• Steel and Composite Structures
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• v.17 no.6
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• pp.803-824
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• 2014

The dynamic characterization is important in making accurate predictions of the seismic response of the hybrid structures dominated by different damping mechanisms. Different damping characteristics arise from the construction of the tower with different materials: steel for the upper part; reinforced concrete for the lower main part and interaction with supporting soil. The process of modeling damping matrices and experimental verification is challenging because damping cannot be determined via static tests as can mass and stiffness. The assumption of classical damping is not appropriate if the system to be analyzed consists of two or more parts with significantly different levels of damping, such as steel/concrete mixed structure - supporting soil coupled system. The dynamic response of structures is critically determined by the damping mechanisms, and its value is very important for the design and analysis of vibrating structures. An analytical approach capable of evaluating the equivalent modal damping ratio from structural components is desirable for improving seismic design. Two approaches are considered to define and investigate dynamic characteristics of hybrid tower of cable-stayed bridges: The first approach makes use of a simplified approximation of two lumped masses to investigate the structure irregularity effects including damping of different material, mass ratio, frequency ratio on dynamic characteristics and modal damping; the second approach employs a detailed numerical step-by step integration procedure in which the damping matrices of the upper and the lower substructures are modeled with the Rayleigh damping formulation.

• Structural Engineering and Mechanics
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• v.71 no.4
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• pp.445-458
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• 2019

This study mainly aims to assess the performance of soil-structure systems designed by direct displacement-based method coupled with strong column-weak beam design concept through various system identification techniques under strong ground motions. To this end, various system identification methods are employed to evaluate the dynamic characteristics of a structure (i.e., modal frequency, system damping, mode shapes, and plastic hinge formation pattern) under a strong seismic excitation considering soil-structure interaction for different site conditions as specified by ASCE 7-10. The scope of the study narrowed down to the code-complying low- to high-rise steel moment resisting frames with various heights (4, 8, 12, 16-story). The comparison of the result of soil-structure systems with fix-based support condition indicates that the modal frequencies of these systems are highly influenced by the structure heights, specifically for the softer soils. This trend is more significant for higher modes of the system which can considerably dominate the response of structures in which the higher modes have more contribution in dynamic response. Amongst all studied modes of the vibration, the damping ratio estimated for the first mode is relatively the closet to the initial assumed damping ratios. Moreover, it was found that fewer plastic hinges are developed in the structure of soil-structure systems with a softer soil which contradicts the general expectation of higher damageability of such structural systems.

• Structural Engineering and Mechanics
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• v.39 no.5
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• pp.683-701
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• 2011

In this study, inelastic displacement ratios and ductility demands are investigated for SDOF systems with period range of 0.1-3.0 s. with elastoplastic behavior considering soil structure interaction. Earthquake motions recorded on different site conditions such as rock, stiff soil, soft soil and very soft soil are used in analyses. Soil structure interacting systems are modeled with effective period, effective damping and effective ductility values differing from fixed-base case. For inelastic time history analyses, Newmark method for step by step time integration was adapted in an in-house computer program. Results are compared with those calculated for fixed-base case. A new equation is proposed for inelastic displacement ratio of interacting system ($\tilde{C}_R$) as a function of structural period of interacting system ($\tilde{T}$), strength reduction factor (R) and period lengthening ratio ($\tilde{T}/T$). The proposed equation for $\tilde{C}_R$ which takes the soil-structure interaction into account should be useful in estimating the inelastic deformation of existing structures with known lateral strength.

• Coupled systems mechanics
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• v.3 no.2
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• pp.171-193
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• 2014

The dynamic characterization is important in making accurate predictions of the seismic response of the hybrid structures dominated by different damping mechanisms. Different damping characteristics arise from the construction of hybrid structure with different materials: steel for the upper part; reinforced concrete for the lower main part and interaction with supporting soil. The process of modeling damping matrices and experimental verification is challenging because damping cannot be determined via static tests as can mass and stiffness. The assumption of classical damping is not appropriate if the system to be analyzed consists of two or more parts with significantly different levels of damping. The dynamic response of structures is critically determined by the damping mechanisms, and its value is very important for the design and analysis of vibrating structures. A numerical algorithm capable of evaluating the equivalent modal damping ratio from structural components is desirable for improving seismic design. Two approaches are considered to explore the dynamic response of hybrid tower of cable-stayed bridges: The first approach makes use of a simplified model of 2 coupled lumped masses to investigate the effects of subsystems different damping, mass ratio, frequency ratio on dynamic characteristics and equivalent modal damping; the second approach employs a detailed numerical step-by step integration procedure.

• Structural Engineering and Mechanics
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• v.45 no.5
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• pp.655-676
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• 2013

In this study, strength reduction factors and inelastic displacement ratios are investigated for SDOF systems with period range of 0.1-3.0 s considering soil structure interaction for earthquake motions recorded on soft soil. The effect of stiffness degradation on strength reduction factors and inelastic displacement ratios is investigated. The modified-Clough model is used to represent structures that exhibit significant stiffness degradation when subjected to reverse cyclic loading and the elastoplastic model is used to represent non-degrading structures. The effect of negative strain - hardening on the inelastic displacement and strength of structures is also investigated. Soil structure interacting systems are modeled and analyzed with effective period, effective damping and effective ductility values differing from fixed-base case. For inelastic time history analyses, Newmark method for step by step time integration was adapted in an in-house computer program. New equations are proposed for strength reduction factor and inelastic displacement ratio of interacting system as a function of structural period($\tilde{T}$, T) ductility (${\mu}$) and period lengthening ratio ($\tilde{T}$/T).

• Structural Engineering and Mechanics
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• v.41 no.3
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• pp.365-378
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• 2012

In this study, strength reduction factors are investigated for SDOF systems with period range of 0.1-3.0 s with elastoplastic behavior considering soil structure interaction for 64 different earthquake motions recorded on different site conditions such as rock, stiff soil, soft soil and very soft soil. Soil structure interacting systems are modeled and analyzed with effective period, effective damping and effective ductility values differing from fixed-base case. For inelastic time history analyses, Newmark method for step by step time integration was adapted in an in-house computer program. Results are compared with those calculated for fixed-base case. A new equation is proposed for strength reduction factor of interacting system as a function of structural period of system (T), ductility ratio (${\mu}$) and period lengthening ratio (T/T). It is concluded that soil structure interaction reduces the strength reduction factors for soft soils, therefore, using the fixed-base strength reduction factors for interacting systems lead to non-conservative design forces.

• Geomechanics and Engineering
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• v.29 no.2
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• pp.155-170
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• 2022

An accurate analysis of structures supported on soft soils and subjected to seismic loading requires the consideration of the soil-foundation-structure interaction. An important aspect of this interaction lies with the energy dissipation due to soil material damping. Unlike advanced constitutive models that can induce energy loss, the use of simple elastoplastic constitutive models requires additional damping. The frequency dependent Rayleigh damping is a formulation that is frequently used in dynamic analysis. The main concern of this formulation is the correct selection of the target damping ratio and the frequency range where the response is frequency independent. The objective of this study is to investigate the effects of the Rayleigh damping parameters in soil-pile-structure and soil-inclusion-platform-structure systems in the presence of soft soil under seismic loading. Three-dimensional analyses of both systems are carried out using the finite difference software Flac3D. Different values of target damping ratios and minimum frequencies are utilized. Several earthquakes are used to study the influence of different excitation frequencies in the systems. The soil response in terms of accelerations, displacements and strains is obtained. For the rigid elements, the results are presented in terms of bending moments and normal forces. The results show that when the frequency of the input motion is close to the minimum (central) frequency in the Rayleigh damping formulation, the overdamping amount is reduced, and the surface spectral acceleration of the analyzed pile and inclusion systems increases. Thus, the bending moments and normal forces throughout the piles and inclusions also increase.

• Interaction and multiscale mechanics
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• v.6 no.4
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• pp.339-356
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• 2013

This paper investigates the optimized parameters of Tuned Mass Dampers (TMDs) for vibration control of high-rise structures including Soil Structure Interaction (SSI). The Artificial Bee Colony (ABC) method is employed for optimization. The TMD Mass, damping coefficient and spring stiffness are assumed as the design variables of the controller; and the objective is set as the reduction of both the maximum displacement and acceleration of the building. The time domain analysis based on Newmark method is employed to obtain the displacement, velocity and acceleration of different stories and TMD in response to 6 types of far field earthquakes. The optimized mass, frequency and damping ratio are then formulated for different soil types; and employed for the design of TMD for the 40 and 15 story buildings and 10 different earthquakes, and well results are achieved. This study leads the researchers to the better understanding and designing of TMDs as passive controllers for the mitigation of earthquake oscillations.

• Smart Structures and Systems
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• v.29 no.4
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• pp.549-560
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• 2022

The optimum damping and tuning frequency ratio of the tuned mass damper-inerter (TMDI) for the base-isolated structure is obtained using the numerical searching technique under stationary white-noise and filtered white-noise earthquake excitation. The minimization of the isolated structure's mean-square relative displacement and absolute acceleration, as well as the maximization of the energy dissipation index, were chosen as the criteria for optimality. Using a curve-fitting technique, explicit formulae for TMDI damping and tuning frequency for white-noise excitation are then derived. The proposed empirical expressions for TMDI parameters are found to have a negligible error, making them useful for the effective design of base-isolated structures. The effectiveness of TMDI and its optimum parameters are influenced by the soil condition and isolation frequency, according to the comparison made of the optimized parameters and response with different soil profiles. The effectiveness of an optimally designed TMDI in controlling the displacement and acceleration response of the flexible isolated structure under real and pulse-type earthquakes is also observed and found to be increased as the inertance mass ratio increases.

• Structural Engineering and Mechanics
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• v.45 no.6
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• pp.741-758
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• 2013

In this study, inelastic displacement ratios are investigated for existing systems with known lateral strength considering soil structure interaction. For this purpose, SDOF systems for period range of 0.1-3.0 s with different hysteretic behaviors are considered for a number of 18 earthquake motions recorded on soft soil. The effect of stiffness degradation on inelastic displacement ratios is investigated. The Modified Clough model is used to represent structures that exhibit significant stiffness degradation when subjected to reverse cyclic loading and the elastoplastic model is used to represent non-degrading structures. Soil structure interaction analyses are conducted by means of equivalent fixed base model effective period, effective damping and effective ductility values differing from fixed-base case. For inelastic time history analyses, Newmark method for step by step time integration was adapted in an in-house computer program. A new equation is proposed for inelastic displacement ratio of system with SSI with elastoplastic or degrading behavior as a function of structural period ($\tilde{T}$), strength reduction factor (R) and period lengthening ratio ($\tilde{T}$/T). The proposed equation for $\tilde{C}_R$ which takes the soil-structure interaction into account should be useful in estimating the inelastic deformation of existing structures with known lateral strength.