• Journal of Korean Ophthalmic Optics Society
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• v.12 no.1
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• pp.41-51
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• 2007

Differential equations and their solutions were formulated to describe the deflection of the tapered, nonuniform thickness and width's temple, clamped at one end while the perpendicular force is acting on the other end which is freely suspended. The model was derived based on laws of continuity at every point inside the elastic medium that the deflection, tangent slope, bending moment, shearing force must be continuous within the medium. The model is found to be in good agreement with measurements on the beta titanium temple with the correlation 0.992 and p=0.999(Chi test). Therefore it is possible to predict the effect of various temple parameters such as elastic modulus, thickness, width on the deflection of the temples being considered.

• Journal of the Korea institute for structural maintenance and inspection
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• v.11 no.1
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• pp.171-180
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• 2007

Reliability analysis of prestressed steel and concrete(PSSC) girders is conducted for deflection, stress and moment strength limit state. PSSC girder has strong advantages in terms of construction cost and vertical clearance for the span length of over 40 meters. In this paper, example PSSC girders with different span lengths, section dimensions and design stress levels are designed and analyzed to calculate the midspan deflection, stress and the section moment strength. Deflection limit state, stress limit state and strength limit state functions are assumed and the reliability indexes are obtained by Monte-Carlo simulation and Rackwitz-Fiessler procedure. The results show that the reliability of PSSC girder for deflection limit state is appropriately higher than the stress limit state and the reliability for moment strength is significantly conservative.

• International Journal of Safety
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• v.2 no.1
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• pp.39-44
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• 2003

The present study deals with an approximate integral equation approach to finite deflection of elastic plates with arbitrary plane form. An integral formulation leads to a system of boundary integral equations involving values of deflection, slope, bending moment and transverse shear force along the edge. The basic principles of the development of boundary element technique are reviewed. A computer program for solving for stresses and deflections in a isotropic, homogeneous, linear and elastic bending plate is developed. The fundamental solution of deflection and moment is employed in this program. The deflections and moments are assumed constant within the quadrilateral element. Numerical solutions for sample problems, obtained by the direct boundary element method, are presented and results are compared with known solutions.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.11a
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• pp.9-14
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• 1996

The deflection of an end mill is very important in machining process and cutting simulation because it affects directly workpiece accuracy, cutting force, and chattering. In this study, the deflection of the end mill was studied both experimentally and by using finite element analysis. And the moment of inertia of radial cross sections of tile helical end mill is calculated for the determination of the relation between cross section and rigidity of tile tools. Using tile Bernoulli-Euler beam and and the concept of equivalent diameter, a deflection model is established, which includes most influence from tool geomety parameters. It was found that helix angle attenuates the rigidity of the end mill.

• Steel and Composite Structures
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• v.49 no.5
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• pp.473-486
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• 2023

A through-railway bridge with an inclined girder has recently been applied to optimize the cross-section of a slender bridge structure in railway bridges. To achieve the additional cross-section optimization effect by the bolted end-plate connection, it is necessary to investigate the application of the bolted end-plate tension connection between the inclined girder and the crossbeam. This basic study was conducted on the application of the bolted end-plate moment connection of crossbeams to half-through girders with inclined webs. The combined behavior of vertical deflection and rotational behavior was observed due to the effect of the web inclination in the inclined girder where the steel crossbeam was connected to the girder by the bolted end-plate moment connection. Therefore, in the experiment, the deflection of the inclined girder was 1.77-2.93 times greater than that of the vertical girder but the lateral deflection of the inclined girder was 0.4 times less than that of the vertical girder. Moreover, the tensile stress of the upper bolts in the inclined girder with low crossbeams was clearly 0.81 times lower than that of the vertical girder. According to the results, the design formula for vertical girders does not reflect the influence of the web inclination. Therefore, this study proposed the design procedures for the inclined girder to apply the bolted end-plate moment connection of the crossbeam to the inclined girder by reflecting the design change factors according to the effect of the web inclination.

• Proceedings of the Korea Concrete Institute Conference
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• 2008.11a
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• pp.989-992
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• 2008

Recently, high-strength concrete has been frequently used for long-span bridges and high-rise buildings. Deflection of reinforced concrete structures is uncertain, so that many researchers have proposed various equations in order to predict deflection through experiments. Domestic concrete specification offers a procedure to evaluate deflection using effective moment of inertia which was proposed by Branson. However, it is inaccurate for high strength concrete compared to the method suggested in Eurocode 2 in that Eurocode 2 predicts deflection by using curvature integration of effective moment of inertia. In this study, experimental data about deflection of reinforced concrete beams were analyzed to compare domestic standard and Eurocode 2.

• Journal of the Korea Concrete Institute
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• v.21 no.1
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• pp.93-103
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• 2009

The concept of the effective moment of inertia has been generally used for the deflection estimation of reinforced concrete flexural members. The KCI design code adopted Branson's equation for simple calculation of deflection, in which a representative value of the effective moment of inertia is used for the whole length of a member. However, the code equation for the effective moment of inertia was formulated based on the results of beam tests subjected to uniformly distributed loads, which may not effectively account for those of members under different loading conditions. Therefore, this study aimed to verify the influences of moment shapes resulting from different loading patterns by experiments. Six beams were fabricated and tested in this study, where primary variables were concrete compressive strengths and loading distances from supports, and test results were compared to the code equation and other existing approaches. A method utilizing variational analysis for the deflection estimation has been also proposed, which accounts for the influences of moment shapes to the effective moment of inertia. The test results indicated that the effective moment of inertia was somewhat influenced by the moment shape, and that this influence of moment shape to the effective moment of inertia was not captured by the code equation. Compared to the code equation, the proposed method had smaller variation in the ratios of the test results to the estimated values of beam deflections. Therefore, the proposed method is considered to be a good approach to take into account the influence of moment shape for the estimation of beam deflection, however, the differences between test results and estimated deflections show that more researches are still required to improve its accuracy by modifying the shape function of deflection.

• Journal of the Korea institute for structural maintenance and inspection
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• v.14 no.2
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• pp.184-192
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• 2010

The member deflection is one of the most important considerations for the serviceability evaluation of reinforced concrete (RC) structures, and the concept of the effective moment of inertia has been generally used for its estimation. However, the actual service load applied on an existing RC beam may not be easily obtained, for which the estimation of beam deflection by existing methods can be difficult to obtain. Therefore, based on the correlation between cracks and deflection in a RC beam, this study proposed a method to estimate the deflection of RC beams directly from the condition of cracks not using the actual loads acting on the member as its input data. The proposed method extensively utilized the relationships among sums of crack widths, average strains, and curvatures, and modification factors obtained from regression analysis were also introduced to improve its accuracy. The deflections of members were successfully estimated by the proposed method independent from applied loads, which was also easy to apply compared to the existing methods based on the effective moment of inertia.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.16 no.4
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• pp.89-96
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• 2017

A cable tray is a structure made of metal or a non-combustible material that supports cables in the electrical wiring of buildings. Cable trays should be developed to meet the various requirements of the construction site. In this study, a design system was developed to calculate the maximum support load and the maximum deflection according to the cross-sectional shape of the cable tray. The cross-sections of cable trays were modeled by combining linear and arc elements, and cross-sectional characteristics such as the 2nd moment of area were calculated. The distributed load and the concentrated load were applied to the cable tray using the Euler beam theory, and then the deflection profiles and maximum stress were calculated. To verify the developed system, deflection distributions and maximum stresses for two types of cable trays were calculated and compared. The maximum deflection and maximum stress errors calculated from the developed system were found to be less than 4% compared with numerical analysis results.

• Structural Engineering and Mechanics
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• v.43 no.2
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• pp.147-161
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• 2012

This paper presents a curvature method for analysis of beam-columns with different materials and arbitrary cross-section shapes and subjected to combined biaxial moments and axial load. Both material and geometric nonlinearities (the p-delta effect in this case) were incorporated. The proposed method considers biaxial curvatures and uniform normal strains of discrete cross-sections of beam-columns as basic unknowns, and seeks for a solution of the column deflection curve that satisfies force equilibrium conditions. A piecewise representation of the beam-column deflection curve is constructed based on the curvatures and angles of rotation of the segmented cross-sections. The resulting bending moments were evaluated based on the deformed column shape and the axial load. The moment curvature relationship and the beam-column deflection calculation are presented in matrix form and the Newton-Raphson method is employed to ensure fast and stable convergence. Comparison with results of analytic solutions and eccentric compression tests of wood beam-columns implies that this method is reliable and effective for beam-columns subjected to eccentric compression load, lateral bracings and complex boundary conditions.