• Earthquakes and Structures
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• v.9 no.3
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• pp.481-501
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• 2015

Current design codes and technical recommendations often provide rough indications on how to assess effective stiffness of Reinforced Concrete (R/C) frames subjected to seismic loads, which is a key factor when a linear analysis is performed. The Italian design code (NTC-2008), Eurocode 8 and ACI 318 do not take into account all the structural parameters affecting the effective stiffness and this may not be on the safe side when second-order $P-{\Delta}$ effects may occur. This paper presents a study on the factors influencing the effective stiffness of R/C beams, columns and walls under seismic forces. Five different approaches are adopted and analyzed in order to evaluate the effective stiffness of R/C members, in accordance with the scientific literature and the international design codes. Furthermore, the paper discusses the outcomes of a parametric analysis performed on an actual R/C building and analyses the main variables, namely reinforcement ratio, axial load ratio, concrete compressive strength, and type of shallow beams. The second-order effects are investigated and the resulting displacements related to the Damage Limit State (DLS) under seismic loads are discussed. Although the effective stiffness increases with steel ratio, the analytical results show that the limit of 50% of the initial stiffness turns out to be the upper bound for small values of axial-load ratio, rather than a lower bound as indicated by both Italian NTC-2008 and EC8. As a result, in some cases the current Italian and European provisions tend to underestimate second-order $P-{\Delta}$ effects, when the DLS is investigated under seismic loading.

• Structural Engineering and Mechanics
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• v.51 no.3
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• pp.471-485
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• 2014

Until now, the finite corner stiffness of the right-angle frames used as horizontal girders in a bonnet, have not been considered during the design process to result in not a precise result. This paper presents a design equation set for right-angle frames used as horizontal girders in a bonnet assuming rigid corner stiffness. By comparing the center stresses of the right-angle frame according to the design equation set with the results of the finite element method, the master curves for the empirical corner stiffness can be determined as a function of slenderness ratio. A second design equation set for a right-angle frame assuming finite corner stiffness was derived and compared with the first equation set. The master curves for the corner stiffness and the second design equation set can be used to determine the design moments at the centers of the girder so that the bending stresses can be analyzed more precisely.

• Proceedings of the Korea Institute of Convergence Signal Processing
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• 2000.08a
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• pp.113-116
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• 2000

This paper analyzes the singularity of an anthropomorphic robot associated with joint and operational stiffness generation from muscle stiffness. The singularity analysis is made simply based on the signs of the actual and the desired coupling joint stiffness. First, the relationships of the muscle stiffness and the actual joint stiffness, and the operational stiffness and the desired joint stiffness are examined. Second, according to the sign restriction on the actual coupling joint stiffness, the operational space is divided into the semi-singular(SS), the regular(R), and the semi-regular(SR) regions. Third, from the sign comparison of tile actual and the desired coupling joint stiffness, the sufficient condition for the semi-singularity in operational stiffness generation is derived. The limitation on the allowable operational stiffness when a task point belongs to SS, R, and SR regions is also discussed. Simulation results are given.

• Smart Structures and Systems
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• v.16 no.1
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• pp.47-65
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• 2015

A novel finite element (FE) model updating method based on multi-resolution analysis (MRA) is proposed. The true stiffness of the FE model is considered as the superposition of two pieces of stiffness information of different resolutions: the pre-defined stiffness information and updating stiffness information. While the resolution of former is solely decided by the meshing density of the FE model, the resolution of latter is decided by the limited information obtained from the experiment. The latter resolution is considerably lower than the former. Second generation wavelet is adopted to describe the updating stiffness information in the framework of MRA. This updating stiffness in MRA is realized at low level of resolution, therefore, needs less number of updating parameters. The efficiency of the optimization process is thus enhanced. The proposed method is suitable for the identification of multiple irregular cracks and performs well in capturing the global features of the structural damage. After the global features are identified, a refinement process proposed in the paper can be carried out to improve the performance of the MRA of the updating information. The effectiveness of the method is verified by numerical simulations of a box girder and the experiment of a three-span continues pre-stressed concrete bridge. It is shown that the proposed method corresponds well to the global features of the structural damage and is stable against the perturbation of modal parameters and small variations of the damage.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2008.04a
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• pp.72-77
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• 2008

Stability is a very important part which we must consider in structural design. In this paper, we take advantage of finite element method, and study about parametrical instability of star-dome structures, which is subjected to harmonically pulsating load. When calculating stiffness matrix, we consider elastic stiffness and geometrical stiffness simultaneously. In equation of motion, we represent displacements and accelerations by trigonometric series expansions, and then obtain Hill's infinite determinants. After first order approximation, we can get first and second order dynamic instability region finally.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.20 no.1
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• pp.40-46
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• 2011

This paper is to investigate the effects of the asymmetrical support stiffness on the stability of a supercritical driveshaft with asymmetrical shaft stiffness and anisotropic bearings. The equations of motion is derived for a system including a rigid disk, a massless flexible asymmetric shaft, anisotropic bearings and a support beam. The Floquet theory is applied to perform the stability analysis with the variation of the support stiffness, the shaft asymmetry, the shaft damping and the shaft speed. The results show that the asymmetric support stiffness is closely related to the stability caused by primary resonance as well as the supercritical operation. First, the stiffness variation can stabilize the system around primary resonance by weakening the parametric resonance from the shaft asymmetry. Second, it also improve the stability characteristics at a supercritical operation when the support stiffness is not so high relative to the shaft stiffness.

• Structural Engineering and Mechanics
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• v.11 no.4
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• pp.423-442
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• 2001

This paper presents a method of elastic-plastic analysis for planar steel frames that provides the accuracy of distributed plasticity methods with the computational efficiency that is greater than that of distributed plasticity methods but less than that of plastic-hinge based methods. This method accounts for the effect of spread of plasticity accurately without discretization through the cross-section of a beam-column element, which is achieved by the following procedures. First, nonlinear equations describing the relationships between generalized stresses and strains of the cross-section are derived analytically. Next, nonlinear force-deformation relationships for the beam-column element are obtained through lengthwise integration of the generalized strains. Elastic-plastic flexibility coefficients are then calculated by differentiating the above element force-deformation relationships. Finally, an elastic-plastic stiffness matrix is obtained by making use of the flexibility-stiffness transformation. Adding the conventional geometric stiffness matrix to the elastic-plastic stiffness matrix results in the tangent stiffness matrix, which can readily be used to evaluate the load carrying capacity of steel frames following standard nonlinear analysis procedures. The accuracy of the proposed method is verified by several examples that are sensitive to the effect of spread of plasticity.

• Journal of the Korean Society of Safety
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• v.37 no.6
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• pp.60-70
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• 2022

This paper proposes an optimal design method of a seismic reinforcement system for the seismic performance of adjacent asymmetric-stiffness structures with viscous dampers. The first method considers plan asymmetry for efficient seismic reinforcement, and evaluates the seismic performance of optimal design applied to two cases of modeling: adjacent stiffness-asymmetric structures and adjacent stiffness-symmetric structures. The second method considers the response of asymmetric structures to derive the optimal objective function, and evaluates seismic efficiency of the objective function applied to two cases of responses: horizontal displacement and torsion. Numerical analyses are conducted on 7- and 10-story structures with a uni-asymmetric-stiffness plan using six cases of historic earthquakes, normalized to 0.4g. The results indicate that the seismic performance is excellent as modeled by adjacent asymmetric-stiffness structures and how much horizontal displacement is applied as the objective function.

• Structural Engineering and Mechanics
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• v.51 no.5
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• pp.773-792
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• 2014

In this paper, we study the inverse mode shape problem for an Euler-Bernoulli beam, using an analytical approach. The mass and stiffness variations are determined for a beam, having various boundary conditions, which has a prescribed polynomial second mode shape with an internal node. It is found that physically feasible rectangular cross-section beams which satisfy the inverse problem exist for a variety of boundary conditions. The effect of the location of the internal node on the mass and stiffness variations and on the deflection of the beam is studied. The derived functions are used to verify the p-version finite element code, for the cantilever boundary condition. The paper also presents the bounds on the location of the internal node, for a valid mass and stiffness variation, for any given boundary condition. The derived property variations, corresponding to a given mode shape and boundary condition, also provides a simple closed-form solution for a class of non-uniform Euler-Bernoulli beams. These closed-form solutions can also be used to check optimization algorithms proposed for modal tailoring.

• Steel and Composite Structures
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• v.2 no.3
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• pp.209-222
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• 2002

This paper describes the buckling phenomenon of a tubular truss with unsupported length through a full-scale test and presents a practical computational method for the design of the trusses allowing for the contribution of torsional stiffness against buckling, of which the effect has never been considered previously by others. The current practice for the design of a planar truss has largely been based on the linear elastic approach which cannot allow for the contribution of torsional stiffness and tension members in a structural system against buckling. The over-simplified analytical technique is unable to provide a realistic and an economical design to a structure. In this paper the stability theory is applied to the second-order analysis and design of the structural form, with detailed allowance for the instability and second-order effects in compliance with design code requirements. Finally, the paper demonstrates the application of the proposed method to the stability design of a commonly adopted truss system used in support of glass panels in which lateral bracing members are highly undesirable for economical and aesthetic reasons.