• Structural Engineering and Mechanics
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• v.19 no.6
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• pp.679-705
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• 2005

This paper presents a practical method to evaluate the effective length factors for columns in multi-storey unbraced frames based on the concept of storey-based elastic buckling by means of decomposing a multi-storey frame into a series of single-storey partially-restrained (PR) frames. The lateral stiffness of the multi-storey unbraced frame is derived and expressed as the product of the lateral stiffness of each storey. Thus, the stability analysis for the multi-storey frame is conducted by investigating the lateral stability of each individual storey, which is facilitated through decomposing the multi-storey frame into a series of single-storey PR frames and applying the storey-based stability analysis proposed by the authors (Xu and Liu 2002) for each single-storey PR frame. Prior to introducing decomposition approaches, the end rotational stiffness of an axially load column is derived and rotational stiffness interaction between the upper and lower columns is investigated. Three decomposition approaches, characterized by means of distributing beam-to-column rotational-restraining stiffness between the upper and lower columns, are proposed. The procedure of calculating storey-based column effective length factors is presented. Numerical examples are then given to illustrate the effectiveness of the proposed procedure.

• Structural Engineering and Mechanics
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• v.58 no.1
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• pp.103-119
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• 2016

Multi-storey frame structures are frequently exposed to static and dynamic forces. Therefore analyses of static (buckling) and dynamic stability come into prominence for these structures. In this study, the effects of number of storey, static and dynamic load parameters, crack depth and crack location on the in-plane static and dynamic stability of cracked multi-storey frame structures subjected to periodic loading have been investigated numerically by using the Finite Element Method. A crack element based on the Euler beam theory is developed by using the principles of fracture mechanics. The equation of motion for the cracked multi-storey frame subjected to periodic loading is achieved by Lagrange's equation. The results obtained from the stability analysis are presented in three dimensional graphs and tables.

• Structural Engineering and Mechanics
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• v.11 no.1
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• pp.1-16
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• 2001

This paper discusses the elastic stability of unbraced frames under non-proportional loading based on the concept of storey-based buckling. Unlike the case of proportional loading, in which the load pattern is predefined, load patterns for non-proportional loading are unknown, and there may be various load patterns that will correspond to different critical buckling loads of the frame. The problem of determining elastic critical loads of unbraced frames under non-proportional loading is expressed as the minimization and maximization problem with subject to stability constraints and is solved by a linear programming method. The minimum and maximum loads represent the lower and upper bounds of critical loads for unbraced frames and provide realistic estimation of stability capacities of the frame under extreme load cases. The proposed approach of evaluating the stability of unbraced frames under non-proportional loading has taken into account the variability of magnitudes and patterns of loads, therefore, it is recommended for the design practice.

• International Journal of High-Rise Buildings
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• v.3 no.1
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• pp.81-87
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• 2014

The use of Buckling Restrained Braces (BRB) for enhancing the performance of the buildings is gaining wider acceptance. This paper presents the first application of these devices in a major high-rise building in the Philippines. A 50-storey residential reinforced concrete building tower, with ductile core wall, with BRB system is investigated. The detailed modeling and design procedure of buckling restrained brace system is presented for the optimal design against the two distinct levels of earthquake ground motions; serviceable behavior for frequent earthquakes and very low probability of collapse under extremely rare earthquakes. The stiffness and strength of the buckling restrained brace system are adjusted to optimize the performance of the structural system under different levels of earthquakes. Response spectrum analysis is conducted for Design Basis Earthquake level and Service level, while nonlinear time history analysis is performed for the most credible earthquake. The case study results show the effectiveness of buckling restrained braces.

• Structural Engineering and Mechanics
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• v.11 no.3
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• pp.287-299
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• 2001

Columns in multi-storey frames are presently categorised as either braced or unbraced, usually by means of the stability index criterion, for estimating their effective length ratios by design aids such as 'alignment charts'. This procedure, however, ignores the transition in buckling behaviour between the braced condition and the unbraced one. Hence, this results in either an overestimation or an underestimation of effective length estimates of columns in frames that are in fact 'partially braced'. It is shown in this paper that the transitional behaviour is gradual, and can be approximately modelled by means of a 'fuzzy logic' based technique. The proposed technique is simple and intuitively agreeable. It fills the existing gap between the braced and unbraced conditions in present codal provisions.

• Earthquakes and Structures
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• v.8 no.2
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• pp.423-442
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• 2015

The effects of accidental eccentricity on the seismic response of four-storey steel buildings laterally stabilized by buckling restrained braced frames are studied. The structures have a square, symmetrical footprint, without inherent eccentricity between the center of lateral resistance (CR) and the center of mass (CM). The position of the bracing bents in the buildings was varied to obtain three different levels of torsional sensitivity: low, intermediate and high. The structures were designed in accordance with the seismic design provisions of the 2010 National Building Code of Canada (NBCC). Three different analysis methods were used to account for accidental eccentricity in design: (1) Equivalent Static Procedure with static in-plane torsional moments assuming a mass eccentricity of 10% of the building dimension (ESP); (2) Response Spectrum Analysis with static torsional moments based on 10% of the building dimension (RSA-10); and (3) Response Spectrum Analysis with the CM being displaced by 5% of the building dimension (RSA-5). Time history analyses were performed under a set of eleven two-component historical records. The analyses showed that the ESP and RSA-10 methods can give appropriate results for all three levels of torsional sensitivity. When using the RSA-5 method, adequate performance was also achieved for the low and intermediate torsional sensitivity cases, but the method led to excessive displacements (5-10% storey drifts), near collapse state, for the highly torsionally sensitive structures. These results support the current provisions of NBCC 2010.

• Earthquakes and Structures
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• v.8 no.1
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• pp.253-273
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• 2015

The current investigation has been conducted to examine the effect of gravity loads on the seismic responses of the doubly asymmetric, three-dimensional structures comprising walls and frames. The proposed model includes the P-${\Delta}$ effects induced by the building weight. Based on the variational approach, a 3D finite element with two nodes and six DOF per node including P-${\Delta}$ effects is formulated. Dynamic and static governing equations are derived for dynamic and buckling analyzes of buildings braced by wall-frame systems. The influences of P-${\Delta}$ effects and height of the building on tip displacements under Hachinohe earthquake record are investigated through many structural examples.

• Earthquakes and Structures
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• v.9 no.1
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• pp.29-48
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• 2015

The main purpose of this work is to compare different criteria for the seismic strengthening of RC framed buildings in order to find the optimal combinations of these retrofitting techniques. To this end, a numerical investigation is carried out with reference to the town hall of Spilinga (Italy), an RC framed structure with an L-shaped plan built at the beginning of the 1960s. Five structures are considered, derived from the first by incorporating: carbon fibre reinforced polymer (FRP)-wrapping of all columns; base-isolation, with high-damping-laminated-rubber bearings (HDLRBs); added damping, with hysteretic damped braces (HYDBs); FRP-wrapping of the first storey columns combined with base-isolation or added damping. A three-dimensional fibre model of the primary and retrofitted structures is considered; bilinear and trilinear laws idealize, respectively, the behaviour of the HYDB, providing that the buckling be prevented, and the FRP-wrapping, without resistance in compression, while the response of the HDLRB is simulated by using a viscoelastic linear model. The effectiveness of the retrofitting solutions is tested with nonlinear dynamic analyses based on biaxial accelerograms, whose response spectra match those in the Italian seismic code.

• Earthquakes and Structures
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• v.18 no.1
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• pp.27-44
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• 2020

This work presents a comparison of three performance-based seismic design methods (PBSD) as applied to plane steel frames having eccentric braces (EBFs) and buckling restrained braces (BRBFs). The first method uses equivalent modal damping ratios (ξ_k), referring to an equivalent multi-degree-of-freedom (MDOF) linear system, which retains the mass, the elastic stiffness and responds in the same way as the original non-linear MDOF system. The second method employs modal strength reduction factors (${\bar{q}}_k$) resulting from the corresponding modal damping ratios. Contrary to the behavior factors of code based design methods, both ξ_k and ${\bar{q}}_k$ account for the first few modes of significance and incorporate target deformation metrics like inter-storey drift ratio (IDR) and local ductility as well as structural characteristics like structural natural period, and soil types. Explicit empirical expressions of ξ_k and ${\bar{q}}_k$, recently presented by the present authors elsewhere, are also provided here for reasons of completeness and easy reference. The third method, developed here by the authors, is based on a hybrid force/displacement (HFD) seismic design scheme, since it combines the force-base design (FBD) method with the displacement-based design (DBD) method. According to this method, seismic design is accomplished by using a behavior factor (q_h), empirically expressed in terms of the global ductility of the frame, which takes into account both non-structural and structural deformation metrics. These expressions for q_h are obtained through extensive parametric studies involving non-linear dynamic analysis (NLDA) of 98 frames, subjected to 100 far-fault ground motions that correspond to four soil types of Eurocode 8. Furthermore, these factors can be used in conjunction with an elastic acceleration design spectrum for seismic design purposes. Finally, a comparison among the above three seismic design methods and the Eurocode 8 method is conducted with the aid of non-linear dynamic analyses via representative numerical examples, involving plane steel EBFs and BRBFs.