Influence of detailing of short links on seismic response of eccentrically braced frames

Transcription

1 Bauhaus Summer School in Forecast Engineering: From Past Design to Future Decision August 215, Weimar, Germany Influence of detailing of short links on seismic response of eccentrically braced frames VĂTĂMAN, Adina Politehnica University of Timişoara, Department of Steel Structures and Structural Mechanics GRECEA,Daniel Politehnica University of Timişoara, Department of Steel Structures and Structural Mechanics, Romanian Academy, Timişoara Branch, Romania CIUTINA, Adrian Politehnica University of Timişoara, Department of Steel Structures and Structural Mechanics Abstract The Eccentrically Braced Frames represent highly dissipative seismic systems due to the formation of plastic hinges in link elements. In function of their length, they can work in shear (short), bending (long) and respectively combined bending and shear (intermediate links). Based on the ratio between the plastic bending and plastic shear resistances of the link element, and a minimum number of stiffeners on the link, the normative requirements do not differentiate between minimum/maximum required length of the link nor the increased number of stiffeners present on the link. The paper presents the performances of short steel link elements subjected to shear under the form of a parametrical study performed using Abaqus FEM tool. An initial FE model is calibrated based on an experimental test performed within the CEMSIG laboratory at Politehnica University for monotonic loading. In a second step the numerical analysis investigates three parameters that can affect the behaviour of such systems, whilst remaining in the range of short shear links: (i) use of compact/slender webs; (ii) influence of the number of web stiffeners and (iii) influence of link length. The results are presented under the forms of V-γ response curves and judged in function of characteristic parameters. 1. Introduction The steel Eccentrically Braced Frames (EBF) represent structures recognized for their good dissipation capacities, including the case of seismic forces. The EBF structures are characterized in design by high values of the behaviour factor (q greater than 6 in ductility class high case) with failure mechanisms based on the plasticization of link elements. These elements are highly loaded in case of lateral loads in bending and shear by the triangulated adjacent systems. According to the modern design norms, such as Eurocode 8 (CEN 24), the dissipative link elements can be short, medium or long, the characterisation being made on the ratio between shear force and bending moment: if the link length e s is smaller than 1.6(M pl/v pl) [mm], the link is short and subjected preponderantly to shear; for e s values greater than 3(M pl/v pl), the link is considered long and working in bending; intermediate values are for links working in both shear and bending. However, in order to allow full development of plastic hinges, the links should not be directly loaded, as to avoid the formation of unwanted stress combinations produced by gravitational loads (Ioan, Dima 21). The ductile behaviour of steel link elements has been proved by several researchers, by investigating different solutions for best performance. Numerical results by Danku et al. (Danku et al 213)

2 VĂTĂMAN, Adina, GRECEA, Daniel, CIUTINA, Adrian / FE confirmed the good dissipation capacity of short links in EBF structures, with a similar behaviour factor q as prescribed in EC8 for DCH and with the mention that the limiting value proposed by EC8-1, , of 8 mrad for short links in EBF might be insufficient for dual frame structure. In 21, Degee et al. (Degee et al 21) conducted a parametrical numerical study, that focused on eccentrically braced frames with short vertical links in shear, analysing the influence of material properties on the seismic response, with partial conclusions showing a good behaviour of the vertical shear links in case of behaviour factors values close to 6. Regarding the use of web stiffeners on the dissipative link, Yurisman et al. (Yurisman et al, 21) performed both experimental tests and numerical simulations on links with diagonal web stiffeners showing the good capacity of such a configuration working in shear. Also, an extensive experimental study was performed by Okazaki et al. (Okazaki et al 25) that also involved the investigation of the disposition and geometrical form of web stiffeners, revealing interesting results regarding link flange slenderness and the importance of an appropriate loading protocol. Although the definition of short link elements is expressed in Eurocode 8 by the comparison with a certain length (1.6Mpl/Vpl), several other parameters can influence the response of the link elements, such as the presence of stiffeners, profile shape or link length. The numerical study presented herein is dedicated to the influence of such details on the local shear response of short link elements. In a first part, the response of the link elements is calibrated on the basis of existent experimental results, by using the Abaqus FEM software. The second part of the research is concentrated on a parametric study, including stiffening details (none, one or two stiffeners), type of steel link (HEA or IPE profile with close shear area) or link length (3 to 75mm). 2. Experimental Background The numerical approach is based on a larger experimental research developed within the CEMSIG Research Centre at the Politehnica University of Timisoara regarding the response of steel and composite link elements. The detailed report can be found elsewhere (Danku 211). The specimen used as reference for the numerical approach was a pure-steel EBF, as detailed below Steel Eccentrically Braced Frame Model The eccentrically braced frame was part of a designed dual frame (MRF+EBF) structure with five storeys, 3 spans (2 outer spans of 6m and one internal span of 4.5m) and 3 bays (2 outer bays of 6m and one internal bay of 4.5m) in a seismic region. The following conditions were used in design: Location: Bucharest (a g =.24 g, T C = 1.6 sec); Loads: 4 kn/m 2 permanent load, 3 kn/m 2 live load and Conditions for steel design and detailing: EN (CEN 25) and EN The considered reference steel EBF testing specimen (EBF-LF-M) consisted of the first story central bay structure. The frame beam is a HE2A profile for the entire length including the dissipative zone (short link). Other element cross sections can be distinguished on Figure 1.a. The beam-to-column connections were fully resistant by considering bolted end-plates. The braces were splice connected while the column-base connection was pinned in order to reduce the lateral force needed for the complete development of the plastic hinge (Figure 1.b).

3 VĂTĂMAN, Adina, GRECEA, Daniel, CIUTINA, Adrian / FE a) b) Figure 1. a) Dimensions of the steel EBF specimen ; b) Experimental lay-out (Source: Danku et al, 211) Although both monotonic and cyclic loading was applied to different tests (through a top lateral actuator), the calibration was made on monotonic loading. The resulting force-displacement curve corresponding to the monotonic specimen (EBF-LF-M) can be observed in Figure 2a), where the force represents the load induced by the actuator, while the top displacement represents the displacement at the top left corner of the EBF in the area of load application, monitored by a displacement transducer. Figure 2b) shows the characteristic V-γ curve of the link element, where V is the shear force in the link, computed according to the static schema, while γ represents the distortion angle of the link web, computed on the basis of displacement transducers located on the specimen. The other frame elements such as braces, columns and frame connections only exhibited an elastic behaviour. The termination of the experimental test was due to the attainment of the displacement limit of the actuator. At maximum displacement the web of the link suffered significant crippling due to shear force, as is shown in Figure 3. However, noticeable deformation was recorded in brace and brace connections up to 4mm per brace. The overall deformation of the frame was very large, based on the ductile behaviour of the link, leading to values greater than 25mrad, about four times greater than required by the norms (8mrad). a) b) Figure 2. a) Force-displacement curve for steel EBF; b) Rotation of link (Source: Danku et al, 211) 3. Numerical Model and Calibration The numerical modelling of the tested specimen by considering FEM was done using Abaqus software (Dassault Systemees Simulia Corp 211). The layout of the steel frame was modelled in correspondence to the experimental specimen for both global geometrical dimensions and crosssectional properties. The frame components were modelled as solid finite elements type (see Figure 3). The assigned material properties were corresponding to the true stress-strain curve for the beam and dissipative link, considering the material tests performed on coupons. The analysis procedure used was Dynamic

4 VĂTĂMAN, Adina, GRECEA, Daniel, CIUTINA, Adrian / FE Explicit type with a monotonic applied displacement of 18 mm on the top of the left column, similar to the maximum recorded displacement for the corresponding displacement transducer in experimental testing. Hex type elements have been used for meshing, considering sweep technique and mixed medial axis and advancing front algorithms. An element size of 6mm was used for the dissipative part of the frame (link element and adjacent beam ends) as shown in Figure 3. The frame components, which were expected to remain in the elastic domain, have been assigned larger size elements, ranging from 25mm for columns and column stiffeners, 2mm for beam and beam stiffeners and respectively 15mm for braces. a) b) c) d) Figure 3. a) Mesh of the finite element EBF model; frame cross-sections, b) material characteristics used in calibration; deformed shape of the dissipative link elements: c) FE Model d) Laboratory test The resulting force-displacement curve (denoted as FEModel in Figure 4 a) appropriately follows the experimental curve, with the main remark that the initial stiffness of the numerical model is slightly higher than that of the experimental model. Since the experimental EBF model has recorded a slip of the bolted connections for braces, this was further integrated in the numerical model by a connection slip using a connector section. This was assigned for each brace by an elastic deformation considering a maximum 1.5mm slip at a force of 3kN. The FEM response corresponding to this situation is shown as curve FEModel+Slip in Figure 4 a). As this additional effect was shifting the maximum resistance point, adjustments on the applied constraints and boundary conditions were considered for re-fitting the experimental results. As a consequence, the lateral supporting system of the beam was re-positioned along the length of the beam with a clearance of 2mm on each side of the beam. This allowed a limited out-of-plane displacement of the beam as in the case of experimental test. The outcome of these modifications could be seen in the force-displacement curve LS3-H in Figure 4 a) which closely follows the experimental curve EBF-LF-M-DHTL. Figure 4 b) shows the resulting deformed shape of the modelled EBF. The deformed shape of the link element at the end of the analysis can be observed in Figure 3 c) compared to the deformed shape of the experimental specimen, presented in Figure 3 d).

5 VĂTĂMAN, Adina, GRECEA, Daniel, CIUTINA, Adrian / FE Figure 4. a) Calibration of the force-displacement curve b) Deformed shape of calibrated EBF model including slip connectors and out-of-plane supporting system 4. Parametric Study of a Steel Eccentrically Braced Frame Table 1. Configurations of analysed EBF models Name of FE model Number of stiffeners Link section Link length e [mm] Name of FE model Number of Link section Link length e [mm] LS3-H (Reference) LS3-H1 LS3-H2 LS3-I LS3-I1 LS3-I HE2A HE2A HE2A IPE24 IPE24 IPE LS4-H LS5-H LS6-H LS7.5- H LS4-I LS5-I LS6-I LS7.5-I HE2A HE2A HE2A HE2A IPE24 IPE24 IPE24 IPE Following the calibration described above, the parametric study was focused on three main directions that can influence the global behaviour of the link elements: the stiffening of the link, the steel section profile of the link beam and respectively the length of the short link. The names of the link models follow the three considered parameters: LS is the generic name of the series, first number describes the length of the link, H/I describes the cross-section profile of the beam and the last figure indicates the number of stiffeners evenly distributed on the length of the link - see Table 1. The transition from HE2A profile to IPE24 was made with the consideration of similar shear area of the two profiles. The value for shear area A v was calculated according to Chapter 6.8 on design and detailing rules for eccentrically braced frames from Eurocode 8: Part 1. The resulting values for the shear area of the link of 126mm 2 for HE2A and 1427mm 2 for IPE24, represent reduced values for dissipative links, compared to the standard shear area of the two profiles of 188mm 2 respectively 191mm 2 as used for normal gravitational shear verifications Influence of steel link section The influence of the steel section on the behaviour of the EBF was addressed by changing the default HE2A beam profile with a slender IPE24 profile. The reason for choosing an IPE24 was the minimum change in the shear area of the two profiles. The other components of the EBF members were not modified, neither the geometrical dimensions (height, span) of the EBF. However, the angle of the braces was slightly changed by the modification of the beam profile.

6 VĂTĂMAN, Adina, GRECEA, Daniel, CIUTINA, Adrian / FE The response of the two models is shown in Figure 5. Both responses are characterised by a threelinear behaviour: - an initial elastic behaviour up to plastification; - a linear post-elastic hardening branch with important stiffness; - a discharging branch with similar stiffness as for hardening. Comparing the two responses it could be observed an identical elastic behaviour, the main difference between the two elements consists in the post-elastic zone: the model with the slender web (IPE profile) shows a slightly smaller maximum resistance, explained by a smaller shear area. This is accompanied by an important reduction in the distortion corresponding to maximum load: the local instability appeared earlier in case of slender web. The deformed shape of the link elements is presented in Figure 5 right side. A similar shear hinge formed in both cases is noticed by web crippling due to large horizontal differences of the two lateral sides. The stress amplitudes outside the panel are much smaller than those of the internal web itself. HEA2 IPE IPE Figure 5. Comparison between the link responses for HE2A and IPE24 profiles: V-γ response curves and plastic deformed shapes 4.2. Influence of the link element stiffening According to the normative requirements considering the Eurocode 8, the stiffening of the link elements is required by intermediate stiffeners disposed at intervals of (3t w-d/5) with t w being the web thickness and d the height of the cross-section of the link. It results a maximum distance of 155mm between stiffeners for HEA 2 profile and respectively 138mm for IPE 24 profile. Within this study, the influence of the stiffness of the link s web on the overall behaviour of the steel frame was analysed by comparing three configurations of web stiffening: one model considering no stiffeners on the dissipative link, a second model with one stiffener in the middle of the link (representing the normative solution) and a third model with 2 stiffeners on the link, at equal intervals from the centre and from the end of the link. Both HE2A and IPE24 profiles were considered. In both HEA and IPE cases, the elastic behaviour, initial stiffness and the point of plasticisation are independent of the number of stiffeners, as shown in Figure 6. However, important differences are recorded in post-elastic range: - in both cases the stiffening of the link element conducted to linear increases of maximum loads; - accordingly, the hardening branch stiffness increased significantly with the numbers of stiffeners; - the influence on the discharging branch stiffness is not important.

7 VĂTĂMAN, Adina, GRECEA, Daniel, CIUTINA, Adrian / FE Important to notice is the fact that in case of the slender web (IPE profile), the point of maximum load was shifted from.12rad to.16rad in case of using one stiffener and respectively.25rad in case of using two stiffeners. The increase in initial maximum resistance is by about 2% for each additional stiffener. The same trend can be noted in case of HEA webs, but the real increase of the ultimate rotation is observed only when using two stiffeners. a) b) Figure 6. Comparison with regard to the parameter web stiffness a) for the FE models with HE2A b) for the FE models with IPE24 The analysis of failure modes, as shown in Figure 7 has proven that in both cases additional stiffeners leads to division of the original shear panel into multiple panels, each of these having its own web deformation. Although in the elastic and initial plastic loading conditions the multiple panels are working together, in the final loading conditions the plasticisation is concentrated in one of the panels, the other contributing only partially to the global deformation. Concluding the study on this parameter, it could be said that the number of stiffeners on link elements is important but only in the plastic domain, as it increases the ultimate resistance and corresponding distortion. Figure 7. Deformed shape of the HE2A and IPE24 link elements with regard to the number of stiffeners 4.3. Influence of link length The third parameter monitored within the study was considering the length of the link, which was computed according to the guidelines in Eurocode 8, in order to maintain the characteristics of a short dissipative link. The normative limitations limit only the maximum length, without specifying the minimum value. Considering that the maximum admissible length of the elements was 76mm, in analyses there have been considered 5 different lengths: 3, 4, 5, 6 and 75 mm respectively. The modifications to the length of the link were made to both the model with the HE2A beam and

8 VĂTĂMAN, Adina, GRECEA, Daniel, CIUTINA, Adrian / FE to the model with the IPE24 beam profile by keeping the original bay of 4.5m and changing the angle of the braces. a) b) Figure 8. V-γ response curves by changing the length of the link: a) HE2A models; b) IPE24 models. The response V- γ curves as function of link lengths are shown in Figure 8 for both HEA and IPE profiles. For the case of stiffer web (HEA link element), the link length has little influence on both elastic and post-elastic ranges: the elastic and ultimate strengths are decreasing with the length, but the difference between the resistances is less than 8% for ultimate and maximum 2% in case of elastic strength respectively. However, for IPE profile with a slender web, even the elastic range is practically identical for all the models, the maximum strengths as well as the overall plastic behaviour is different: the maximum strengths are obtained in case of 6mm model, almost coincident with the resistance of the models with the link lengths of 5 and 4 mm. However, by passing to larger lengths, such as 75 mm, the web loses the stability earlier, thus having a limited ultimate resistance and ductility. This can be seen also in the failure modes, presented in Figure 3 and Figure 9. The links with shortest dimensions (3 to 4 mm) are characterized by a global-type shear plastification while the longer link elements (5 to 75 mm) are characterised by web crippling on sides of the panel, while the other side remaining plain but with high levels of shear stresses. Figure 9. Deformed shape of the HE2A and IPE24 link elements with regard to the link length Evaluation of results The evaluation of numerical simulation results is done by considering some analytical values, computed on the basis of V-γ response curves which are compared with the normative values given in norms. The following analytical values were computed on the basis of V-γ responses: S j,ini the (initial) elastic stiffness of the V-γ diagrams; V y the elastic shear force, determined in accordance to ECCS (ECCS 1986) procedure for determining yield characteristics: this represents the intersection of the initial stiffness directory line S j,ini with a directory line of a stiffness equal to S j,ini / 1 which is tangent to the V-γ diagram; γ y is the yield distortion which corresponds to Vy;

9 VĂTĂMAN, Adina, GRECEA, Daniel, CIUTINA, Adrian / FE V max is the maximum shear load on the V-γ diagram; γ Vmax is the distortion corresponding to V max. The theoretical values of the link stiffness S j,th and the design resistances V wp,rd were computed in accordance to the normative formulae offered by Eurocode 3-Part 1-8. The following formulae were considered for the computation of S j,th and V wp,rd: where: -f y yield strength of the link, taken as resulting from the ECCS procedure A v,link the shear area of the link E longitudinal elasticity modulus for steel (21 N/mm 2 ) β transformation parameter regarding moment and shear force distribution as found in EC3-1-8, 5.3, taken as 2. It is to be noted that the shear area for both formulae was evaluated considering the formula in EC8-1- 1, 6.8. (where t w web thickness, h is the height of the steel profile and t f thickness of the flange): Table 2. Comparison of analytical results of the numerical models Name S j,ini [kn/rad] V y [kn] γ y [rad] V max [kn] γ Vmax [rad] S j,th [kn/rad] V wp,rd [kn] LS3-H 93, , LS3-H1 95, , LS3-H2 96, , LS3-I 148, , LS3-I1 151, , LS3-I2 153, , LS4-H 86, , LS5-H 74, , LS6-H 72, , LS7.5- H 58, , LS4-I 139, , LS5-I 94, , LS6-I 131, , LS7.5-I 69, , The resulting values can be found in Table 2. Comparing the results, the following conclusions can be drawn: Although not visible in charts, there are important differences in the initial stiffness values. These are varying from simple to double in function of the parameters considered. Thus, the increase of the numbers of stiffeners disposed on the link has a small influence on the elastic stiffness. However, the link length changes significantly this parameter: practically, the longer the link, the smaller the initial stiffness. The most important drop in the initial stiffness is between the models with 6 mm and those having 75mm, in case of IPE profiles where the second stiffness is half of the first one;

10 VĂTĂMAN, Adina, GRECEA, Daniel, CIUTINA, Adrian / FE Vy and γ y values are tributary to their definition and to the particular shapes of the V-γ curves, being characterised by high values of initial stiffness. In consequence higher or smaller values are obtained, based on the S j,ini value. As in case of the initial stiffness, the elastic points are almost coincident in links without stiffeners or increased number of stiffeners, while the values are resulting different when changing the length. In general smaller V y values are obtained for longer links; As mentioned in the specific paragraph, the maximum load it is highly affected by the number of stiffeners, each additional stiffener conducts to an increase of 15-2% in maximum load and also in the distortion corresponding to the maximum load. In what concerns the influence of the link length, the increase in the link length decreases with small increments for the compact web (HEA profile), while little increase was recorded for the slender web (IPE profile). However, the IPE link type with a length of 75 mm represents a particular case due to early beginning of the local buckling of the web. It is to be mentioned that the link length is at the limit of short link elements and additional stiffeners should be considered; As a general observation, the design resistance V wp,rd, computed with the help of (1) present safer values as compared to numerical results V y, independent on the number of disposed stiffeners or the link length, including here the cases of longer links with premature web crippling, such is the case of the model LS7.5-I. In return, the initial stiffness, computed by (2) shows in all cases smaller values than the values extracted from the results of numerical simulations. The design and numerical values are comparable only for link elements having the length closer to the maximum normative limiting value of 1.6M pl/v pl. For smaller values however, or the stiffness increases significantly, in some cases of more than twice the design stiffness. 5. Conclusions Present paper investigates the performances of steel short link elements subjected to shear through numerical analyses by finite element models. This situation corresponds to lateral seismic loads induced in EBF systems. Based on an existing experimental test, an initial calibration was done. The study was followed by a parametric investigation considering three variables: use of a compact/slender web, an increase numbers of intermediate stiffeners and the variation of the link length. The study revealed the following conclusions: The steel experimental tests can be modelled with good accuracy by FE models only by including in the finite modelling the actual behaviour of experimental conditions: in this case the model should consider the slip in braces and lateral supporting conditions; High levels of ductility can be achieved by steel shear short links, in the order of 25 mrad, at least under monotonic loading conditions; The change in the web slenderness has influence only on the plastic domain as long as the shear area remains similar. Even with smaller shear area, the compact web (HEA 2 profile) proves a better performance both in ultimate resistance and corresponding distortion; The increase in the number of stiffeners changes the hardening stiffness and the ultimate resistance, without affecting the elastic response. The failure mode begins in the new-formed panel but eventually only one leads to web crippling; The increase in the length of the link, while remaining in the range of short link elements, decreases significantly the initial stiffness of the characteristic V-γ curves. Post-elastic behaviour with earlier failure was observed for the specimens with the longest length. The failure is formed in these cases only in a side of the link;

11 VĂTĂMAN, Adina, GRECEA, Daniel, CIUTINA, Adrian / FE the design resistance of the link, computed as a web panel according to EC3-1-8 but considering the shear area as presented in Eurocode remains safe, independent of the link length or number of stiffeners. Despite this, the value of the theoretical initial stiffness, computed on the basis of the column web panels (according to EC3-1-8 prescriptions) is similar to the numerical one only for the long links (75 mm). It is certain that the results of the study should be judged in the context of the initial experimental test. Other loading conditions such as cyclic loading, presence of the concrete slab with/without connection over the link or higher link lengths might affect the proved performances. These issues are considered for further investigation by the research team. 6. Acknowledgements This work was partially supported by the strategic grant POSDRU/159/1.5/S/ of the Ministry of National Education of Romania, co-financed by the European Social Fund Investing in People, within the Sectorial Operational Programme Human Resources Development References Danku, G. (211). Study of the development of plastic hinges in composite steel-concrete structural members subjected to shear and/or bending, Ph.D. Thesis, Politehnica University of Timisoara. Danku, G.; Ciutina, A.; Dubina, D. (213). Influence of steel-concrete interaction in dissipative zones of frames: II Numerical study Steel and Composite Structures, Vol. 15, No. 3, ISSN , pp: Dassault Systèmes Simulia Corp, Abaqus , 211. Degée, H.; Lebrun, N.; Plumier, A. (21). Considerations on the design, analysis and performances of eccentrically braced composite frames under seismic action, Proceedings of SDSS 21 Conference Stability and Ductility of Steel Structures,8-1 September 21, Rio de Janeiro, Brazil, Pages: ECCS TWS 1.3 N.45/86, Recommended Testing Procedure for Assessing the Behaviour of Structural Steel Elements under Cyclic Loads. European Committee for Standardisation CEN. EN , 25. Eurocode 3: Design of steel structures. European Committee for Standardization CEN. EN , 24. Eurocode 8: Design of structures for earthquake resistance - Part 1, General rules, seismic actions and rules for buildings. Ioan, P.; Dima, S., (21). Behavior of eccentrically braced structures having active links connected or not with r.c. slab, Proceedings of the 9 th Nordic Steel Conference, 18-2 June 21, Helsinki, Finland Stratan, A. (1998). Studiul Comportării Clădirilor Multietajate cu Cadre Metalice Duale Amplasate Ín Zone Seismice, PhD thesis, Universitatea Politehnica Timişoara. Okazaki, T., Arce, G., Ryu H.C., Engelhardt M.D. (25). Experimental study of local buckling, overstrength, and fracture of links in eccentrically braced frames, Journal of Structural Engineering ASCE, 131(1), Yurisman Y., Budiono B., Moestopo M., Suarjana, M. (21). Behavior of shear link of WF section with diagonal web stiffener of Eccentrically Braced Frame (EBF) of steel structure, ITB Journal of Engineering Science, 42(2),