• Steel and Composite Structures
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• v.39 no.4
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• pp.419-433
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• 2021

In composite structures, shear connectors are crucial components to resist the relative slip between the steel and concrete, and thereby to achieve the composite actions. In the service stage, composite structures are usually in elastic state, so the elastic stiffness of the shear connection is a quite important parameter in the structural analysis of composite structures. Nevertheless, the existing studies mainly focus on the load-slip relationship rather than the tangent stiffness at the initial elastic stage. Furthermore, when composite beams subjected to torque or local load, shear connections are affected by both tensile force and shear force. However, the stiffness of shear connections under combined effects appears not to have been discussed hitherto. This paper investigates the initial elastic stiffness of stud connections under combined effects of biaxial forces. The initial expression and the relevant parameters are obtained by establishing a simplified analytical model of the stud connection. Afterwards, parametric finite element analysis is performed to investigate the effects of the relevant factors, including the stud length, stud diameter, elastic modulus of concrete, elastic modulus of steel and volume ratio of reinforcement. The feasibility of the proposed modelling has been proved by comparing with sufficient experimental tests. Based on the analytical analysis and the extensive numerical simulations, design equations for predicting the initial elastic stiffness of stud connections are proposed. The comparison between the equations and the data of finite element models demonstrates that the equations are accurate enough to serve for engineering communities.

• Structural Engineering and Mechanics
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• v.55 no.4
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• pp.801-813
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• 2015

Flexural stiffness of bridge spans has become even more important parameter since Eurocode 1 introduced for railway bridges the serviceability limit state of resonance. For simply supported bridge spans it relies, in general, on accurate assessment of span moment of inertia that governs span flexural stiffness. The paper presents three methods of estimation of the equivalent moment of inertia for such spans: experimental, analytical and numerical. Test loading of the twin truss bridge spans and test results are presented. Recorded displacements and the method of least squares are used to find an "experimental" moment of inertia. Then it is computed according to the analytical method that accounts for joint action of truss girders and composite deck as well as limited span shear stiffness provided by diagonal bracing. Finally a 3D model of finite element method is created to assess the moment of inertia. Discussion of results is given. The comparative analysis proves efficiency of the analytical method.

• Wind and Structures
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• v.25 no.5
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• pp.459-474
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• 2017

In this study an analytical expression is derived for the natural frequency of the wind turbine towers supported on flexible foundation. The derivation is based on a Euler-Bernoulli beam model where the foundation is represented by a stiffness matrix. Previously the natural frequency of such a model is obtained from numerical or empirical method. The new expression is based on pure physical parameters and thus can be used for a quick assessment of the natural frequencies of both the real turbines and the small-scale models. Furthermore, a relationship between the diagonal and non-diagonal element in the stiffness matrix is introduced, so that the foundation stiffness can be obtained from either the p-y analysis or the loading test. The results of the proposed expression are compared with the measured frequencies of six real or model turbines reported in the literature. The comparison shows that the proposed analytical expression predicts the natural frequency with reasonable accuracy. For two of the model turbines, some errors were observed which might be attributed to the difference between the dynamic and static modulus of saturated soils. The proposed analytical solution is quite simple to use, and it is shown to be more reasonable than the analytical and the empirical formulas available in the literature.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.10a
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• pp.209-216
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• 2000

The purpose of this study is to investigate elasto-plastic behaviour and estimate ultimate resistance capacity of the residential-commercial building subjected to lateral force along the height of structure. Four types of residential-commercial building are chosen as analytical models and investigated by pushover analysis. Pushover analysis estimates initial elastic stiffness, post-yielding stiffness, and plastic hinges on each story of structures through three-dimensional nonlinear analysis program CANNY-99. Skeleton curve of bending stiffness model is bilinear, shear stiffness model is trilinear, and axial stiffness model is elastic. Skeleton curve of axial stiffness model has the axial compression and tension stiffness of reinforced concrete members. This study presents the change of inter story drift, story stiffness and hinge of story and member.

• Steel and Composite Structures
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• v.35 no.1
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• pp.29-41
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• 2020

Cross-beams of modern through truss bridges are connected to truss chord at its nodes and between them. It results in variable rotational end restraint for cross-beams, thus variable bending moment distribution. This feature is captured in three-dimensional modelling of through truss bridge structure. However, for preliminary design or rapid assessment of service load effects such technique of analysis may not be available. So an analytical method of assessment of rotational end restraint for cross-beam of through truss bridges was worked out. Two cases - nodal cross-beam and inter-nodal cross-beam - were analyzed. Flexural and torsional stiffness of truss members, flexural stiffness of deck members and axial stiffness of wind bracing members in the vicinity of the analyzed cross-beam were taken into account. The provision for reduced stiffness of the X-type wind bracing was made. Finally, general formula for assessment of rotational end restraint was given. Rotational end restraints for cross-beams of three railway through truss bridges were assessed basing on the analytical method and the finite element method (three-dimensional beam-element modelling). Results of both methods show good agreement. The analytical method is able to reflect effects of some structural irregularities. On the basis of the obtained results the general values of rotational end restraint for nodal and inter-nodal cross-beams of railway through truss bridges were suggested.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2001.04a
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• pp.287-295
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• 2001

The purpose of this paper to describe an analytical model that is capable of reproducing the hysteretic behavior of beam-column joints under cyclic loading and to suggest the variable of hysteretic model for the inelastic analysis of R/C frame structures to do this quasi-static analysis using IDARC program was performed for the beam-column joints. The effort to obtain the result of analysis similar to those of experiment was made by determining the value for hysteretic parameters representing stiffness degradation, strength deterioration and pinching effect. The accuracy and reliability of the proposed analytical model was demonstrated by comparison of load-displacement relation, maximum strength, stiffness degradation and energy dissipation.

• Structural Engineering and Mechanics
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• v.8 no.1
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• pp.27-38
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• 1999

Cables are used in many applications such as cable-stayed bridges, suspension bridges, transmission lines, telephone lines, etc. Generally, the linear relationship is inadequate to present the behavior of cable structure. In finite element analysis, cables have always been modeled as truss elements. For these types of model, the nonlinear behavior of cables has been always ignored. In order to investigate the importance of the nonlinear effect on the structural system, the effect of cable stiffness has been studied. The nonlinear behavior of cable is due to its sag. Therefore, the cable pretension provides a large portion of the inherent stiffness. Since a cable-stayed bridge has numerous degrees of freedom, analytical methods at present are not convenient to solve this type of structures but numerical methods may be feasible. It is necessary to provide a different and more representative analytical model in order to present the effect of cable stiffness on cable-stayed bridges in numerical analysis. The characteristics of cable deformation have also been well addressed. A formulation of modified modulus of elasticity has been proposed using a numerical parametric study. In order to investigate realistic bridges, a cable-stayed bridge having the geometry similar to that of Quincy Bayview Bridge is considered. The numerical results indicate that the characteristics of the cable stiffness are strongly nonlinear. It also significantly affects the structural behaviors of cable-stayed bridge systems.

• Earthquakes and Structures
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• v.2 no.1
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• pp.43-64
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• 2011

One-dimensional rod theory is very effective as a simplified analytical approach to large scale or complicated structures such as high-rise buildings, in preliminary design stages. It replaces an original structure by a one-dimensional rod which has an equivalent stiffness in terms of global properties. The mechanical behavior of structures composed of distinct constituents of different stiffness such as coupled walls with opening is significantly governed by the local variation of stiffness. Furthermore, in structures with setback the distribution of the longitudinal stress behaves remarkable nonlinear behavior in the transverse-wise. So, the author proposed the two-dimensional rod theory as an extended version of the rod theory which accounts for the two-dimensional local variation of structural stiffness; viz, variation in the transverse direction as well as longitudinal stiffness distribution. This paper proposes how to deal with the two-dimensional rod theory for structures with setback. Validity of the proposed theory is confirmed by comparison with numerical results of computational tools in the cases of static, free vibration and forced vibration problems for various structures. The transverse-wise nonlinear distribution of the longitudinal stress due to the existence of setback is clarified to originate from the long distance from setback.

• Steel and Composite Structures
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• v.51 no.3
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• pp.325-335
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• 2024

Yielding dampers exhibit varying cyclic behavior based on their geometry. These dampers not only increase the energy dissipation of the structure but also increase the strength and stiffness of the structure. In this study, parametric investigations were carried out to explore the impact of angled U-shape damper (AUSD) dimensions on its cyclic behavior. Initially, the numerical model was calibrated using the experimental specimen. Subsequently, analytical equations were presented to calculate the yield strength and elastic stiffness, which agreed with the experimental results. The outcomes of the parametric studies encompassed ultimate strength, effective stiffness, energy dissipation, and equivalent viscous damper ratio (EVDR). These output parameters were compared with similar dampers. Also, the magnitude of the effect of damper dimensions on the results was investigated. The results of parametric studies showed that the yield strength is independent of the damper width. The length and thickness of the damper have the greatest effect on the elastic stiffness. Reducing length and width resulted in increased energy dissipation, effective stiffness, and ultimate strength. Damper width had a more significant effect on EVDR than its length. On average, every 5 mm increase in damper thickness resulted in a 3.6 times increase in energy dissipation, 3 times the effective stiffness, and 3 times the ultimate strength of the model. Every 15 mm reduction in damper width and length increased energy dissipation by 14% and 24%, respectively.

• Smart Structures and Systems
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• v.26 no.4
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• pp.481-493
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• 2020

The negative stiffness spring and inerter are both characterized by the negative stiffness effect in the force-displacement relationship, potentially yielding an amplifying mechanism for dashpot deformation by being incorporated with a series tuning spring. However, resisting forces of the two mechanical elements are dominant in different frequency domains, thus leading to necessary complementarity in terms of vibration control and the amplifying benefit. Inspired by this, this study proposes a Negative Stiffness Inerter System (NSIS) as an earthquake protection system and developed analytical design formulae by fully utilizing its advantageous features. The NSIS is composed of a sub-configuration of a negative stiffness spring and an inerter in parallel, connected to a tuning spring in series. First, closed-form displacement responses are derived for the NSIS structure, and a stability analysis is conducted to limit the feasible domains of NSIS parameters. Then, the dual advantageous features of displacement reduction and the dashpot deformation amplification effect are revealed and clarified in a parametric analysis, stimulating the establishment of a displacement-based optimal design framework, correspondingly yielding the design formulae in analytical form. Finally, a series of examples are illustrated to validate the derived formulae. In this study, it is confirmed that the synergistic incorporation of the negative stiffness spring and the inerter has significant energy dissipation efficiency in a wide frequency band and an enhanced control effect in terms of the displacement and shear force responses. The developed displacement-based design strategy is suitable to utilize the dual benefits of the NSIS, which can be accurately implemented by the analytical design formulae to satisfy the target vibration control with increased energy dissipation efficiency.