Investigation of nonlinear behaviour of eccentrically braced frames with different link configuration

Five different samples of eccentrically braced frames by a vertical plane with a height of 30.5 m and a length of 35 m at each direction in the horizontal plane were modeled using SAP2000 computer program and analyzed and designed based on ASCE 7-10, AISC 360-10, and AISC 341-10. In determining the models, the same link length and all the loads, with no period effect were used to rule out potential effects of circumstances excluding the configuration. Then, based on the nonlinear pushover analysis via OpenSEES program, and using base shear- roof drift curves, the behaviors, capacity, and overstrength factors of these systems were compared. In the light of the literature review provided in Part 2, the systems defined in earlier studies have been limited to typical eccentrically braced frames. Thus, this study may provide important information on different systems. In describing the models of eccentrically braced frames, the definition of eccentricity in AISC 341-10 has been influential, and all the models have been based on this definition. Yielding of the link beam in eccentrically braced frame occurs in three forms due to variations in the elements; shear yielding, flexural yielding and combination of shear and flexural yielding. In this study, modeling was made according to shear yielding state and hence, the systems were designed. Length of the link beam is smaller than 1.6Mp/Vp, it is contained that the strain hardening effects of moment and shear capacity of the beam. Furthermore, AISC 360-10 advocates involvement of second order effects in element sizing. There are three types of design methods in AISC 360-10: direct analysis method, effective length method and first-order analysis method. Second order effects were considered within amplification factors and one of the three methods, effective length method, has been used as described in the regulations. To be able to use this method, it was proven that the ratio of maximum second-order drift to maximum first order drift is less than 1.5 for all type of eccentrically braced frame structures. Morover, all deformations (axial member, flexural member and shear member), uncertainity in stiffness and strength, stiffness reductions (residual stress and plasticity) and geometric imperfections were considered. According to AISC 360-10 the effective length factor ,K, was taken as 1.0 because of braced frames system. Initial imperfections were taken into account by applying notional loads as mentioned in the regulation (AISC 360-10). It is considered 0.2% of the total gravity load (LRFD)at each level. Load and Resistance Factor Design (LRFD) and Allowable Stress Design (ASD) are the two methods which are presented by AISC. Load and resistance factor design approach was used. Load combinations were determined based on LRFD in ASCE 7-10. All connections of columns and braceds to their foundations are pinned. Braced to link beam connections are rigid (fixed). ASTM A992 was used as a material. Secondary beams have pinned connections. Floor diaphragms are assumed and modeled as a rigid diaphragm without any discontinuities. The loads used have been categorized as horizontal and vertical. The definition of vertical load involves loads of dead and live. While the dead loads can be used based on the materials to be used in the design without a requirement for regulations, the lower limits of live loads are defined by ASCE 7-10. The calculations of earthquake and wind loads considered horizontal loads are also defined in the relevant sections of ASCE 7-10. All structures were thought in the same seismic and wind region, so all of the parameters related to wind and seismic calculation were assumed the same. 5% additional eccentricity at each story was taken into account in 3D analysis. Seismic design category was determined as E for the models. The earthquake loads contain 100% of forces for one direction (x or y) plus 30% of forces for another direction (y or x). Directional procedure was used for wind loads. Basic wind speed was determined from a given map in ASCE 7-10 and taken into account as a 100mph. It was checked that displacements and second order effects are within the limits of the regulations based on the results of analyses. The definition of irregularities contains vertical and horizontal structural irregularities. Also, all irregularities which is defined in ASCE 7-10 were checked. Lateral load resisting systems have different energy dissipation mechanisms. In eccentrically braced frame which is one of the lateral load resisting systems, ductility and energy dissipation capacity depends on link beams. Inelastic deformation of link beam will be expected during an earthquake occurs, therefore plastic link rotation capacity is an important property of eccentrically braced frame structures. In sizing of the eccentrically braced frames, when the plasticity of link beam parts occur, the beam that remains outside the link beam, column, and braced are expected to remain in the elastic area. To ensure this, the forces that occur on the elements except link beam have been increased at ratio of expected shear capacity over shear force that develops on the link beam due to earthquake effects. Because of this, B2 was equal to 1. Since all sections used as a column and braced have to ensure highly ductile section property, these sections were controlled in according to AISC 341-10. According to AISC 341-10 links whose length are smaller than 1.6Mp/Vp are permitted to meet moderately ductile members' section requirement. The link beam had been designed and its section had been determined. Then the expected shear capacity of the link was determined using with Ry, the ratio of expected yield strength to minimum specified yield strength, and ratio of expected shear capacity over shear force that develops on the link beam due to earthquake effects were determined. At the same time, columns' axial forces were estimated based on the failure mode of the structures. To built up nonlinear model in 3D (6 degree of freedom); coordinate system was defined, and node coordinates of models were determined in this system. Material and section properties were defined. After determining which elements should be used, elements with convenient sections were defined by connecting the relevant nodes. Before the pushover loads had been defined, static vertical loads and mass were assigned. As the systems, the sections of which were determined, were modeled by OpenSEES computer program, their conformity to the model set by SAP2000 computer program was checked by comparison of the periods. After model development, using nonlinear static pushover analysis, base shear- roof displacement curves for all the systems and demand/capacity ratios for system elements were obtained. Demand/capacity ratio of column and braced were determined under compression force and moment interaction. As a results, it occurred that some of link rotations are larger than 0.08 rad which is determined by AISC 341-10. It had been observed in different academic studies before. As it has been assumed before, inelastic behavior of link beam was controlled by shear yielding and all parts of structures were remain elastic. Overstregth factors of these eccentrically braced frames were determined and compared to each other.