• 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.

• Computers and Concrete
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• v.2 no.6
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• pp.423-437
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• 2005

In this study two single-bay, three-storey space frames, one with brick masonry infill in the second and third floors representing a soft-storey frame and the other without infill were designed and their 1:3 scale models were constructed according to non-seismic detailing and the similitude law. The models were excited with an intensity of earthquake motion as specified in the form of response spectrum in Indian seismic code IS 1893-2002 using a shake table. The seismic responses of the soft-storey frame such as fundamental frequency, mode shape, base shear and stiffness were compared with that of the bare frame. It was observed that the presence of open ground floor in the soft-storey infilled frame reduced the natural frequency by 30%. The shear demand in the soft-storey frame was found to be more than two and a half times greater than that in the bare frame. From the mode shape it was found that, the bare frame vibrated in the flexure mode whereas the soft-storey frame vibrated in the shear mode. The frames were tested to failure and the damaged soft-storey frame was retrofitted with concrete jacketing and, subjected to same earthquake motions as the original frames. Pushover analysis was carried out using the software package SAP 2000 to validate the test results. The performance point was obtained for all the frames under study, therefore the frames were found to be adequate for gravity loads and moderate earthquakes. It was concluded that the global nonlinear seismic response of reinforced concrete frames with masonry infill can be adequately simulated using static nonlinear pushover analysis.

• 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.

• Coupled systems mechanics
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• v.9 no.4
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• pp.311-323
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• 2020

This paper deals with the effect of the mode shapes on the dynamic response of a multi-storey frame subjected to moving train loads which are modelled as loads of constant intervals with constant velocity using the finite element method. The multi-storey frame is modelled as a number of Bernoulli-Euler beam elements. First, the first few modes of the multi-storey frame are determined. Then, the effects of force span length to beam length ratio and velocity on dynamic magnification factor (DMF) are evaluated via 3D velocity-force span length to beam length ratio-DMF graphics and its 2D projections. By using 3D and 2D graphics, the directions of critical speeds that force the structure under resonance conditions are determined. Last, the mode shapes related to these directions are determined by the time history and frequency response graphs. This study has been limited by the vibration of the frame in the vertical direction.

• Structural Engineering and Mechanics
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• v.73 no.6
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• pp.699-714
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• 2020

Force based design (FBD) approach is prevalent in most of the national seismic design codes world over. Direct displacement based design (DDBD) and energy based design (EBD) approaches are relatively new methods of seismic design which claims to be more rational and predictive than the FBD. These three design approaches are conceptually distinct and imparts different strength, stiffness and ductility property to structural members for same plan configuration. In present study behavioural assessment of frame of six storey RC building designed using FBD, DDBD and EBD approaches has been performed. Lateral storey forces distribution, reinforcement design and results of nonlinear performance using static and dynamic methods have been compared. For the three approaches, considerable difference in lateral storey forces distribution and reinforcement design has been observed. Nonlinear pushover analysis and time history analysis results show that in FBD frame plastic deformation is concentrated in the lower storey, in EBD frame large plastic deformation is concentrated in the middle storeys though the inelastic hinges are well distributed over the height and, in DDBD frame plastic deformation is approximately uniform over the height. Overall the six storey frame designed using DDBD approach seems to be more rational than the other two methods.

• Advances in concrete construction
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• v.2 no.4
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• pp.261-280
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• 2014

In many parts of the world, reinforced concrete (RC) buildings, designed and built in accordance with older codes, have suffered severe damage or even collapse as a result of recent near-fault earthquakes. This is particularly due to the deficiencies of most of the older (and even some of the recent) codes in dealing with near fault events. In this study, a tested three-storey frame designed for gravity loads only was selected to represent those deficient buildings. Nonlinear time history analyses were performed, followed by damage assessment procedures. The results were compared with experimental observation of the same frame showing a good match. Damage and fragility analyses of the frame subjected to 204 pulse-type motions were then performed using a selected damage model and inter-storey drifts. The results showed that the frame located in near-fault regions is extremely vulnerable to ground motions. The results also showed that the damage model better captures the damage distribution in the frame than inter-storey drifts. The first storey was identified as the most fragile and the inner columns of the first storey suffered most damage as indicated by the damage index. The findings would be helpful in the decision making process prior to the strengthening of buildings in near-fault regions.

• Steel and Composite Structures
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• v.14 no.6
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• pp.523-545
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• 2013

In this study, the effect of presence and distribution of masonry infill walls on the mid-rise steel frame structures having soft ground storey was evaluated by implementing finite element (FE) methods. Masonry infill walls were distributed randomly in the upper storey keeping the ground storey open without any infill walls, thus generating the worst case scenario for seismic events. It was observed from the analysis that there was an increase in the seismic design forces, moments and base shear in presence of randomly distributed masonry infill walls which underlines that these design values need to be amplified when designing a mid-rise soft ground storey steel frame with randomly distributed masonry infill. In addition, it was found that the overstrength related force modification factor increased and the ductility related force modification factor decreased with the increase in the amount of masonry infilled bays and panels. These must be accounted for in the design of mid-rise steel frames. Based on the FE analysis results on two mid-rise steel frames, design equations were proposed for determining the over strength and the ductility related force modification factors. However, it was recommended that these equations to be generalized for other steel frame structure systems based on an extensive analysis.

• Smart Structures and Systems
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• v.5 no.5
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• pp.565-585
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• 2009

Superelastic Shape Memory Alloys (SMAs) are gaining acceptance for use as reinforcing bars in concrete structures. The seismic behaviour of concrete frames reinforced with SMAs is being assessed in this study. Two eight-storey concrete frames, one of which is reinforced with regular steel and the other with SMAs at the plastic hinge regions of beams and regular steel elsewhere, are designed and analyzed using 10 different ground motion records. Both frames are located in the highly seismic region of Western Canada and are designed and detailed according to current seismic design standards. The validation of a finite element (FE) program that was conducted previously at the element level is extended to the structure level in this paper using the results of a shake table test of a three-storey moment resisting steel RC frame. The ten accelerograms that are chosen for analyzing the designed RC frames are scaled based on the spectral ordinate at the fundamental periods of the frames. The behaviour of both frames under scaled seismic excitations is compared in terms of maximum inter-storey drift, top-storey drift, inter-storey residual drift, and residual top-storey drift. The results show that SMA-RC frames are able to recover most of its post-yield deformation, even after a strong earthquake.

• Structural Engineering and Mechanics
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• v.65 no.1
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• pp.9-17
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• 2018

This study concerns about calculating exact natural frequencies of frames using a single variable shear deformation theory (SVSDT) which considers the parabolic shear stress distribution across the cross section. Free vibration analyses are performed for multi-bay, multi-storey and multi-bay multi-storey type frame structures. Dynamic stiffness formulations are derived and used to obtain first five natural frequencies of frames. Different beam and column cross sections are considered to reveal their effects on free vibration analysis. The calculated natural frequencies are tabulated with the results obtained using Euler-Bernoulli Beam Theory (EBT) and Timoshenko Beam Theory (TBT). Moreover, the effects of inner and outer columns on natural frequencies are compared for multi-bay frames. Several mode shapes are plotted.

• International Journal of High-Rise Buildings
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• v.3 no.1
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• pp.21-33
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• 2014

The tied braced frame (TBF) system was developed to achieve uniform seismic inelastic demand along the height of multi-storey eccentrically braced steel frames. A modular tied braced frame (M-TBF) configuration has been recently proposed to reach the same objective while reducing the large axial force demand imposed on the vertical tie members connecting the link beams together in TBFs. M-TBFs may however experience variations in storey drifts at levels where the ties have been removed to form the modules. In this paper, the possibility of reducing the discontinuity in displacement response of a 16-storey M-TBF structure by introducing energy dissipating (ED) devices between the modules is examined. Two M-TBF configurations are investigated: an M-TBF with two 8-storey modules and an M-TBF with four 4-storey modules. Three types of ED devices are studied: friction dampers (FD), buckling restrained bracing (BRB) members and self-centering energy dissipative (SCED) members. The ED devices were sized such that no additional force demand was imposed on the discontinuous tie members. Nonlinear response history analysis showed that all three ED systems can be used to reduce discontinuities in storey drifts of M-TBFs. The BRB members experienced the smallest peak deformations whereas minimum residual deformations were obtained with the SCED devices.