• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.33 no.5
• /
• pp.279-286
• /
• 2020

In this study, we investigate the accuracy of higher order derivatives in the moving least square (MLS) difference method. An interpolation function is constructed by employing a Taylor series expansion via MLS approximation. The function is then applied to the mixed variational theorem in which the displacement and stress resultants are treated as independent variables. The higher order derivatives are evaluated by solving simply supported beams and cantilevers. The results are compared with the analytical solutions in terms of the order of polynomials, support size of the weighting function, and number of nodes. The accuracy of the higher order derivatives improves with the employment of the mean value theorem, especially for very high-order derivatives (e.g., above fourth-order derivatives), which are important in a classical asymptotic analysis.

• Steel and Composite Structures
• /
• v.22 no.6
• /
• pp.1417-1443
• /
• 2016

Cellular and castellated steel beams are used to obtain higher stiffness and bending capacity using the same weight of steel. In addition, the beam openings may be used as a pass for different mechanical fixtures such as ducts and pipes. The aim of this study is to investigate the effect of different parameters on both elastic and inelastic critical buckling stresses of steel web plates with openings. These parameters are plate aspect ratio; opening shape (circular or rectangular); end distance to the first opening; opening spacing; opening size; plate slenderness ratio; steel grade; and initial web imperfection. The web/flange interaction has been simplified by web edge restraints representing simply supported boundary conditions. A numerical parametric study has been performed through linear and nonlinear finite element (FE) models, where the FE results have been verified against both experimental and numerical results in the literature. The web plates are subject to in-plane linearly varying compression with different loading patterns, ranging from uniform compression to pure bending. A buckling stress modification factor (${\beta}$-factor) has been introduced as a ratio of buckling stress of web plate with openings to buckling stress of the corresponding solid web plate. The variation of ${\beta}$-factor against the aforementioned parameters has been reported. Furthermore, the critical plate slenderness ratio separating elastic buckling and yielding has been identified and discussed for two steel grades of DIN-17100, namely: ST-37/2 and ST-52/3. The FE results revealed that the minimum ${\beta}$-factor is 0.9 for web plates under uniform compression and 0.7 for those under both compression and tension.

• Journal of the Korean Wood Science and Technology
• /
• v.26 no.4
• /
• pp.6-12
• /
• 1998

Test results of domestic softwood lumber were presented to examine the notch effect of beams and compare to present AIJ(Architecture Institute of Japan) formula in notched wood member especially positioned in bottom side (tension side) of a beam. Notched lumber was tested under following condition : each specimen supported simply, and subjected to third-point loading at points of 1/3 of the span length. Notch was located opposite side to loading direction and notch depth were 1/6, 1/4, 1/3 of beam depth. Deflection and load were measured by digital dial guage each in 25kgf increment. Bending test results were as follows; Mpro/Mmax range (proportional and maxium bending moment ratio in notched beam) was 0.5 - 0.65. It was considered that maxium bending moment was about 1.5 times to proportional bending moment in notched beam and showed same tendency in the test result of ordinary wood specimens. AU standard formula for the tension side notch, Mmat = 0.6 ${\times}$ (Zo $\sigma$), the constant 0.6 was suitble for notch ratio(notch depth to beam depth) 1/6, but this ratio for 1/4, and 1/3 was not. So it is preferable to accept smaller value than 0.6 for notch ratio more than 1/3. These experiment results showed critical effect in tension side notched wood beam especially in greater than notch ratio 1.3 of wood beam. From the above results, it is recommened to revise design formula adoptable to domestic wood constructon member with tension side notched member.

• Steel and Composite Structures
• /
• v.18 no.2
• /
• pp.425-442
• /
• 2015

This paper addresses theoretically the bending and buckling behaviors of size-dependent nanobeams made of functionally graded materials (FGMs) including the thickness stretching effect. The size-dependent FGM nanobeam is investigated on the basis of the nonlocal continuum model. The nonlocal elastic behavior is described by the differential constitutive model of Eringen, which enables the present model to become effective in the analysis and design of nanostructures. The present model incorporates the length scale parameter (nonlocal parameter) which can capture the small scale effect, and furthermore accounts for both shear deformation and thickness stretching effects by virtue of a sinusoidal variation of all displacements through the thickness without using shear correction factor. The material properties of FGM nanobeams are assumed to vary through the thickness according to a power law. The governing equations and the related boundary conditions are derived using the principal of minimum total potential energy. A Navier-type solution is developed for simply-supported boundary conditions, and exact expressions are proposed for the deflections and the buckling load. The effects of nonlocal parameter, aspect ratio and various material compositions on the static and stability responses of the FGM nanobeam are discussed in detail. The study is relevant to nanotechnology deployment in for example aircraft structures.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.31 no.3
• /
• pp.127-132
• /
• 2018

In this paper, a scheme for the evaluation of variability in the eigen-modes of functionally graded material(FGM) beams is proposed within the framework of perturbation-based stochastic analysis. As a random parameter, the spatially varying elastic modulus of FGM along the axial direction at the mid-surface of the beam is chosen, and the thru-thickness variation of the elastic modulus is assumed to follow the original form of exponential variation. In deriving the formulation, the first order Taylor expansion on the eigen-modes is employed. As an example, a simply supported FGM beam having symmetric elastic modulus with respect to the mid-surface is chosen. Monte Carlo analysis is also performed to check if the proposed scheme gives reasonable outcomes. From the analyses it is found that the two schemes give almost identical results of the mean and standard deviation of eigen-modes. With the propose scheme, the standard deviation shape of respective eigen-modes can be evaluated easily. The deviated mode shape is found to have one more zero-slope points than the mother modes shapes, irrespective of order of modes. The amount of deviation from the mean is found to have larger values for the higher modes than the lower modes.

• Journal of Korean Society of Steel Construction
• /
• v.24 no.5
• /
• pp.535-547
• /
• 2012

PSRC column is a concrete encased steel angle column. In the PSRC column, the steel angles placed at the corner of the cross-section resists bending moment and compression load. The lateral re-bars welded to steel angles resist the column shear and the bond between the steel angle and concrete. In the present study, current design procedures in KBC 2009 were applied to the flexure-compression, shear, and bond design of the PSRC composite column. To verify the validity of the design method and failure mode, simply supported 2/3 scaled PSRC and correlated SRC beams were tested under two point loading. The test parameters were the steel angle ratio and lateral bar spacing. The test results showed that the bending, shear, and bond strengths predicted by KBC 2009 correlated well with the test results. The flexural strength of the PSRC specimens was much greater than that of the SRC specimen with the same steel ratio because the steel angles were placed at the corner of the column section. However, when the bond resistance between the steel angle and concrete was not sufficient, brittle failures such as bond failure of the angle, spalling of cover concrete, and the tensile fracture of lateral re-bar occurred before the development of the yield strength of PSRC composite section. Further, if the weldability and toughness of the steel angle were insufficient, the specimen was failed by the fracture of the steel angle at the weld joint between the angle and lateral bars.

• Journal of the Korea Concrete Institute
• /
• v.19 no.6
• /
• pp.763-771
• /
• 2007

Over the last few decades, many researches have been conducted in order to find solution to the problem of corrosion in steel reinforced concrete. As a result, methods such as the use of stainless steel bars, epoxy coatings, and concrete additives, etc., have been tried. While effective in some situations, such remedies may still be unable to completely eliminate the problems of steel corrosion. Fiber reinforced polymer (FRP) elements are appealing as reinforcement due to some material properties such as high tensile strength, low density, and noncorrosive. However, due to the generally lower modulus of elasticity of FRP in comparison with the steel and the linear behavior of FRP, certain aspects of the structural behavior of RC members reinforced with FRP may be substantially different from similar elements reinforced with steel reinforcement. This paper presents the flexural behavior of one-way concrete slabs reinforced with FRP bars. They were simply supported and tested in the laboratory under static loading conditions to investigate their crack pattern and width, deflections, strains and mode of failure. The experimental results shows that behavior of the FRP reinforced slabs was bilinearly elastic until failure. Also, the results show that the FRP overreinforced concrete beams in this study can be safe for design in terms of deformability.

• Magazine of the Korea Concrete Institute
• /
• v.5 no.4
• /
• pp.167-178
• /
• 1993

The objective of this paper is to look into the possibility of the detailed and practical optimum design of rt:inforced concrete beam using methods oi discrete mathematical programming. In this discrete optimum formulation, the design variables are the overall depth, width and effective depth of members, and area of longitudinal reinforcement. In addition, the details such as the amount of web reinforcement and cutoff points of longitudinal reinforcement are also considered as variables. Total cost has been used as the objective function. The constraints include the code requirments such as flexural strength, shear strength, ductility, serviceability, concrete cover. spacing, web reinforcement, and development length and cutoff points of longitudinal renforcement. An optimization algorithm is presented for effective optimum design of R.C. beam with discrete de sign variables. First, the continuous variable optimization can be achieved by Feasible Direction Method. Using the results obtained from the continuous variable optimization, a branch and bound method is used to obtained the discrete design values. The proposed algorithm is applied to test problem for reliability, and the results are compared with those of graphical method and rounded-up method. And a simply supported R.C. beam and a two-span continuous R.C. beam are presented as numerical examples for effectiveness and applicability. It is considered that the presented algorithm can be effectively applied to the discrete optimum design of R.C. beams.

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