• Journal of the Korean Mathematical Society
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• v.58 no.5
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• pp.1227-1237
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• 2021

This paper is concerned with a reaction-diffusion logistic model. In [17], Lou observed that a heterogeneous environment with diffusion makes the total biomass greater than the total carrying capacity. Regarding the ratio of biomass to carrying capacity, Ni [10] raised a conjecture that the ratio has a upper bound depending only on the spatial dimension. For the one-dimensional case, Bai, He, and Li [1] proved that the optimal upper bound is 3. Recently, Inoue and Kuto [13] showed that the supremum of the ratio is infinity when the domain is a multi-dimensional ball. In this paper, we generalized the result of [13] to an arbitrary smooth bounded domain in ℝⁿ, n ≥ 2. We use the sub-solution and super-solution method. The idea of the proof is essentially the same as the proof of [13] but we have improved the construction of sub-solutions. This is the complete answer to the conjecture of Ni.

• Steel and Composite Structures
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• v.17 no.4
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• pp.497-516
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• 2014

The ultimate carrying capacity of axially loaded welded square box section members made of medium and high strength steels (nominal yield stresses varying from 345 MPa to 460 MPa), with large width-to-thickness ratios ranging from 35 to 70, is analyzed by finite element method (FEM). At the same time, the numerical results are compared with the predicted results using Direct Strength Method (DSM), modified DSM and Effective Yield Strength Method (EYSM). It shows that curve a, rather than curve b recommended in Code for design of steel structures GB50017-2003, should be used to check the local-overall interaction buckling strength of welded square section columns fabricated from medium and high strength steels when using DSM, modified DSM and EYSM. Despite all this, EYSM is conservative. Compared to EYSM and modified DSM, DSM provides a better prediction of the ultimate capacities of welded square box compression members with large width-thickness ratios over a wide range of width-thickness ratios, slenderness ratios and steel grades. However, for high strength steels (nominal yield strength greater than 460 MPa), the numerical and existent experimental results indicate that DSM overestimates the load-carrying capacities of the columns with width-thickness ratio smaller than 45 and slenderness ratio less than 80. Further, for the purpose of making it suitable for a wider scope, DSM has been modified (called proposed modified DSM). The proposed modified DSM is in excellent agreement with the numerical and existing experimental results.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.17 no.12
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• pp.730-736
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• 2016

In a previous study, the impact factor response spectrum and corresponding method for evaluating the load carrying capacity of bridges was suggested to improve the existing evaluation method. To verify the applicability of the suggested method, which is based on the frequency of bridges, the dynamic characteristic test for an actual single span simply-supported bridge was conducted. Through a field test under ambient traffic conditions, the dynamic response of the bridge was obtained using wireless accelometers and its fundamental frequency was identified. The peak impact factor was determined from the identified frequency and the impact factor response spectrum. The load carrying performance variation of the bridge was estimated considering the performance reduction factor, which was calculated using the current and previous natural frequency and impact factor. From the result, the load carrying capacity of the bridge was decreased, but the capacity was still enough because its value is greater than the design live load. Through the overall procedures and technical details presented in this paper, the suggested evaluation method can be applied to actual bridges with the acceleration data measured under ambient traffic conditions and the impact factor response spectrum.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.35 no.1
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• pp.31-38
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• 2015

In this paper, change of load carrying capacity of bridges with time was analyzed referring to the safety inspect data stored in the KISTEC. From this study, it was known that the capacity is rated differently by various parameters such as inspector's subjective. Accordingly, an improved method, in this paper, is suggested which can correct deviation due to several uncertainties involved in rating process. The suggested method can be utilized for efficient maintenance of bridges such as cycles and determination of priority of retrofit, and estimation of service life etc.

• Structural Engineering and Mechanics
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• v.34 no.4
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• pp.399-416
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• 2010

The purpose of this paper is to utilize the numerical assembly method (NAM) to determine the exact natural frequencies and mode shapes of a multi-step beam carrying multiple rigid bars, with each of the rigid bars possessing its own mass and rotary inertia, fixed to the beam at one point and supported by a translational spring and/or a rotational spring at another point. Where the fixed point of each rigid bar with the beam does not coincide with the center of gravity the rigid bar or the supporting point of the springs. The effects of the distance between the "fixed point" of each rigid bar and its center of gravity (i.e., eccentricity), and the distance between the "fixed point" and each linear spring (i.e., offset) are studied. For a beam carrying multiple various concentrated elements, the magnitude of each lumped mass and stiffness of each linear spring are the well-known key parameters affecting the free vibration characteristics of the (loaded) beam in the existing literature, however, the numerical results of this paper reveal that the eccentricity of each rigid bar and the offset of each linear spring are also the predominant parameters.

• Structural Engineering and Mechanics
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• v.22 no.6
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• pp.701-717
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• 2006

In the existing reports regarding free transverse vibrations of the Euler-Bernoulli beams, most of them studied a uniform beam carrying various concentrated elements (such as point masses, rotary inertias, linear springs, rotational springs, spring-mass systems, ${\ldots}$, etc.) or a stepped beam with one to three step changes in cross-sections but without any attachments. The purpose of this paper is to utilize the numerical assembly method (NAM) to determine the exact natural frequencies and mode shapes of the multiple-step Euler-Bernoulli beams carrying a number of lumped masses and rotary inertias. First, the coefficient matrices for an intermediate lumped mass (and rotary inertia), left-end support and right-end support of a multiple-step beam are derived. Next, the overall coefficient matrix for the whole vibrating system is obtained using the numerical assembly technique of the conventional finite element method (FEM). Finally, the exact natural frequencies and the associated mode shapes of the vibrating system are determined by equating the determinant of the last overall coefficient matrix to zero and substituting the corresponding values of integration constants into the associated eigenfunctions, respectively. The effects of distribution of lumped masses and rotary inertias on the dynamic characteristics of the multiple-step beam are also studied.

• Computers and Concrete
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• v.25 no.1
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• pp.1-14
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• 2020

This study presents applications of the multivariate adaptive regression splines (MARS) method for predicting the ultimate loading carrying capacity (N_u) of rectangular concrete-filled steel tubular (CFST) columns subjected to eccentric loading. A database containing 141 experimental data was collected from available literature to develop the MARS model with a total of seven variables that covered various geometrical and material properties including the width of rectangular steel tube (B), the depth of rectangular steel tube (H), the wall thickness of steel tube (t), the length of column (L), cylinder compressive strength of concrete (f'_c), yield strength of steel (f_y), and the load eccentricity (e). The proposed model is a combination of the MARS algorithm and the grid search cross-validation technique (abbreviated here as GS-MARS) in order to determine MARS' parameters. A new explicit formulation was derived from MARS for the mentioned input variables. The GS-MARS estimation accuracy was compared with four available mathematical methods presented in the current design codes, including AISC, ACI-318, AS, and Eurocode 4. The results in terms of criteria indices indicated that the MARS model was much better than the available formulae.

• Structural Engineering and Mechanics
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• v.28 no.6
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• pp.659-676
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• 2008

The reports regarding the free vibration analysis of uniform beams carrying single or multiple spring-mass systems are plenty, however, among which, those with inertia effect of the helical spring(s) considered are limited. In this paper, by taking the mass of the helical spring into consideration, the stiffness and mass matrices of a spring-mass system and an equivalent mass that may be used to replace the effect of a spring-mass system are derived. By means of the last element stiffness and mass matrices, the natural frequencies and mode shapes for a uniform cantilever beam carrying any number of springmass systems (or loaded beam) are determined using the conventional finite element method (FEM). Similarly, by means of the last equivalent mass, the natural frequencies and mode shapes of the same loaded beam are also determined using the presented equivalent mass method (EMM), where the cantilever beam elastically mounted by a number of lumped masses is replaced by the same beam rigidly attached by the same number of equivalent masses. Good agreement between the numerical results of FEM and those of EMM and/or those of the existing literature confirms the reliability of the presented approaches.

• Journal of Information Processing Systems
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• v.15 no.2
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• pp.331-343
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• 2019

Dynamic thermal rating of the overhead transmission lines is affected by many uncertain factors. The ambient temperature, wind speed and wind direction are the main sources of uncertainty. Measurement uncertainty is an important parameter to evaluate the reliability of measurement results. This paper presents the uncertainty analysis based on Monte Carlo. On the basis of establishing the mathematical model and setting the probability density function of the input parameter value, the probability density function of the output value is determined by probability distribution random sampling. Through the calculation and analysis of the transient thermal balance equation and the steady- state thermal balance equation, the steady-state current carrying capacity, the transient current carrying capacity, the standard uncertainty and the probability distribution of the minimum and maximum values of the conductor under 95% confidence interval are obtained. The simulation results indicate that Monte Carlo method can decrease the computational complexity, speed up the calculation, and increase the validity and reliability of the uncertainty evaluation.

• Earthquakes and Structures
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• v.23 no.3
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• pp.221-229
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• 2022

The external post-tension technique is one of the best strengthening methods for reinforcement and improvement of the various steel structures and substructure components such as beams. In the present work, the load carrying capacity of the post-tensioned tapered steel beams with external shape memory alloy (SMA) tendons are studied. 3D nonlinear finite element method with ABAQUS software is used to determine the effects of the increase in the flexural strength, and the improvement of the load carrying capacity. The effect of the different parameters, such as geometrical characteristics and the post-tension force applied to the tendons are also studied in this research. The results reveal that the external post-tension with SMA tendons in comparison with the steel tendons causes a significant improvement of the loading capacity. According to this, using SMA tendon for the reinforcement of the tapered beams causes a decrease in weight of these structures and as a consequence causes economic benefits for their application. This method can be used extensively for steel beams due to low executive costs and simplicity of the operation for post-tension.