Research Collection. Numerical analysis on the fire behaviour of steel plate girders. Conference Paper. ETH Library
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1 Research Collection Conference Paper Numerical analysis on the fire behaviour of steel plate girders Author(s): Scandella, Claudio; Knobloch, Markus; Fontana, Mario Publication Date: 14 Permanent Link: Rights / License: In Copyright - Non-Commercial Use Permitted This page was generated automatically upon download from the ETH Zurich Research Collection. For more information please consult the Terms of use. ETH Library
2 8 th International Conference on Structures in Fire Shanghai, China, June 11-13, 14 NUMERICAL ANALYSIS ON THE FIRE BEHAVIOUR OF STEEL PLATE GIRDERS Claudio Scandella*, Markus Knobloch* and Mario Fontana* * ETH Zurich, Institute of Structural Engineering, 8093 Zurich, Switzerland s: scandella@ibk.baug.ethz.ch, knobloch@ibk.baug.ethz.ch, fontana@ibk.baug.ethz.ch Keywords: Fire behaviour, Fire resistance, steel plate girders, elevated temperatures, shear buckling Abstract. This paper presents a numerical analysis on the fire behaviour of steel plate girders. The numerical model, used to perform a parametric study, was validated with results of an experimental study. The parametric study shows that steel plate girders, which develop local flange buckling due to bending moments at, may fail due to shear web buckling under fire conditions. A comparative study reveals that common simplified analytical models adopted from design using hot material properties only are not suitable and can even lead to unconservative design results for standard fire situations. 1 INTRODUCTION Stability effects strongly influence the structural behaviour and the resistance of steel structures subjected to fire. Recent studies on the cross-sectional capacity considering local buckling as well as global member buckling are described in [1]. buckling is crucial for steel plate girders and is an important factor for the safe and economical design of buildings and bridges. Therefore, analytical fire design models that pay attention to this kind of instability effect are important. Due to elevated temperatures in fire, the strength and stiffness of steel decreases rapidly, and the stressstrain-relationship becomes distinctly nonlinear. Furthermore, compatibility stresses caused by constrained thermal expansion can have a strong influence on the stability behaviour of steel members. During a fire, thin webs heat up faster than flanges of common I-shaped steel cross-sections, which lead to compressive stresses in the web. These compressive stresses can aggregate or even cause shear buckling. Additionally, steel plate girders, which develop local flange buckling due to bending moments at may fail due to shear web buckling under fire conditions [2,3]. Three basic analytical models, namely the Cardiff model [4], the Basler model [5] and the rotated stress field theory [6] adopted in EN [7] are commonly used for the design of steel plate girders subjected to shear. It is not yet finally investigated whether these analytical models for ambient temperature design can directly be adapted to fire design. Based on an experimental investigation of steel plate girders loaded mainly in shear at elevated temperatures, Vimonsatit et al. [8] conclude that shear buckling becomes less apparent for higher temperatures and nonlinear stress-strain response. In a recent study, Salminen and Heinisuo [9] found that for the shear resistance of steel plate girders at elevated temperatures there is a strong influence if whether the temperature distribution across the web plate is uniform or non-uniform. A comparative study by Glassman and Garlock [10] shows that the analytical model of Basler [5] using hot material properties for the yield strength and Elastic modulus according to [11] leads to conservative design results for isolated steel plates. Kodur and Naser [12] show that shear limiting state can be a dominant failure mode in steel plate girders subjected to fire. A recent study [13] confirms that the stress-strain relationship strongly influences the load-carrying behaviour of steel members in shear. A distinct nonlinear behaviour decreases the shear strength. Furthermore, a simplified model for the shear load-displacement behaviour of steel plate girders with slender webs in fire is proposed.
3 2 NUMERICAL ANALYSIS OF STEEL PLATE GIRDERS IN FIRE 2.1 Numerical Model A three-dimensional FEM-model for transversely stiffened steel plate girders loaded in a four-point bending configuration was developed using the implicit Finite-Element-Code ABAQUS/Standard. The web and the flanges forming the double-symmetric I-shaped cross-sections of the girders were modelled as plates using four-node shell-elements with a reduced integration scheme (S4R elements in the ABAQUS element-library). The longitudinal axis of the girders coincided with the global X-axis and the vertical deflection direction with the global Z-axis as illustrated in Figure 3a. A shape according to the first eigenmode was implemented as an initial geometric imperfection with an amplitude of h/0, with h being the clear depth of the web plates between the flanges. The boundary conditions of the simply supported beam were applied in the reference nodes of analytical rigid surfaces modelling stiff plates of rocker-bearing type supports. Lateral buckling was prevented by constraining the corresponding displacement of points of the upper flange equidistantly at s/15, with s being the span of the girders. The concentrated loads were applied in the reference nodes of analytical rigid surfaces representing stiff loading plates. The welded joints between the different plates forming the girders (flanges, webs and transverse stiffeners) were modelled with multi-point constraints enforcing full coupling of all global displacements and rotations at the contacting nodes. The classical von Mises-plasticity model was used for the material behaviour of the steel, considering temperature-dependence of the stress-strain-relationship and the thermal expansion according to EN [11]. 2.2 Validation of the Numerical Model The numerical model was validated with results of an extensive experimental study on steel plate girders at performed by Basler et al. [14]. Basler et al. conducted collectively 33 tests on steel plate girders with different cross-sections and different test setups. For the validation of the numerical model of the present study, 12 tests on I-shaped cross-sections were considered, namely the tests G2T1, G4T1, G6T1, G6T2, G7T1, G8T1, G8T2, G8T3, G8T4, G9T1, G9T2 and G9T3 according to the labelling of [14]. Figure 1 (left) shows a comparison between the numerical and the experimental results of the ultimate load Fu. An agreement of the calculated ultimate load with the experimental data within a range of 8% could be established. Figure 1 (right, bottom) compares the load-deflection behaviour of the numerical simulation (continuous line) to the experiment (dotted line) of test G6T1 as an example. The test setup is also shown in Figure 1 (right, top). In this specific test, two concentrated loads, F, were applied at girders end, where the pictured deflection, w, is also measured. Figure 1. Validation of the numerical model (left) and results of girder G6T1 (right)
4 2.3 Simulation procedure The simulation procedure evaluating numerically the fire resistance of preloaded steel plate girders was divided into four different calculation steps containing: (1) An eigenmode analysis to determine the shape of the initial geometric imperfection, (2) an ultimate load analysis at, (3) a heat transfer analysis in order to determine the varying temperature field in time of the girders when subjected to ISO 834 standard fire and (4) a fire resistance analysis of the preloaded girder by implementing the varying temperature field in time in a static analysis until failure. 2.4 Fire behaviour of steel plate girders The fundamental structural fire behaviour of preloaded steel plate girders was analysed using the numerical results. The behaviour of girders, which fail due to shear buckling in fire, can be divided into two phases: (1) A pre-critical range starting with the beginning of the fire exposure and ending when web buckling has fully developed. The latter occurring due to an increase of compressive stresses in the web because of constrained thermal strains. (2) A post-critical range characterised at the beginning by constant rates of the girders deformations (midspan deflection, out-of-plane deflection of the web) until a runaway failure sets in at the end. The structural behaviour of steel plate girders subjected to fire is analysed in detail using the results of girder G48 as an example. This girder featured a change in failure mode from bending failure at ambient temperature (Figure 2, top) to shear failure in fire (Figure 2, bottom). The geometry of this girder is listed in Table 1 together with the prevailing load ratio (with respect to ultimate load at ) of, μ R = 0.6, and the fire resistance reached at, t R = 856 s, under ISO 834 standard fire exposure. Figure 2. of girder G48 at (top, scale factor = 2.0) and in fire (bottom, scale factor = 5.0) Figure 3 shows the setup of the numerical simulation and the deformations calculated during the standard fire exposure starting at, t = 0 s. The midspan deflection, w, and its rate, w, (Figure 3d), were selected as quantities detecting global failure when increasing unboundedly. Additionally an unbounded increase of: (1) the out-of-plane deflection, v, of the web in cross-section A-A and its rate, v, (Figure 3e), would indicate shear buckling failure, whereas (2) the rotation, φ, of the upper flange in cross-section B-B and its rate, φ, (Figure 3f), would indicate bending failure. At the beginning of the fire exposure the girder shows a midspan deflection of, w = 36.5 mm, due to the preloading of, F R = kn. Figure 3g depicts the temperature-time-curves at different points in the girder s cross-section A-A (Figure 3b) and indicates that the thin web (tw = 7 mm) heats up faster than the flanges (tf = mm). However, due to the compatibility condition of the cross-section, the web is partially constrained in its thermal expansion by the flanges. Therefore, a self-equilibrating stress state arises within the cross-section leading to additional compressive stresses in the web (σ 3 and σ 4, Figure 3h) and tension stresses in the flanges (σ 1 and σ 2, Figure 3h).
5 Figure 3. Setup of the numerical simulation and results of girder G48 in fire
6 The increase in compressive stresses in the web is limited by the beginning of local web buckling starting at, t 1 = 51 s, of fire exposure (Figure 3e). Simultaneously, bending stresses develop in the web lowering the compressive stresses on the convex side of the buckle, σ 4, and increasing them on the concave side, σ 3 (Figure 3h). Buckling of the web is accomplished at the point in time, t 2 = 100 s, when the out-ofplane deflection, v, ceases to increase (Figure 3e). From this moment onwards the girder is in the postcritical range and its midspan deflection increases with an almost constant rate, w, until the onset of a runaway failure at, t 3 = 700 s. of the girder finally occurs at, t R = 856 s, when both the rate of the midspan deflection, w, and the rate of the out-of-plane deflection, v, approach a vertical asymptote. Simultaneously, the rotation of the upper flange, φ, however, remains bounded indicating thus shear failure. Additional numerical studies were conducted in order to check whether the thermally induced compressive stresses in the web caused the change in failure mode from a bending failure at ambient temperature to a shear failure in fire. Therefore, the entire girders cross-section was heated up uniformly with a moderate constant rate of 7.3 C/min. Figure 4 shows girder G48 in its ultimate state when heated up uniformly. In this case, there is no temperature difference between the flanges and the web. Hence, the lack of additional compressive stresses in the web prevents the latter from buckling, as can be seen in Figure 4 (in opposition to Figure 2, bottom). Figure 4. of girder G48 when heated up uniformly (scale factor = 5.0) Figure 5 illustrates the numerical results of girder G48 when heated up uniformly. After a fire exposure with a constant heating rate of 7.3 C/min at, t = 4162 s, the fire resistance, t R, is reached when the curves of, w, and, w, approach a vertical asymptote. At this point in time, the curves of the rotation of the upper flange, φ, and its rate, φ, approach a vertical asymptote too, indicating failure due to bending. This is in opposition to the change in failure mode of girder G48 when subjected to ISO 834 standard fire. This indicates that the change in failure mode from a bending failure at to a shear failure in fire is induced by compatibility stresses due to a temperature difference between the flanges and the web. Figure 5. Results of girder G48 when heated up uniformly
7 2.5 Parametric study The influence of different parameters on the fire resistance and the failure mode was comprehensively analysed in a numerical parametric study containing 105 numerical fire simulations. The parameters varied included: (1) The depth-to-thickness ratio β of the web plate, (2) the load ratio μ R (with respect to ultimate load at Fu,amb) and (3) the aspect ratio α of the web plate. Table 1 shows the geometry, input parameters, fire resistance and failure mode of three different types of girders: (1) Type I with transverse stiffeners over the whole girders length, (2) Type II with transverse stiffeners only between the supports and the loads and (3) Type III, analogous to Type II but with higher aspect ratios α of the web plate. The results of the numerical study show that some steel plate girders which fail due to bending at, develop shear failure in fire (e.g. girder G49). Increasing the load ratio led to a bending failure even under fire conditions (e.g. girder G50). Steel girders with smaller depth-to-thickness ratios of the web also failed due to bending in fire (e.g. girder G54). Steel plate girders with a high aspect ratio of the web plate, however, failed due to the development of shear buckling even for small depth-to-thickness ratios of the webs (e.g. girder G89). 3 COMPARATIVE STUDY Common analytical models according to Eurocode 3 [7], Basler [5] and Cardiff [4] originally developed to determine the shear capacity of steel plate girders at were adapted for fire design using temperature-dependent material properties for the Elastic modulus and the yield strength according to EN [11]. The temperatures of the web and the flanges, needed to calculate the reduction-factors k E (Elastic modulus) and ky (yield strength), were taken with their maximal value from the numerical simulation at failure time t R. For design, all three analytical models lead to suitable results. For fire design, however, the simplified analytical models neglecting thermal strains lead to inappropriate results for some cases. Figure 6 compares the shear resistance in fire according to Basler (left) and Eurocode 3 (right) to the numerical results. A simplified analytical model according to Eurocode 3 adapted only for temperature related reduction of the Elastic modulus and the yield strength leads to higher shear capacities than the numerical results for girders with high aspect ratios (α = 2.5). For girders with small aspect ratios (α = 1.0), the simplified analytical model leads to lower shear capacities than the numerical results (Figure 6, right). On the other hand, a simplified analytical model according to Basler (without considering an M-Vinteraction) adapted only for temperature dependent reduction of the Elastic modulus and the yield strength overestimates the shear capacities for almost all girders (Figure 6, left), regardless of whether the aspect ratio is small (α = 1.0) or high (α = 2.5). Figure 6. Comparative study: Fire-adapted model Basler (left); Fire-adapted model Eurocode 3 (right)
8 Table 1. Geometry, input parameters and numerical results CONSTANT PARAMETERS FOR ALL TYPES I - III TYPE I TYPE II TYPE III Span of girder Clear depth of web plate Width of flanges Thickness of flanges Thickness of web plate Yield stress at ambient temperature Depth-to-thickness ratio of web plate Load ratio in fire Girder Width of web plate Aspect ratio of web plate Ultimate load at Fire resistance mode at mode in fire Girder Width of web plate Aspect ratio of web plate Ultimate load at Fire resistance mode at mode in fire Girder Width of web plate Aspect ratio of web plate Ultimate load at Fire resistance mode at mode in fire s h b t f t w f y μ R G a Fu,amb t R ambient fire G a F u,amb t R ambient fire G a F u,amb t R [mm] [mm] [mm] [mm] [mm] [N/mm 2 ] [-] [-] [-] [mm] [-] [kn] [s] [-] [-] [-] [mm] [-] [kn] [s] [-] [-] [-] [mm] [-] [kn] [s] [-] [-] ambient fire ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' '
9 4 CONCLUSIONS The paper presented a detailed numerical study on the and fire behaviour of steel plate girders. It shows that constrained thermal strains have a marked influence on the shear capacity of steel members under fire conditions and can aggregate or even cause shear web buckling. Steel plate girders, which fail due to bending at, may develop shear web buckling in fire. A comparative study reveals that commonly simplified analytical models adopted from design using only hot material properties for the Elastic modulus and the yield strength are not suitable and can lead to unconservative design results for standard fire situations. An experimental study on the fire behaviour of steel plate girders is desirable and could confirm the findings of the presented numerical study. REFERENCES [1] Knobloch M., Fontana M. (14). Stability of steel structures in fire. State-of-the-art, recent studies in Switzerland and future trends. In: Stahlbau 83 (14), Heft 4 [2] Scandella C. (13). Numerische Untersuchungen zum Schubbeulverhalten im Brandfall. Master Thesis. Institute of Structural Engineering, ETH Zurich (unpublished) [3] Knobloch M. (01). Theoretische Untersuchungen zum Tragverhalten von dünnwandigen I-Profilen bei erhöhten Temperaturen. Diploma Thesis. Institute of Structural Engineering, ETH Zurich (unpublished) [4] Porter D.M., Rockey K.C., Evans H.R. (1975). The collapse behaviour of plate girders loaded in shear. In: The Structural Engineer, 53 (8), p [5] Basler K. (1961). Strength of plate girders in shear. In: Journal of the Structural Division ASCE, 87 (ST7), p [6] Höglund T. (1973). Design of thin plate I girders in shear and bending with special reference to web buckling. In: Division of Building Statics and Structural Engineering, Royal Institute of Technology, Stockholm, Sweden, Bulletin No. 94 [7] CEN (10). EN : Eurocode 3: Design of steel structures Part 1.5: Plated structural elements. Brussels [8] Vimonsatit V., Tan K., Qian Z. (07). Testing of Plate Girder Web Panel Loaded in at Elevated Temperature. In: Journal of Structural Engineering, 133 (6), p [9] Salminen M., Heinisuo M. (14). Numerical analysis of thin steel plates loaded in shear at nonuniform elevated temperatures. In: Journal of Constructional Steel Research, 97 (14), p [10] Glassman J., Garlock M. (13). Buckling Behavior of Steel Plate Girders at Elevated Temperatures. In: Structures Congress 13, p [11] CEN (10). EN : Eurocode 3: Design of steel structures Part 1.2: General rules Structural fire design. Brussels [12] Kodur V.K.R., Naser M.Z. (14). Effect of shear on fire response of steel beams. In: Journal of Constructional Steel Research, 97 (14), p [13] Ohtsuka T., Knobloch M., Fontana M. (13) capacity of steel plate girders with slender webs in fire. In: Research and Applications in Structural Engineering, Mechanics and Computation. Proceedings of the fifth International Conference on Structural Engineering, Mechanics and Computation, Cape Town, South Africa [14] Basler K., Yen B.T., Mueller J.A., Thürlimann B. (1960). Web buckling tests on welded plate girders. Fritz Engineering Laboratory, Lehigh University, Bethlehem, Pennsylvania. Lehigh University Institute of Research, Report No
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