• Structural Engineering and Mechanics
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• v.69 no.5
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• pp.511-525
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• 2019

This paper presents an analytical study of wave propagation in simply supported graduated functional plates resting on a two-parameter elastic foundation (Pasternak model) using a new theory of high order shear strain. Unlike other higher order theories, the number of unknowns and governing equations of the present theory is only four unknown displacement functions, which is even lower than the theory of first order shear deformation (FSDT). Unlike other elements, the present work includes a new field of motion, which introduces indeterminate integral variables. The properties of the materials are assumed to be ordered in the thickness direction according to the two power law distributions in terms of volume fractions of the constituents. The wave propagation equations in FG plates are derived using the principle of virtual displacements. The analytical dispersion relation of the FG plate is obtained by solving an eigenvalue problem. Numerical examples selected from the literature are illustrated. A good agreement is obtained between the numerical results of the current theory and those of reference. A parametric study is presented to examine the effect of material gradation, thickness ratio and elastic foundation on the free vibration and phase velocity of the FG plate.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.33 no.6
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• pp.2195-2209
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• 2013

The effective strength of concrete struts must be determined accurately for the reliable strut-tie model analysis and design of structural concrete. In this study, the equations of the effective strength, which are useful for the three types of determinate and indeterminate strut-tie models of reinforced concrete deep beams employed in current design codes, are proposed. The effects of shear span-to-effective depth ratio, compressive strength of concrete, and flexural and shear reinforcement ratios are reflected in the development of the proposed equations. To examine the appropriateness of the proposed equations, the strengths of 241 reinforced concrete deep beams, all tested to shear failure, are evaluated by using the three types of strut-tie models with the existing and proposed equations.

• Computers and Concrete
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• v.10 no.2
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• pp.149-171
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• 2012

The problem of a concrete cross section under flexural and axial loading is indeterminate due to the existence of more unknowns than equations. Among the infinite solutions, it is possible to find the optimum, which is that of minimum reinforcement that satisfies certain design constraints (section ductility, minimum reinforcement area, etc.). This article proposes the automation of the optimum reinforcement calculation under any combination of flexural and axial loading. The procedure has been implemented in a program code that is attached in the Appendix. Conventional-strength or high-strength concrete may be chosen, minimum reinforcement area may be considered (it being possible to choose between the standards ACI 318 or Eurocode 2), and the neutral axis depth may be constrained in order to guarantee a certain sectional ductility. Some numerical examples are presented, drawing comparisons between the results obtained by ACI 318, EC 2 and the conventional method.

• The korean journal of orthodontics
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• v.50 no.5
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• pp.356-359
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• 2020

Forces and moments delivered by a straight wire connecting two orthodontic brackets are statically indeterminate and cannot be estimated using the classical equations of static equilibrium. To identify the mechanics of such two-bracket systems, Burstone and Koenig used the principles of linear beam theory to estimate the resulting force systems. In the original publication, however, it remains unclear how the force systems were calculated because no reference or computational details on the underlying principles have been provided. Using the moment carry-over principle and the relative angulation of the brackets, a formula was derived to calculate the relative moments of the two brackets. Because of the moment equilibrium, the vertical forces that exist as a force-couple on the two brackets can also be calculated. The accuracy of the proposed approach can be validated using previously published empirical data.

• Journal of the Society of Naval Architects of Korea
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• v.41 no.2
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• pp.98-105
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• 2004

This study focuses on an analytical approach to calculate four crane lifting forces for heavy ship hull blocks considering elongations of lilting slings. Four-crane-lifting is a redundant problem. During lifting procedures, in addition to the force and moment equilibrium equations, a compatibility condition is introduced to determine 4 unknown lifting forces. For verification of the method, a ship hull block with field measurements data is analyzed and the result shows that the information obtained by current method could be useful to engineers to conduct lifting work at shipyards.

• Journal of Ocean Engineering and Technology
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• v.17 no.3 s.52
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• pp.33-38
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• 2003

This study focuses on an analytical approach to calculate crane-lifting forces for a sunken ship, with consideration to elongation of crane ropes. The method takes into account the relation of lifting forces acting in wire rope slings to the inclination of the ship's hull, including the effect of lug positions. For lifting analysis, the Euler angles are defined to represent the inclination of a sunken ship in developing the static force and moment equations. An additional compatibility condition is introduced in order to solve an indeterminate lifting analysis problem with 4 cranes. A set of lifting forces along the 4 crane ropes is calculated. A 3-dimensional example of the G/T 1500 oil tanker is analyzed. The results show that the information obtained by the method could be useful to engineers when conducting salvage work.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.34 no.4
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• pp.1081-1094
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• 2014

The strut-tie model approach has proven to be effective in the ultimate analysis and design of structural concrete with disturbed regions. For the reliable analysis and safe design of the structural concrete, however, the effective strengths of concrete struts must be determined accurately. In this study, the equations of the effective strengths of concrete struts, which are useful for the three types of determinate and indeterminate strut-tie models of reinforced concrete corbels, were proposed. The effects of shear span-to-effective depth ratio, the vertical-to-horizontal force ratio, and flexural and horizontal shear reinforcement ratios were reflected in the development of the proposed equations. To examine the appropriateness of the proposed and existing equations, the ultimate strengths of 243 reinforced concrete corbels tested to failure were evaluated by using the three types of corbel strut-tie models.

• Steel and Composite Structures
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• v.27 no.1
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• pp.109-122
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• 2018

In This work an analysis of the propagation of waves of functionally graduated plates is presented by using a high order hyperbolic (HSDT) shear deformation theory. This theory has only four variables, which is less than the theory of first order shear deformation (FSDT). Therefore, a shear correction coefficient is not required. Unlike other conventional shear deformation theories, the present work includes a new field of displacement which introduces indeterminate integral variables. The properties of materials are supposed classified in the direction of the thickness according to two simple distributions of a power law in terms of volume fractions of constituents. The governing equations of the wave propagation in the functionally graded plate are derived by employing the Hamilton's principle. The analytical dispersion relation of the functionally graded plate is obtained by solving an eigenvalue problem. The convergence and the validation of the proposed theoretical numerical model are performed to demonstrate the efficacy of the model.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2003.05a
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• pp.179-184
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• 2003

This study focuses on an analytical approach to calculate crane lifting forces for a sunken ship in consideration oj elongation of crane ropes. The method takes into account the relation of lifting forces acting in wire rope slings to the inclination of the ship's hull including the effect of lug positions. For lifting analysis, the Euler angles are defined to represent the inclination of a sunken ship in developing the static force and moment equations. An additional compatability condition is introduced in order to solve an indeterminate lifting analysis problem with 4 cranes and a set of lifting forces along the 4 crane ropes is calculated. A 3-dimensional example of the G/T 1500 oil tanker is analyzed and the results show that the information obtained by the method could be useful to engineers to conduct salvage work.

• Wind and Structures
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• v.28 no.1
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• pp.49-62
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• 2019

In this paper, an analytical analysis for the study of vibratory behavior and wave propagation of functionally graded plates (FGM) is presented based on a high order shear deformation theory. The manufacture of these plates' defects can appear in the form of porosity. This latter can question and modify the global behavior of such plates. A new shape of the distribution of porosity according to the thickness of the plate was used. The field of displacement of this theory is present of indeterminate integral variables. The modulus of elasticity and the mass density of these plates are assumed to vary according to the thickness of the plate. Equations of motion are derived by the principle of minimization of energies. Analytical solutions of free vibration and wave propagation are obtained for FGM plates simply supported by integrating the analytic dispersion relation. Illustrative examples are given also to show the effects of variation of various parameters such as(porosity parameter, material graduation, thickness-length ratio, porosity distribution) on vibration and wave propagation of FGM plates.