• Structural Engineering and Mechanics
• /
• v.81 no.1
• /
• pp.29-37
• /
• 2022

The present paper deals with the application of one dimensional piezoelectric materials in particular piezo-thermoelastic nanobeam. The generalized piezo-thermo-elastic theory with two temperature and Euler Bernoulli theory with small scale effects using nonlocal Eringen's theory have been used to form the mathematical model. The ends of nanobeam are considered to be simply supported and at a constant temperature. The mathematical model so formed is solved to obtain the non-dimensional expressions for lateral deflection, electric potential, thermal moment, thermoelastic damping and frequency shift. Effect of frequency and nonlocal parameter on the lateral deflection, electric potential, thermal moment with generalized piezothermoelastic theory are represented graphically using the MATLAB software. Comparisons are made with the different theories of thermoelasticity.

• Structural Engineering and Mechanics
• /
• v.67 no.3
• /
• pp.255-265
• /
• 2018

The prestress force effect on the fundamental frequency and deflection shape of Prestressed Concrete I (PCI) beams was studied in this paper. Currently, due to the conflicts among existing theories, the analytical solution for properly considering the structural behavior of these prestressed members is not clear. A series of experiments were conducted on a large-scale PCI beam of high strength concrete with an eccentric straight unbonded tendon. Specifically, the simply supported PCI beam was subjected to free vibration and three-point bending tests with different prestress forces. Subsequently, the experimental data were compared with analytical results based on the Euler-Bernoulli beam theory. It was proved that the fundamental frequency of PCI beams is unaffected by the increasing applied prestress force, if the variation of the initial elastic modulus of concrete with time is considered. Vice versa, the relationship between the deflection shape and prestress force is well described by the magnification factor formula of the compression-softening theory assuming the secant elastic modulus.

• Journal of the Korea institute for structural maintenance and inspection
• /
• v.4 no.1
• /
• pp.111-120
• /
• 2000

This study discusses the issues related to the accuracy of deflection measurement in the testing of FRC. Some deflection methods may include large extraneous deformations. such as local crushing at the loading points, elastic and inelastic deformations of the loading fixture, etc. A faulty load-deflection curve will be obtained if an unstable deflection measuring system is used, and incorrect toughness evaluation can be reached on the basis of this faulty curve. In this paper, the discussion will focus on the effects of the deflection measuring system on both the measurement of the load-deflection response of FRC and the evaluation of FRC toughness. It is observed that ASTM toughness indices which is based on measuring deflection at first cracking is influenced significantly by extraneous deformation in deflection measurement. But extraneous deformation in deflection measurement result in negligible errors in toughness evaluation using JSCE and JCI definition. However, in order to evaluate toughness accuracy, it is desirable to use net load-deflection curve eliminated extraneous deformation.

• Transactions of the Korean Society of Machine Tool Engineers
• /
• v.10 no.3
• /
• pp.68-74
• /
• 2001

In the drawing of large size automotive panels, elastic deflection of die components is induced by the contact force between them. The deflection is nonuniform and locally distributed, and results in nonuniform material flow. In order to arrange such a nonuniform die gap, a correcting operation, so called die spotting, is inevitable, which requires trial and error works and consuming time. A prediction of the bending deflection prior to a try-out must be useful to reduce the die spotting time. In this study, drawing process of a front fender is simulated first. and the deflection of the blank holder is calculated from the contact force imposing on th blank holder. The balance block heights ensuring a uniform deflection are optimized by the analysis and design of experiments.

• Journal of the Korean Society for Precision Engineering
• /
• v.26 no.11
• /
• pp.116-123
• /
• 2009

The elastic properties of core affect mechanical properties and deformation behaviours of the lightweight sandwich panel. The objective of the present paper is to estimate experimentally Young's and shear moduli of a core in internally structured boned (ISB) panel with woven metal as inner structures using the deflection theory of sandwich beam considered core stiffness. Three points bending experiments were performed to obtain force-deflection curves of the designed ISB panel in each material direction. The elastic and shear moduli of the core in each material direction were estimated from slopes and intercepts of relationships between compliance per the span length and square of the span length, respectively. The results of the estimation showed that the fabric technology of the woven metal affects the variation of the elastic properties in the core. Through the comparison of shear moduli and force-deflection curves of the proposed method and those without considering the core stiffness, it was shown that the core stiffness should be considered to estimate properly the Young's and shear moduli of ISB panels. Finally, the contribution ratio of bending and shear deflections of ISB panels to the total deflection was quantitatively examined.

• Smart Structures and Systems
• /
• v.22 no.6
• /
• pp.689-697
• /
• 2018

This paper presents a model of the elastic curve for rectangular beams with straight haunches under uniformly distributed load and moments in the ends considering the bending and shear deformations (Timoshenko Theory) to obtain the deflections and rotations on the beam, which is the main part of this research. The traditional model of the elastic curve for rectangular beams under uniformly distributed load considers only the bending deformations (Euler-Bernoulli Theory). Also, a comparison is made between the proposed and traditional model of simply supported beams with respect to the rotations in two supports and the maximum deflection of the beam. Also, another comparison is made for beams fixed at both ends with respect to the moments and reactions in the support A, and the maximum deflection of the beam. Results show that the proposed model is greater for simply supported beams in the maximum deflection and the traditional model is greater for beams fixed at both ends in the maximum deflection. Then, the proposed model is more appropriate and safe with respect the traditional model for structural analysis, because the shear forces and bending moments are present in any type of structure and the bending and shear deformations appear.

• Structural Engineering and Mechanics
• /
• v.38 no.2
• /
• pp.157-169
• /
• 2011

In this paper the time-dependent closed-form static solution of the suspended pre-stressed biconcave and biconvex cable trusses with unmovable, movable and elastic or viscoelastic yielding supports subjected to various types of vertical load is presented. Irvine's forms of the deflections and the cable equations are modified because the effects of the rheological behaviour needed to be incorporated in them. The concrete cable equations in the form of the explicit relations are derived and presented. From a solution of a vertical equilibrium equation for a loaded cable truss with rheological properties, the additional vertical deflection as a time-function is determined. The time-dependent closed-form model serves to determine the time-dependent response, i.e., horizontal components of cable forces and deflection of the cable truss due to applied loading at the investigated time considering effects of elastic deformations, creep strains, temperature changes and elastic supports. Results obtained by the present closed-form solution are compared with those obtained by FEM. The derived time-dependent closed-form computational model is used for a time-dependent simulation-based reliability assessment of cable trusses as is described in the second part of this paper.

• Structural Engineering and Mechanics
• /
• v.13 no.2
• /
• pp.211-230
• /
• 2002

The objective of this study is to investigate the dynamic behavior of elastic beams subjected to moving loads. Although analytical methods are available, they have limitations with respect to complicated structures. The use of computer technology in recent years is an effective way to solve the problem; thus using the latest technology this study establishes a finite-element solution procedure to investigate dynamic behaviors of a typical elastic beam having a set of constant geometric properties and various span lengths. Both the dead load of the beam and traffic load are applied in which the traffic load is considered a concentrated moving force with various traveling passage speeds on the beam. Dynamic behaviors including deflection, shear, and bending moment due to moving loads are obtained by both analytical and finite element methods; for simple structures, they have an excellent agreement. The numerical results show that based on analytical methods the fundamental mode is good enough to estimate the dynamic deflection along the beam, but is not sufficient to simulate the total response of the shear force or the bending moment. The linear dynamic behavior of the elastic beams subjected to multiple exciting loads can easily be found by linear superposition, and the geometric nonlinear results caused by large deformation and axial force of the beam are always underestimated with only a few exceptions which are indicated. In order to make the results useful, they have been nondimensionalized and presented in graphical form.

• Structural Engineering and Mechanics
• /
• v.48 no.4
• /
• pp.519-545
• /
• 2013

An outline of the Timoshenko beam theory is presented. Two differential equations of motion in terms of deflection and rotation are comprised into single equation with deflection and analytical solutions of natural vibrations for different boundary conditions are given. Double frequency phenomenon for simply supported beam is investigated. The Timoshenko beam theory is modified by decomposition of total deflection into pure bending deflection and shear deflection, and total rotation into bending rotation and axial shear angle. The governing equations are condensed into two independent equations of motion, one for flexural and another for axial shear vibrations. Flexural vibrations of a simply supported, clamped and free beam are analysed by both theories and the same natural frequencies are obtained. That fact is proved in an analytical way. Axial shear vibrations are analogous to stretching vibrations on an axial elastic support, resulting in an additional response spectrum, as a novelty. Relationship between parameters in beam response functions of all type of vibrations is analysed.

• International Journal of Ocean System Engineering
• /
• v.2 no.3
• /
• pp.195-199
• /
• 2012

This paper reports a new analytical method to calculate the planar displacement of structures. The cross-sections were assumed to remain in plane and the deflection curve was evaluated using the curvature values geometrically, despite being solved with differential equations. The deflection curve was parameterized with the arc-length of the curvature values, and was taken as an assembly of chains of circular arcs. Fast and accurate solutions of complex deflections can be obtained easily. This paper includes a comparison of the nonlinear displacements of an elastic tapered cantilever beam with a uniform moment distribution among the proposed analytical method, numerical method of the theory and large deflection FEM solutions.