• Smart Structures and Systems
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• v.26 no.3
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• pp.361-371
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• 2020

Exact solution for nonlinear behavior of clamped-clamped functionally graded (FG) buckled beams is presented. The effective material properties are considered to vary along the thickness direction according to exponential-law form. The in-plane inertia and damping are neglected, and hence the governing equations are reduced to a single nonlinear fourth-order partial-integral-differential equation. The von Kármán geometric nonlinearity has been considered in the formulation. Galerkin procedure is used to obtain a second order nonlinear ordinary equation with quadratic and cubic nonlinear terms. Based on the mode of the corresponding linear problem, which readily satisfy the boundary conditions, the frequencies for the nonlinear problem are obtained using the Jacobi elliptic functions. The effects of various parameters such as the Young's modulus ratio, the beam slenderness ratio, the vibration amplitude and the magnitude of axial load on the nonlinear behavior are examined.

• Journal of the Earthquake Engineering Society of Korea
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• v.20 no.6
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• pp.361-368
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• 2016

Coupling beams serve as primary source of energy dissipation in coupled shear wall systems during large earthquakes. However, the overestimation of the shear strength of diagonally reinforced coupling beams may be adverse effect on the seismic performance of coupled shear wall systems. In order to force coupling beams to properly work during earthquakes, coupling beams should be designed with accurate shear strength equations. The objective of this study is to propose the accurate shear strength equation for slender diagonally reinforced coupling beams. For this purpose, experimental tests were conducted using three diagonally reinforced coupling specimens with different amount of transverse reinforcement under reversed cyclic loads to evaluate the hysteretic behavior of the specimens. The test results show that transverse reinforcement of slender diagonally reinforced coupling beam affects the maximum strength and drift ratio.

• Journal of the Korean Society for Precision Engineering
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• v.21 no.3
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• pp.109-116
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• 2004

This paper investigates the characteristics of deflection for circular plate that has same supporting boundary condition along the width direction of plate according to the length change of supporting end. For two boundary conditions such as simple supporting and clamping on both ends, this study derives maximum deflection formula of circular plate using differential equation of elastic curve, assuming that a circular plate is a beam with different widths along the longitudinal direction. The deflection formula of circular plate is verified by carrying out finite element analysis with regard to the ratio of length of supporting end to radius of circular plate.

• Steel and Composite Structures
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• v.42 no.5
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• pp.671-683
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• 2022

To investigate and predict the long-term time-dependent behavior, such as creep, shrinkage, and relaxation of PS strands, and prestress loss in prestressed steel-concrete composite beams, named Precom, full-scale tests were conducted and the collected data were compared with those obtained from the two proposed analytical models. The combined effective modulus method (EMM)-empirical model proposed with a flowchart considered the creep effect to determine the prestress loss. Conversely, the age-adjusted effective modulus method (AEMM) with CEB-FIP equation was developed to account for the concrete aging. The results indicated that the AEMM with CEB-FIP model predicts the long-term behavior of Precom effectively.

• Steel and Composite Structures
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• v.46 no.3
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• pp.335-344
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• 2023

This investigation presents nonlinear free vibration of a carbon nanotube reinforced composite beam based on the Von Kármán nonlinearity and the Euler-Bernoulli beam theory The material properties of the structure is considered as made of a polymeric matrix by reinforced carbon nanotubes according to different material distributions. The governing equations of the nonlinear vibration problem is delivered by using Hamilton's principle and the Galerkin's decomposition technique is utilized to discretize the governing nonlinear partial differential equation to nonlinear ordinary differential equation and then is solved by using of multiple time scale method. The nonlinear natural frequency and the nonlinear free response of the system is obtained with the effect of different patterns of reinforcement.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2005.04a
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• pp.408-415
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• 2005

Existing results of some related experiments report that variation in the magnitude of prestressing force may leads to a change of dynamic properties of a PSC girder system. Since a usual dynamic equilibrium equation doesn't explain these phenomena, a modified dynamic equilibrium equation is derived in this paper by considering prestressing force as an internal energy of the system. The derived equation is applied to a modified beam element model is proposed. The proposed model validated by comparing the natural frequencies computed by the model with those from an existing experiment result.

• Transactions of the Korean Society of Automotive Engineers
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• v.9 no.5
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• pp.165-172
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• 2001

Wheel bearing units were almost exclusively used for car front wheel, where the two ball rows are directly side by side with integrated rubber seal. The seal is of important for wheel bearing units due to the adverse environmental conditions with mud and splash water. The seal of wheel bearing units was designed to have geometry with multi lips, which elastic lip contacts and deforms with bearing. The equation of reaction force for deformed lip as cantilever beam was previously used for seal lip design. But it's result was not useful because deflection of the beam differs from lip's. In this study, deformed shape of the lip was assumed to and order function which is more similar to lip deformation and made the equation for reaction force prediction. The Reaction forces from each other equations were compared with results by FEA to prove usefulness of new equation.

• Journal of the Korean Society of Industry Convergence
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• v.3 no.1
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• pp.43-51
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• 2000

The response statistics of a hinged-clamped beam under broad-band random excitation is investigated. The random excitation is applied at the nodal point of the second mode. By using Galerkin's method the governing equation is reduced to a system of nonautonomous nonlinear ordinary differential equations. A method based upon the Markov vector approach is used to generate a general first-order differential equation in the dynamic moment of response coordinates. By means of the Gaussian and non-Gaussian closure methods the dynamic moment equations for the random responses of the system are reduced to a system of autonomous ordinary differential equations. The case of two mode interaction is considered in order to compare it with the case of three mode interaction. The analytical results for two and three mode interactions are also compared with results obtained by Monte Carlo simulation.

• Interaction and multiscale mechanics
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• v.2 no.4
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• pp.333-352
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• 2009

We introduce a radial basis collocation method to solve axially moving beam problems which involve $2^{nd}$ order differentiation in time and $4^{th}$ order differentiation in space. The discrete equation is constructed based on the strong form of the governing equation. The employment of multiquadrics radial basis function allows approximation of higher order derivatives in the strong form. Unlike the other approximation functions used in the meshfree methods, such as the moving least-squares approximation, $4^{th}$ order derivative of multiquadrics radial basis function is straightforward. We also show that the standard weighted boundary collocation approach for imposition of boundary conditions in static problems yields significant errors in the transient problems. This inaccuracy in dynamic problems can be corrected by a statically condensed semi-discrete equation resulting from an exact imposition of boundary conditions. The effectiveness of this approach is examined in the numerical examples.

• Structural Engineering and Mechanics
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• v.16 no.4
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• pp.469-478
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• 2003

The primary aim of this study was to investigate the bond strength between reinforcement and concrete. Large sized nine beams, which were produced from concrete with approximately ${f_c}^{\prime}=30$ MPa, were tested. Each beam was designed to include two bars in tension, spliced at the center of the span. The splice length was selected so that bars would fail in bond, splitting the concrete cover in the splice region, before reaching the yield point. In all experiments, the variable used was the reinforcing bar diameter. In the experiments, beam specimens were loaded in positive bending with the splice in a constant moment region. In consequence, as the bar diameter increased, bond strength and ductility reduced but, however, the stiffnesses of the beams (resistance to deflection) increased. Morever, a empirical equation was obtained to calculate the bond strength of reinforcement and this equation was compared with Orangun et al. (1977) and Esfahani and Rangan (1998). There was a good agreement between the values computed from the predictive equation and those computed from equations of Orangun et al. (1977) and Esfahani and Rangan (1998).