Proceedings of the th WSEAS International Conference on Sustainability in Science Engineering Numerical simulation of composite steel-concrete eccentrically braced frames (EBF) under cyclic actions GELU DANKU DAN DUBINA Department Of Steel Structures and Structural Mechanics University Politehnica of Timisoara Str. Ioan Curea, nr. ROMANIA gelu.danku@ct.upt.ro Abstract: - In case of beam-to-column connections, beams and dissipative bars within eccentrically braced frames, one should consider that the practical solution of ensuring a ductile and controllable behaviour by usual means is to not apply connectors between the steel elements and the reinforced concrete slab. Experimental tests will be planned in order to prove that the steel elements which are disconnected from the concrete will function independently. We will try to calibrate these experimental tests based on numerical simulations with FEM (Finite Element Method) which will also be used later on in some global elasto-plastic structural analises with accelerograms. These investigations will be done based on a complete parametric study regarding the safety of using such procedures (deconnecting the composite elements in areas where ductility is needed) in seismic regions such as Romania. The check and dimensioning according to Eurocode 3 and P will be presented and also the results of Time-History structural analysis for 3 earthquakes, and push-over analysis. The results will be commented upon in terms of structural performance, according to FEMA 356, regarding structural damage after earthquake. Key-Words: - Plastic hinges, composite sections, action, monotonous, cyclic Introduction The design at limit states of structures situated in seismic areas can be approached generally by two methods: - by considering the structures to be ductile; - by isolating the structures from the ground motion. The first concept leads to the design of dissipative structures, which are capable to withstand earthquakes by entering the plstic domain. Dissipative structures are meant to allow the yielding of the material in certain sections, called dissipative zones. These must dissipate the kinetic energy of the earthquake by having a histeretic behaviour in the plastic domain. The development of dissipative mechanisms depend on the structural configuration. In addition to this, the sections which are meant to remain in the elastic domain must be designed such that they don t yield ; that is why they are usually designed to be more resistant than necessary with respect to the efforts transmitted by the dissipative elements. The main types of dissipative frames can be classified function of the type and the location of the dissipative elements. One can mention three cathegories: - centrically braced frames, as shown in fig. a), b), d) ; - eccentricaly braced frames, as in fig. c) ; - moment resisting frames, as in fig. e). The dissipative elements of the centrically braced frames Figure a), b), d) are the diagonals in tension, hence the compressed diagonals work by buckling. The multistory frame structures equiped with eccentric braces (EBF) are the alternative to the above mentioned centrically braced frames (CBF). Their behaviour is characterised by a stiffening effect given by the eccentric braces. Due to this fact, each beam is divided into two or more parts, which have a different behaviour when acted upon by an earthquake. The shortest element, also called a link or link element, represents the dissipative part of the beam. Function its length, the seismic energy is dissipated by means of elasto-plastic shear cycles (for the short link), bending cycles (for the long link) and shear and bending cycles (for the intermediate link). ISSN: 79-769 43 ISBN: 978-96-474-8-
Proceedings of the th WSEAS International Conference on Sustainability in Science Engineering a) b) c) d) e) Fig. Frequent examples of braced frames (a-d) and moment resisting frames The EBF are used world-wide for the multistory frame structures of reduced or medium height. These systems are capable of offering a sufficient dissipative capability, due to the many dissipative elements. This way, the neccessary requirements for the buildings safety are met, even in case of severe earthquakes. The dissipative elements of eccentrically braced frames are characterised by the forming of plastic hinges, situated at the extremities of frame elements, preferably in the beams, and only at limit states in columns. The Analysed Frame Initially, the base frame was considered to be made only of steel, and later on a frame with composite beams was also analysed, the results being commented upon in tables. The differences appeared in the order the plastic hinges were developing and the maximum rotations of the hinges. The frame to be analysed is part of a dual frame structure MRF+EBF, having 3 spans and 3 bays, like in the figure: stories and 3 spans, the central span being eccentrically braced, while the first and the last spans are moment resisting frames. All spans have 4.5 m each, and the story height is.4 m. The dissipative element (the link) from the EBF has the characteristics of a short link (a length of.3 m) and was modeled in stages, first as a fixed link and then as a detachable link, by decreasing its shear rigidity. This hypothesis comes from the fact that in a detachable link the rigidity is affected by the effect of slip at the bolt holes (because of tolerances) phenomenon known as pinching effect and the rotations at the end of the link, which appear during a dynamic loading. This structure was chosen because its dimensions allow the extraction of a single frame (the most stressed frame) which will than be tested in the CEMSIG laboratory, in order to be able to compare the results obtained analitically with the experimental ones. Fig. Floor plan of the structure From this structure a facade frame was extracted, namely the frame from the first axis, because this one had less gravitational loads. The frame has 5 Fig. 3 The dual frame which was analysed Onto this frame the loads applied were computed using the valid romanian norms. These loads included dead load, live load and level masses. The load combinations which were applied onto the structure are the following: a) Fundamental combination: ULS:.35G +.5Q ISSN: 79-769 44 ISBN: 978-96-474-8-
Proceedings of the th WSEAS International Conference on Sustainability in Science Engineering SLS:.G +.Q b) Special combination: ULS: G + E +.4Q [dissipative] ULS: G + ΩE +.4Q [non-dissipative] SLS: G + q γ E +.4Q The design spectra used was the one for Bucharest (elastic spectra/q), having the following characteristics: - corner period: Tc =.6 s - ground acceleration a g =.4g These characteristics were taken from the romanian earthquake design code P/-6. The behavior factor q was considered for a structure of high ductility, so q=6 (according to P- ch. 6/ table 6.3), as follows: q=.*5 = 6 (high ductility class) The value of the multiplication of. γ ov Ω was taken to be.5, for dual frames made of eccentrically braced frames and moment resisting frames. (according to annex F.4./P-/6) The design and check of structural elements was performed according to Eurocode 3, taking into account the provisions of P for the dissipative elements. The check was performed separately for the beams of the MRF and for the link using the combinations at ULS (fundamental) and ULS (special). The columns, braces and beams of the EBF were checked under the action of ULS (nondissipative) combination of loads. (G +.*.5* ΩE +.4Q) Following this design procedure, the following sections resulted for the structural elements: - columns ECBF HEB - columns MRF HEB6 - beams ECBF IPE4 - link IPE4 - beams MRF IPE 4 3 Performed Analyses On the dimensioned frame the following Pushover and Time-history analyses were performed in two frame configurations: - with a standard link (continuous) - with a detachable link The incremental dynamic analyses of Timehistory type (TH) was performed using the scaled recordings of 3 earthquakes from Vrancea region, from 977, 986 and 99. The accelerograms used were recorded at INCERC Bucharest site. The most powerful earthquake (Vrancea 977, NS component) has the peak value PGA=.9g. Fig. 4 Earthquake Vrancea 77 Fig. 5 Earthquake Vrancea 86 Fig. 6 Earthquake Vrancea 86 4 The studied para The incremental analysis was scaled at values of.,.4,.6,.8,.,.,.4.6,.8 and. from the value of the recorded quake, following the development of plastic hinges and interstory drift. The obtained values were compared to the allowed values from SR EN-998-. Following these analyses the values of the interstory drift and the rotations in the plastic hinges were extracted as results, in order to compare them on performance levels. 5 Modelling procedure The functioning mechanism of the plastic hinge in the link is given by a force-displacement curve of rigid-plastic type with strengthtening and degradation, as follows: Fig. 7 The force-displ. curve which models the behavior of the link In the following figures one can observe the behavior of the dissipative link, and also the ISSN: 79-769 45 ISBN: 978-96-474-8-
Proceedings of the th WSEAS International Conference on Sustainability in Science Engineering maximum allowed rotation function of the bar s length: Fig. 8 Rotation of the link Fig. Hinges formed after the push-over The following diagrams present the differences in terms of drift between the structure equipped with a standard (fixed) link and a detachable link respectively, function the earthquake recording used in the analysis: 6. Vrancea 77 Earthquake standard and detachable link Fig. 9 Maximum allowed rotation.5 6 Numerical results The results extracted after the analyses were used to compare the behavior of the structure function the earthquake it was acted upon and to measure the interstory drift, being able to confirm whether the structure had an appropriate behavior or not. The dissipated energies were calculated by: λu q =, where λ u the value of the multiplying λ e factor of the accelerogram for which the structure fails (by reaching dynamic instability). λe the value of the multiplying factor for which the first plastic hinge appears. Values of q for Accelerogram Fixed link Detachable link VR77 5.5 5 VR86 3.3 3 VR9 4.6 The push-over analysis performed on the initial model revealed the fact that the structure tends to develop plastic hinges in the MRF s columns when the displacement reaches high values. In order to achieve a satisfactory behavior, a more efficient type of steel was used as a material for the MRF columns. (S355 instead of S35) After this modification, the structure behaved in a considerably better way, as we can observe in the following figure:.5.5.5..5..5.5.5.5..5. One can see that the failure mechanism is producing for a value of the multiplication factor of., and in the case of th detachable link for λ=. 6. Vrancea 86 Earthquake fixed and detachable link.5.5.5.5..5. ISSN: 79-769 46 ISBN: 978-96-474-8-
Proceedings of the th WSEAS International Conference on Sustainability in Science Engineering.5.5.5.5..5. For a value of λ=.8, respectively.6 the structure develops a failure mechanism. 6.3 Vrancea 9 Earthquake fixed and detachable link.5.5.5.5..5..8.6.4..8.6.4..5..5. The failure mechanism is formed at λ=.4 and λ=.6., respectively. The maximum interstory drifts are compared in tables, as follows: Max Inter-story Drift S35/S355 Std. link Limit St. VR77 VR86 VR9 SLS.33.488.6 SLU.547.36.788 CPLS.636.4878.94 Max Inter-story Drift S35/S355 Det. link Limit St. VR77 VR86 VR9 SLS.59.574.558 SLU.495.5565.853 CPLS.598.778.3 The limit states correspond to the following values of the multiplier: SLS λ=.4 ULS λ=. CPLS λ=. One can easily notice that the rigidity of the entire structure is affected by the rigidity of the detachable link, this fact yields to greater story displacement in the second case. In a similar way we can compare the values of the rotations in the plastic hinges in the link. It can be seen that because the ground acceleration is bigger for Vrancea 9 quake, the structural damages are more pronounced in this case although this earthquake had a shorter duration. In the second part of this numerical simulations study, the same structure was considered, having the same geometry and characteristics, but the beams were replaced with composite beams. This lead to a higher structural rigidity overall. The developing of plastic hinges has been favored by considering a composite section only in the areas where no plastic hinges are expected to appear, i.e. at a distance of h (h-beam height) from the beam-to-column connections and outside the link. The incremental-dynamic analysis gave similar results with the first structural configuration, with the comment that the story drift and link rotations have smaller values than in the case of the steel structure. Regarding the interstory drift values, these can be found in the next tables: Max Inter-story Drift S35/S355 link fix Limit St. VR77 VR86 VR9 SLS.96.74.86 SLU.365.4578.654 CPLS.448.655.88 Max Inter-story Drift S35/S355 link det Limit St. VR77 VR86 VR9 SLS.39.44.379 SLU.3987.53.65 CPLS.54.688.897 Just like the structure with steel beams, the structure with composite beams tends to be more deformable when the link is considered to be detachable. Generally the development of plastic hinges started in the links and then spread at CPLS limit state in the MRF beams, but only at the first level, and having values which are within the admissible limits. In the following figures we can see the behaviour of the structure in the second configuration, under the action of the three earthquakes, Vrancea 77, 86 and 9: ISSN: 79-769 47 ISBN: 978-96-474-8-
Proceedings of the th WSEAS International Conference on Sustainability in Science Engineering 6.4 Vrancea 77 Earthquake standard and detachable link composite beams.5.5.5.5.5.5.5..5..5..5. After a close examination, one could see that the structure behaves in a satisfactory way..5.5.5.5..5. 6.5 Vrancea 86 Eartquake standard and detachable link composite beams.5.5.5 7 Conclusion Considering the results obtained, the next step will be the calibration of a valid experimental model. For this model an EBF will be extracted from the structure, and this will be subjected to various analyses and loads, in which the beam will be composite with full or partial interaction to see in which way the dissipative behavior of the composite beam can be favored. References: [] Ciutina, Adrian, 3, Comportamentul seismic al imbinarilor cadrelor necontravantuite metalice si compuse: studiu experimental si simulare numerica, teza de doctorat INSA Rennes..5..5..5 [] A. Aldea, C. Arion, A. Ciutina, T. Cornea, D. Florea, L. Fulop, D. Grecea, A. Stratan, R. Vacareanu, 3, Constructii amplasate in zone cu miscari seismice puternice, Ed. Orizonturi Universitare, Timisoara.5.5 [3] M.A.Conti, V.Piluso, G. Rizzano & I.Tolone, Seismic Reliability of Steel-concrete composite frames, STESSA 6, Taylor & Francis Group, London.5..5. 6.6 Vrancea 9 Earthquake standard and detachable link composite beams.5 [4] Bungale S. Taranath Ph. D., S.E., Wind and Earthquake Resistant Buildings, Taylor & Francis Group, 5 [5] Ciutina, Adrian & Lachal, Alain, L acier dans la construction moderne, Ed. Politehnica, 5.5.5.5..5. ISSN: 79-769 48 ISBN: 978-96-474-8-