• Steel and Composite Structures
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• v.48 no.3
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• pp.321-333
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• 2023

This paper proposes a comprehensive investigation on lateral stiffness of corner-supported steel modular frame using splice connection. A full-scale modular frame with two stacked steel modules under lateral load is tested. Ductile pattern in the transfer of lateral load is found in the final failure mode. Two types of lateral stiffness, including tangent stiffness and secant stiffness, are defined from the load-displacement due to the observed nonlinearity. The difference between these two types of stiffness is found around 20%. The comparisons between the experimental lateral stiffness and the predictions of classical methods are also conducted. The D-value method using hypothesis of independent case is a conservative option for predicting lateral stiffness, which is more recommended than method of contraflexural bending moment. Analyses on two classical short-rod models, including fix-rod model and pin-rod model, are further conducted. Results indicate that fix-rod model is more recommended than pin-rod model to simplify splice connection for simulation on lateral stiffness of modular frame in elastic design stage.

• Computers and Concrete
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• v.23 no.5
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• pp.335-349
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• 2019

A low-cycle loading experiment of 16 transfer column specimens was conducted to study the influence of parameters, likes the extension length of shape steel, the ratio of shape steel, the axial compression ratio and the volumetric ratio of stirrups, on the shear distribution between steel and concrete, the concrete damage state and the degradation of lateral stiffness. Shear force of shape steel reacted at the core area of concrete section and led to tension effect which accelerated the damage of concrete. At the same time, the damage of concrete diminished its shear capacity and resulted in the shear enlargement of shape steel. The interplay between concrete damage and shear force of shape steel ultimately made for the failures of transfer columns. With the increase of extension length, the lateral stiffness first increases and then decreases, but the stiffness degradation gets faster; With the increase of steel ratio, the lateral stiffness remains the same, but the degradation gets faster; With the increase of the axial compression ratio, the lateral stiffness increases, and the degradation is more significant. Using more stirrups can effectively restrain the development of cracks and increase the lateral stiffness at the yielding point. Also, a formula for calculating the yielding lateral stiffness is obtained by a regression analysis of the test data.

• Earthquakes and Structures
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• v.12 no.4
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• pp.437-448
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• 2017

Soft or extreme soft storeys in multi-storied buildings cause localized damage (and even collapse) during strong earthquake shaking. The presence of such soft or extremely soft storey is identified through provisions of vertical stiffness irregularity in seismic design codes. Identification of the irregularity in a building requires estimation of lateral translational stiffness of each storey. Estimation of lateral translational stiffness can be an arduous task. A simple procedure is presented to estimate storey stiffness using only properties of fundamental lateral translational mode of oscillation (namely natural period and associated mode shape), which are readily available to designers at the end of analysis stage. In addition, simplified analytical expressions are provided towards identifying stiffness irregularity. Results of linear elastic time-history analyses indicate that the proposed procedure captures the irregularity in storey stiffness in both low- and mid-rise buildings.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.19 no.9
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• pp.84-90
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• 2018

In constructing the multi-body dynamics model to analyze the behavior of the railway vehicle, it is very important to understand the properties of the suspension elements that constitute the suspension system. Among them, coil springs, which are mainly used in primary and secondary suspension systems, clearly show the axial stiffness in the drawings, but the lateral properties of the coil springs are not specified clearly, making it difficult to construct a dynamic analysis model. Therefore, in this paper, the model for analyzing the lateral stiffness of the coil spring is examined. A finite element method was applied to analyze the lateral stiffness of the coil spring and numerical analysis was performed by applying the coil spring lateral stiffness analysis model proposed by Krettek and Sobczak. And the test to analyze the lateral stiffness of coil spring was conducted. As a result of comparing with the test results, it was found that the results obtained by applying the lateral stiffness analysis model of Krettek and Sobczak and correcting the correction coefficient are similar to those of the test results.

• Journal of International Academy of Physical Therapy Research
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• v.12 no.1
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• pp.2272-2278
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• 2021

Background: Vibration stimulation has emerged as a treatment tool to help reduce spasticity during physical therapy. Spasticity includes problems of reduced range of motion (ROM) and stiffness. However, the benefits of vibration rolling (VR) on interventions for stroke patients are unclear. Objectives: This study aimed to investigate the effect of VR intervention on the ankle ROM and ankle stiffness in stroke patients. Design: A randomized crossover study. Methods: Seven stroke patients completed two test sessions (one VR and one non-VR [NVR]) in a randomized order, with 48 hours of rest between each session. Participants completed intervention and its measurements on the same day. The measurements included ankle dorsiflexion and plantarflexion ROM and stiffness of ankle muscles, including the tibialis anterior, medial, and lateral gastrocnemius muscle. Results: After VR, ankle dorsiflexion ROM, lateral gastrocnemius stiffness, and medial gastrocnemius stiffness improved significantly (all P<.05). After NVR, only the lateral gastrocnemius stiffness improved significantly (P<.05). Furthermore, in the cases of changed values for ankle dorsiflexion ROM and lateral gastrocnemius stiffness were compared within groups, VR showed a more significant difference than NVR (P<.05) Conclusion: VR improved ankle ROM and muscle stiffness. Therefore, we suggest that practitioners need to consider VR as an intervention to improve dorsiflexion ROM and gastrocnemius stiffness in stroke patients.

• Proceedings of the KSR Conference
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• 2010.06a
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• pp.680-683
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• 2010

The lateral stiffness of the track structure is very important mechanical property to prevent the track buckling and progress of misalignment. The increasing methods of the lateral stiffness of the track structure are the following; increases of the lateral ballast resistance, and increases of the lateral stiffness of the track panel. In order to increase the lateral stiffness of the tack panel, some of the sleepers resist together against the lateral movement can be the most economical and mechanical method. In this paper, H-typed sleeper developed to solve this problem is introduced and the mechanical advantages of this sleeper are investigated.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.15 no.2
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• pp.271-279
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• 2002

This study develops the module to find the lateral stiffness influence matrix of each story and performs the displacement sensitivity analysis by virtual load method for the efficiency of optimal design using lateral stiffness influence matrix. Also, resizing technique based on the estimated lateral stiffness increment factors is developed to apply directly the results of optimal design. To this end, resizing technique is divided into the continuous and discrete section design methods. And then the relationships between section properties and section size are established. Specifically, an initial design under strength constraints is first performed, and then the lateral load resistant system is designed to control lateral displacements yet exceeding the drift criteria. Two types of 45-story three dimensional structures we presented to illustrate the features of the lateral drift control and resizing technique for tall buildings proposed in this study.

• Steel and Composite Structures
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• v.46 no.3
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• pp.293-318
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• 2023

This study aims to examine the elastic stiffness properties of Elliptic-Braced Moment Resisting Frame (EBMRF) subjected to lateral loads. Installing the elliptic brace in the middle span of the frames in the facade of a building, as a new lateral bracing system not only it can improve the structural behavior, but it provides sufficient space to consider opening it needed. In this regard, for the first time, an accurate theoretical formulation has been developed in order that the elastic stiffness is investigated in a two-dimensional single-story single-span EBMRF. The concept of strain energy and Castigliano's theorem were employed to perform the analysis. All influential factors were considered, including axial and shearing loads in addition to the bending moment in the elliptic brace. At the end of the analysis, the elastic lateral stiffness could be calculated using an improved relation through strain energy method based on geometric properties of the employed sections as well as specifications of the utilized materials. For the ease of finite element (FE) modeling and its use in linear design, an equivalent element was developed for the elliptic brace. The proposed relation was verified by different examples using OpenSees software. It was found that there is a negligible difference between elastic stiffness values derived by the developed equations and those of numerical analysis using FE method.

• Steel and Composite Structures
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• v.45 no.3
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• pp.437-454
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• 2022

Elliptic-braced simple resisting frame as a new lateral bracing system installed in the middle bay of frame in building facades has been recently introduced. This system not only creates a problem for opening space from the architectural viewpoint but also improves the structural behavior. Despite the researches on the seismic performance of lateral bracing systems, there are few studies performed on the effect of the stiffness parameters on the elastic story drift and calculation of period in simple braced steel frames. To overcome this shortcoming, in this paper, for the first time, an analytical solution is presented for calculating elastic lateral stiffness in a simple steel frame equipped with elliptic brace subjected to lateral load. In addition, for the first time, in this study, a precise formulation has been developed to evaluate the elastic stiffness variation in a steel frame equipped with a two-dimensional single-story single-span elliptic brace using strain energy and Castigliano's theorem. Thus, all the effective factors, including axial and shear loads as well as bending moments of elliptic brace could be considered. At the end of the analysis, the lateral stiffness can be calculated by an improved and innovative relation through the energy method based on the geometrical properties of the employed sections and specification of the used material. Also, an equivalent element of an elliptic brace was presented for the ease of modeling and use in linear designs. Application of the proposed relation have been verified through a variety of examples in OpenSees software. Based on the results, the error percentage between the elastic stiffness derived from the developed equations and the numerical analyses of finite element models was very low and negligible.

• Tribology and Lubricants
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• v.28 no.6
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• pp.289-296
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• 2012

Atomic force microscopy (AFM) has been used for imaging surfaces and measuring surface forces at the nano-scale. Force calibration is important for the quantitative measurement of forces at the nano-scale using AFM. Normal force calibration is relatively straightforward, whereas the lateral force calibration is more complicated since the lateral stiffness of the cantilever is often comparable to the contact stiffness. In this work, the lateral force calibrations of the rectangular cantilever were performed using torsional Sader's method, thermal noise method, and wedge calibration method. The lateral optical lever sensitivity for the thermal noise method was determined from the friction loop under various normal forces as well. Experimental results showed that the discrepancies among the results of the different methods were as large as 30% due to the effect of the contact stiffness on the lateral force calibration of the cantilever used in this work. After correction for the effect of contact stiffness, all the calibration results agreed with each other, within experimental uncertainties.