36. [10] Hibbitt, Karlsson & Sorensen, ABAQUS: Analysis user’s manual, Volumes I–IV, version 6.10, Inc., Providence, R.I, USA, 2010. [11] Kremen, T, Koska, B. Determination of the initial shape and the deformation of the steel beams with high accuracy during the stress tests using laser scanning technology. In: Thirteenth international multidisciplinary scientific geoconference and EXPO, Albena; Bulgaria; 2013, pp. 601–608. [12] Vila Real PMM, Piloto PAG, Franssen JM. A new proposal of a simple model for the lateral-torsional buckling of unrestrained steel I-beams in case of fire: experimental and numerical validation. J Construct Steel Res 2003;59:179–99. [13] Mesquita L, Piloto P, Vaz M, Vila Real P. Experimental and numerical research on the critical temperature of laterally unrestrained steel I beams. J Construct Steel Res 2005;61:1435–46. [14] EN ISO 6892-1, International Standard, Metallic materials – tensile testing – Part 1: Method of test at room temperature, Switzerland; 2009. [15] Couto C, Vila Real P, Lopes N, Zhao B. Effective width method to account for the local buckling of steel thin plates at elevated temperatures. Thin-Walled Struct 2014;84:134–49.