Articles. Ioan Marginean* Florea Dinu Dan Dubina. 1 Introduction

Transcription

1 Articles Ioan Marginean* Florea Dinu Dan Dubina DOI: /stco Simulation of the dynamic response of steel moment frames following sudden column loss. Experimental calibration of the numerical model and application Significant research effort has been devoted in recent years to the evaluation of the capacity of steel frame structures to resist progressive collapse after sudden column loss. Due to the complex load-structure interaction and material behaviour, it can be very difficult to evaluate the ultimate capacity of structural components using current analytical methods. Therefore considerable research effort has been directed to experimental testing and sophisticated numerical simulations. Although sudden column loss is a dynamic process, most experimental studies on fullscale or scaled down specimens were performed under quasi-static loads. This paper presents the results of a study devoted to the evaluation of steel frame response following the loss of a column. Advanced numerical models are calibrated using experimental test results and dynamic increase factors are studied. Several full-scale structures are investigated for a sudden column loss scenario. 1 Introduction The design of building structures should provide sufficient structural robustness in order to reduce the risk of progressive collapse under extreme loading events. In order to achieve robustness in a safe and economical manner, it is necessary to determine the structural features that may produce an adequate response in the event of extreme loading that may cause large localised damage, i.e. loss of some key members. This may be done by using the alternate path (AP) method to ascertain the capacity of a structure to resist the loss of one or more critical loadbearing elements without causing disproportionate collapse [1]. The complex behaviour prior to failure makes it difficult to predict the ultimate capacity of structural components solely by means of the analytical methods used in current practice. Therefore considerable research effort has been devoted to experimental testing and sophisticated numerical simulations. In this regard, El-Tawil et al. in a recent forum paper [2] presented the current trends and the research required to address gaps in the understanding of progressive collapse. Among them the need for improved modelling and design guidance were highlighted and also the necessity of detailed test data. In a review paper, Stylianidis and Nethercot [3] suggest that the development of suitable prediction methods for post-limit stiffness and * Corresponding author: ioan.marginean@upt.ro deformation capacity characteristics should be the aim of future research studies. Testing of full-scale building structures subjected to column loss scenarios is expensive and technically demanding. An exception would be the actual buildings that are planned for demolition, which may be instrumented and tested before demolition. Song et al. [4] investigated the progressive collapse performance of an existing steel frame building in situ by physically removing four first story columns from one of the perimeter frames. Structural system testing involving planar systems or 3D systems, is a more common approach as it can produce an accurate prediction of the response with less (technical and economic) demands. Concerning testing of the structural system, dynamic tests would give the most accurate results, but it is difficult to monitor the structural response during the test and make relevant observations. As the exact load corresponding to the failure point is hard to evaluate, any other distribution and intensity of loads can cause either no damage, or yielding or rupture of the members or connections. As a result, it is not possible to capture the entire post-yielding behaviour using a single model subjected to a single load pattern and amplitude. These limitations and difficulties have led to an increased interest in quasi-static tests to investigate the response of framed buildings under column loss events. In quasi-static tests, the response is investigated either by gradually increasing a point load at the missing column location or by applying a distributed load along the beams while gradually releasing the support force at the lost column. Numerical simulations require much less effort and are considerably less expensive than experimental testing. The use of advanced methods increases the accuracy of the analysis but requires higher computational effort and advanced engineering skills. In addition, reproduction of the actual behaviour with sufficient accuracy requires that models should be validated against experimental data. The transition from the original intact configuration to the damaged state is assumed to be instantaneous, thus exposing the structure to a dynamic effect [5]. Whereas non-linear dynamic analysis provides most accurate results, static non-linear analysis is the preferred method in practice as it requires less resources and engineering skills. However, these benefits come with shortcomings, for example the consideration of the dynamic effect. When first introduced as a general design method to Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin Steel Construction 11 (2018), No. 1 57

2 Fig. 1. View of a test set-up with a specimen ready for testing reduce the progressive collapse potential [6], the alternate path method employed a factor of 2 in the static analysis in order to increase the loads applied to the bays adjacent to and above the lost member (dynamic effect). Subsequent studies [7, 8] revealed some issues with the use of a constant dynamic increase factor DIF. Firstly, a DIF of 2.0 is appropriate for buildings required to remain elastic although for progressive collapse events, structures are typically designed to respond in the non-linear range. Secondly, the DIF did not vary with levels of performance and dissipation capacity of the structure. Thirdly, distinction should be made between linear and non-linear static analysis [9]. Changes incorporated in a revised version of the UFC provisions [10] included evaluation of the DIF as a function of the normalized rotation (allowable plastic rotation divided by the rotation at yield of the cross section) and distinct load increase factors for linear and non-linear static models. More recently, a series of studies were conducted with the aim of investigating the role of catenary action and connection performance on the evaluation of the dynamic behaviour of steel frames subjected to sudden column loss. Fu et al. [11] used the AP method to study the dynamic performance of two-dimensional steel frames with bolted joints under a sudden column removal scenario. Dynamically increased factors were obtained by comparing the dynamic responses with the corresponding non-linear static responses of the bolted angle steel joints. Simplified analytical models were used to predict the dynamic response of frames subjected to a sudden column removal scenario, based on static experimental tests [12, 13]. This paper presents the results of several studies devoted to the evaluation of the response of a steel frame structure following the loss of a column. Scaled-down 2D steel specimens with two bays and a 3D specimen (with two bays in both directions) were constructed and tested under a central column removal scenario. The specimens were tested under monotonic loading applied to the top of the central column until complete failure. Experimental test results were used to calibrate an advanced numerical Extreme Loading for Structures (ELS) model. Using the calibrated numerical model, dynamic analyses were carried out for the tested 3D specimen and full-scale structures. Based on the results of the static and dynamic responses, both displacement-based (DIF D ) and force-based (DIF F ) factors have been calculated. The study is part of a research program devoted to the design of structures to sustain extreme loading events without collapse: Structural conception and collapse control performance based design of multi-storey structures under accidental actions (CODEC). 2 Experimental investigation of steel moment frames subjected to column loss 2.1 2D frame beam-to-column connections tested for column removal Four connection typologies commonly used in practice were experimentally investigated at Politehnica University of Timisoara using 2D frame specimens tested for column removal, consisting of two steel beams and three columns resulting in two 3.0 m spans (Fig. 1). After having prelimi- Fig. 2. Connections initial dimensions and failure modes 58 Steel Construction 11 (2018), No. 1

3 Fig. 3. Force-displacement curves for 2D frame specimens Fig. 5. Force-displacement curve for 3D frame specimen Fig. 4. 3D frame specimen tested for column loss narily studied the collapse resistance of the reference building [14], specimens were extracted and scaled to fit laboratory conditions. Specimen connections, as in the case of the reference building connections, were detailed so as to fulfil specific demands for seismic resistant systems. The tested connection typologies were: i) cover plate flange connection (CWP); ii) haunch end plate bolted connection (EPH); iii) reduced beam section welded connection (RBS); iv) unstiffened extended end plate bolted connection (EP). The boundary conditions, resembling the constraints in the reference structure, are provided using a strong reaction wall on one side, and a brace system on the other side. In order to simulate removal of the central column, the specimen is loaded vertically on top of the middle column with a displacement-controlled actuator. The connection dimensions and failure modes for each connection are given in Fig. 2, detailed results being reported in [15]. With the exception of the EP specimen (designed as a partial-strength connection), which showed limited rotation capacity, the other three specimens demonstrated that rotational capacities are much higher that actually reported in [10], which are based on the ASCE 41 Provisions for Seismic Design. It is also worth mentioning that with the exception of the EP specimen, for which the contribution of catenary action in resisting the vertical load is negligible, catenary action significantly increased the ultimate capacity of the other three specimens (Fig. 3). Therefore, significant performance improvement could be obtained for the EP specimen if the behaviour of the EP connection were optimised to enable the development of catenary action D frame tested for column removal In order to observe the spatial effect and its influence on the development of catenary action, a 3D steel frame specimen with moment frames in both directions was tested for column removal (Fig. 4). The specimen has the same dimensions (3 m spans in both directions), members and detailing as the 2D assemblies presented in the previous sub-section, but with an improved extended end-plate (EP) beam-to-column connection configuration. In order to avoid premature failure of the EP connection (as in the case of the 2D specimens), the bolt diameter and end plate thickness were increased, resulting in a full-strength connection. The bolt layout and weld details were the same as for the EP connection tested experimentally. The overall relationship between the vertical force and the vertical displacement of the central column is shown in Fig. 5, while the failure mode (fracture of the tensioned flange near the central connection) is shown in Fig. 6. The ductility of the improved EP connection has doubled with regards to the initial configuration of the 2D tested EP specimen, being similar to the ductility of the other three 2D tested frame connection typologies. As the behaviour of the EP connection in a static regime is considerably improved for the strengthened connection, it would be of interest to assess the improvement of the dynamic performance of the connection in case of full-scale structures. 3 Numerical model: description and calibration In order to evaluate the response and investigate the specific features of 3D structures, advanced numerical simulations conducted on test-based calibrated models are required. Consequently, a numerical model has been developed to study the response of steel frames following the loss of a column using the advanced non-linear dynamic analysis software Extreme Loading for Structures, which employs a non-linear solver based on the applied element method (AEM). The 3D geometrical model of the tested Steel Construction 11 (2018), No. 1 59

4 Fig. 6. Failure mode of the 3D specimen Fig. 7. Numerical calibration: vertical force-vertical displacement for point load (PL) Fig. 8. Pushdown analysis: force-displacement curve for PL and UDL 3D specimen was constructed as an assembly of small (discrete) elements connected by springs, which are generated at contact points distributed around the mutual surfaces of the elements. Springs are paired as a normal spring with two perpendicular shear springs. These springs can be removed when strain values reach the separation strain or can be generated when contact occurs between elements, thus resulting in the modelling of element separation and collision. Such a type of connectivity can also model fragmentation, fracture propagation and other phenomena, which are essential in simulating column loss events. The steel material properties of plates, profiles, and bolts were defined according to material tensile test results. The numerical model was validated against the experimental data obtained in the monotonic quasi-static test [16]. In the test, the response of a two-span and two-bay steel frame specimen after the loss of a central column was investigated. A point load (PL) was applied on top of the central column and increased until failure occurred. The results of the numerical analysis showed that the model could be used to capture the complex behaviour of the specimen and the failure mode. The overall relationship between the vertical force and the vertical displacement below the central column is shown in Fig Evaluation of the dynamic response factors 4.1 Dynamic response of the experimental specimen In the event of a sudden column loss, the total force acting on the floor is the summation of directly applied gravity loads and inertial forces developed during dynamic response of the structure. A direct method to obtain the complete path of the force-displacement curve under a static gravity load can employ a pushdown analysis, where the column is removed and the distributed load is incremented up to the attainment of failure [17]. The analysis was done for UDL (uniform distributed load) with increasing intensity up to failure. In order to compare the results of the pushdown simulation with the point load (PL) test, the total vertical reaction (sum of total applied loads) needs to be allocated to each column based on their contributory zone. For the central column, the corresponding vertical force was 1/4 of the total reaction. Fig. 8 comparatively shows the vertical force vertical displacement curves for the reference model (validated against the experimental test) and the pushdown analysis. For comparison purposes, the equivalent load uniformly distributed on the floor is also shown on the secondary vertical axis. As can be seen from the two curves, the initial stiffness and post-yielding behaviour are almost identical until the vertical force reaches 380 kn, after which the UDL model exhibits almost constant stiffness until failure is attained at a force of 510 kn (or an equivalent UDL of 62 kn/m 2 ). The ultimate displacement amounted to 410 mm. In comparison, the ultimate resistance and deformation capacity of the model loaded with a point load at the missing column location were much higher at 773 kn and 564 mm respectively. As the case of gravity loads distributed on the floors represents a more realistic loading scenario, the prediction of the structural capacity using the point load method requires further calibrations in order to improve consistency. In order to quantify the dynamic effect on the structure, either the force or displacement response may be 60 Steel Construction 11 (2018), No. 1

5 Fig.11. EP connection frame structure modelled in ELS Fig. 9. Dynamic analysis results: static vs. dynamic force displacement curves used. The two dynamic factors DIF are defined in Fig. 9 [18]. The force-based DIF F and displacement-based DIF D factors calculated based on the numerical analysis results are presented in Fig. 10. The values are compared with the DIF calculated using the formulas proposed in [1] and [18]. Due to the contribution of post-yield stiffness (increased due to the development of catenary action), the force-based amplification factor DIF F is underestimated for normalized rotations larger than 2 when the UFC formula [1] is adopted. A better estimation is given by the analytical methodology proposed by Tsai [18], where the experimental static capacity curve is used to estimate the force-based DIF F. The results obtained for the DIF D are also in good agreement with the analytical expressions in [18]. 4.2 Dynamic response of full-scale structures In order to assess the connection performance of full-scale MRF structures subjected to column loss, several steel frame structures were modelled to be subjected to internal column loss (Fig. 11a). Moment resisting frame (MRF) structures were designed for different seismic conditions, both for design ground acceleration and for ground type (given by the corner period see Table 1). The local conditions are a low-intensity seismic zone LSZ and stiff type ground, and a high-intensity seismic zone HSZ and soft type ground. The structures have 4 spans of 8 m in each direction and 6 storeys, all 4 m high. Dead and live loads are 4 kn/m 2. Seismic loads were computed in accordance with the Romanian Seismic Code provisions P The seismic requirements and structural elements resulting from the design for each type of connection are shown in Table 1. The design of beams is governed by the seismic design situation for HSZ, while for LSZ, the sections result from the permanent design situation. Bolts are class 10.9 and the material of members and connections is S355 structural steel. The numerical models were calibrated based on the 2D and 3D frames tested under column loss [19]. Partial strength EP connections were used, with the same connection/ beam capacity ratio (0.8) as in the case of the 2D frame tested EP connection. As failure did not occur in the beam but in the connection, several dimensions of the connections were modified, such that the failure would occur in the beam (increased bolt size and end plate thickness). The dimensions of the modified configurations, which allowed failure to develop in the tensioned beam flange, thus preventing connection failure, are listed in Table 1 as improved robustness design (marked with *). The connections/beam capacity ratios of the improved configuration are similar to the 3D experimental specimen (full-strength). The dynamic analysis was performed in two steps. First gravity load (with different intensities) is applied on the structure in a static analysis. Then, the internal column (C3 see Fig. 11b) is removed almost instantaneously Fig. 10. Comparison of dynamic increase factors Steel Construction 11 (2018), No. 1 61

6 Table 1. Case study of structures with EP connections Name T c [s] a g Column Beams Connection bolt size Connection end-plate thickness [mm] LSZ g 2xHEB450 IPE450 M24/*M30 25/*35 HSZ g 2xHEB900 IPE750X137 M27/*M36 30/*38 T c corner period a g peak ground acceleration * dimensions for improved robustness design (0.001 seconds) and the dynamic analysis starts from the end of the static analysis. The static capacity is defined as the response of the structure to static loading, without considering inertial effects. The dynamic capacity is the response of a structure at various load factors (λ) in terms of maximum displacement. The neutral capacity [20] is the response of a structure at multiple load factors (λ) in terms of permanent displacements. The dynamic capacity considers the full (maximum) effect of the inertia, while neutral capacity only the permanent effects. Fig. 12 plots the static, dynamic, and neutral capacity curves for the EP-LSZ structure. In the elastic range, the displacement for the same overload factor of the static capacity is half that for the case of dynamic capacity, but equal to the displacement corresponding to the neutral capacity. As no plastic deformations occur, the initial dynamic effect is damped and the permanent response of the dynamically loaded system is the same as the static response. The increase of the dynamic capacity of the LSZ structure due to connection strengthening is about 50% (from 1.26 λ to 1.9 λ). A ductility increase due to connection strengthening can also be seen in the performance of the structure in the case of column removal. The improvement of joint performance due to the use of larger bolt diameters was also reported in [21]. Fig. 13 shows the static, dynamic, and neutral capacity curves for the EP-HSZ structure. A ductility improvement due to connection strengthening can be seen, but the increase in the ultimate capacity is less than for the EP-LSZ structure (only 36%). The maximum overload factor for the LSZ structure with initial (partial-strength) connections is λ = 1.26 for the central column loss scenario. This indicates limited robustness and a high risk of progressive collapse. For this structure, the dynamic increase factors have also been studied. Fig. 14 shows the force and displacement-based dynamic increase factors (DIF) for the EP-LSZ structure. Force-based DIF values range from 2 to 1.14, while the displacement-based DIF even reaches values of 6 in the case of the EP-LSZ structure with an improved connection configuration. For similar overloading factors, the DIF values of the two structures are similar up to an overload factor of 1.25, but slightly lower in the case of DIF D for the structure with an improved connection, as the increased rigidity of the connection enabled the development of smaller dynamic forces. Fig. 12. Static, dynamic and neutral column loss capacity for the EP-LSZ structure Fig. 13. Static, dynamic and neutral column loss capacity for the EP-HSZ structure 62 Steel Construction 11 (2018), No. 1

7 However, it must be emphasised that the results and concluding remarks summarised above are related to bare steel structures. In the case of real multi-storey building structures, a study intended to observe and characterise their response under column loss scenarios should take into consideration the influence of the slab, especially if a reinforced concrete slab system is used. Due to the composite action between the steel beam and concrete slab, the system would reach larger forces than that corresponding to a bare steel specimen, while the ultimate rotation of beams reduces correspondingly [22]. The substantial increase of rigidity and post-yield capacity due to the composite action of the slab has a direct impact on both forcebased and displacement-based DIFs. Acknowledgements Fig. 14. Force-based and displacement-based dynamic increase factors for the EP-LSZ structure 5 Conclusions The study presented in the paper was intended to evaluate the dynamic response of bare steel frame structures due to the sudden removal of a column using numerical simulations. Experimental tests were performed on 2D and 3D steel frames subjected to a column removal scenario using static pushdown monotonic loading. Bolt size and end plate thickness were increased in the case of the 3D frame specimen (full strength) compared to the initial 2D frame EP specimen (partial strength) in order to reach the same ductility as the other 2D connection configurations, thus allowing catenary action to develop and increase the capacity. A numerical model was calibrated for a static loading regime using the test data obtained. The capacity of the system subjected to internal column loss can be significantly reduced if a uniformly distributed load is applied rather than under a column point load. For the evaluation of dynamic response factors, non-linear dynamic analyses were performed and results were compared with similar results obtained using empirical and analytical formulae. The lower limit of the force-based DIF F appears to be higher than in the empirically based results in [1]. Similar observations were reported in [18]. This increase may be explained by the increase of post-yield stiffness under large deformations as a result of the development of catenary action. The performance of experimentally tested extended end plate connections was also evaluated in the case of full-scale structures subjected to column removal using the calibrated AEM model. Structures were designed for different seismic zones. The strength of frames designed for high seismic forces is considerably higher than that of frames designed for low seismic forces, while strengthened EP connection configurations improved the dynamic performance after a sudden column loss, especially for the LSZ structure. Inertia forces reduce the capacity of frames to resist column loss in terms of force, and especially displacement. This work was supported by the Romanian National Authority for Scientific Research and Innovation, CNCS/ CCCDI UEFISCDI, within grants no. PN-III-P PED (FRAMEBLAST) and PN-II-PT- PCCA (CODEC) References [1] DoD. Unified facilities criteria: Design of buildings to resist progressive collapse. Washington (DC), US: United States Department of Defense; [2] El-Tawil, S; Li, H: Kunnath, S. Computational Simulation of Gravity-Induced Progressive Collapse of Steel-Frame Buildings: Current Trends and Future Research Needs. Journal of Structural Engineering. 2014;140:A [3] Stylianidis, P: Nethercot, D. 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8 [12] Liu, C; Tan, KH: Fung, TC. Component-based steel beam column connections modelling for dynamic progressive collapse analysis. Journal of Constructional Steel Research. 2015;107: [13] Demonceau, J-F; Comeliau, L; Hoang, V-L; Jaspart, J-P. How Can a Steel Structure Survive to Impact Loading? Open Civil Engineering Journal. 2017;11: [14] Dinu, F; Dubina, D: Marginean, I. Improving the structural robustness of multi-story steel-frame buildings. Structure and Infrastructure Engineering. 2015;11: [15] Dinu, F; Marginean, I; Dubina, D. Experimental testing and numerical modelling of steel moment-frame connections under column loss. Engineering Structures. 2017;151: [16] Dinu, F; Marginean, I; Dubina, D: Petran, I. Experimental testing and numerical analysis of 3D steel frame system under column loss. Engineering Structures. 2016;113: [17] Marginean, I; Dinu, F; Dubina, D; Petran, I; Senila, M: Szilagyi, H. Numerical modeling of dynamic response of steel moment frames following sudden column loss. The International Colloquium on Stability and Ductility of Steel Structures: ECCS European Convention for Constructional Steelwork; p [18] Tsai, M-H. An analytical methodology for the dynamic amplification factor in progressive collapse evaluation of building structures. Mechanics Research Communications. 2010;37:61-6. [19] Dubina, D; Dinu, F: Marginean, I. Multi-hazard risk mitigation through application of seismic design rules. Behaviour of Steel Structures in Seismic Areas Christchurch, New Zealand: in press; [20] Tsai, M-H: Shyu, W-S. A proper estimation of inelastic dynamic increase factor in support-loss experiments. Journal of the Chinese Institute of Engineers. 2014;38: [21] Cassiano, D; D Aniello, M: Rebelo, C. Parametric finite element analyses on flush end-plate joints under column removal. Journal of Constructional Steel Research. 2017;137: [22] Dinu, F; Marginean, I; Dubina, D; Petran, I; Pastrav, M; Sigauan, A et al. Experimental testing of 3D steel frame with composite beams under column loss. The International Colloquium on Stability and Ductility of Steel Structures: ECCS European Convention for Constructional Steelwork; p Keywords: column loss; dynamic response; experimental testing; numerical model; applied element method; dynamic increase factor Authors Dr.-Ing. Ioan Marginean Politehnica University of Timisoara Department of Steel Structures and Structural Mechanics Ioan Curea Timisoara, Romania ioan.marginean@upt.ro Prof. Dr.-Ing. Florea Dinu Politehnica University of Timisoara Department of Steel Structures and Structural Mechanics Ioan Curea Timisoara, Romania Romanian Academy Center for Fundamental and Advanced Technical Research Mihai Viteazul Timisoara, Romania florea.dinu@upt.ro Prof. Dr.-Ing. Dan Dubina Politehnica University of Timisoara Department of Steel Structures and Structural Mechanics Ioan Curea Timisoara, Romania Romanian Academy Center for Fundamental and Advanced Technical Research Mihai Viteazul Timisoara, Romania dan.dubina@upt.ro 64 Steel Construction 11 (2018), No. 1