• Steel and Composite Structures
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• v.29 no.4
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• pp.483-491
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• 2018

Timoshenko beam model is widely exploited in the literature to examine the mechanical behavior of stubby beam-like components. Timoshenko beam theory is well-known to require the shear correction factor in order to recognize the nonuniform shear distribution at a section. While a variety of shear correction factors are appeared in the literature so far, there is still no consensus on the most appropriate form of the shear correction factor. The Saint-Venant's flexure problem is first revisited in the frame work of the classical theory of elasticity and a highly accurate approximate closed-form solution is presented employing the extended Kantorovich method. The resulted approximate solution for the elasticity field is then employed to introduce two shear correction factors consistent with the Cowper's and energy approaches. The mathematical form of the proposed shear correction factors are then simplified and compared with the results available in the literature over an extended range of Poisson's and aspect ratios. The proposed shear correction factors do not exhibit implausible issue of negative values and do not result in numerical instabilities too. Based on the comprehensive discussion on the shear correction factors, a piecewise definition of shear correction factor is introduced for rectangular cross-sections having excellent agreement with the numerical results in the literature for both shallow and deep cross-sections.

• Coupled systems mechanics
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• v.12 no.2
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• pp.151-165
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• 2023

In this study, a simple method for the determination of the shear correction factor for composites beam with a rectangular cross section is presented. The plane stress elasticity assumption is used after simplifications of the expression of the stress distribution in the beam. The different fiber orientation angle and volume fraction are considered in this work. The studied structure is subjected to various loading type (thermal and hygrothermal). The numerical results obtained show that there is a dependence of the shear coefficient on the orientation of the fibers. The evolution of the shear correction factors depends not only on the orientation of the fibers and also on the volume fraction and the environment. the advantage of this developed formula of the shear correction factor is to obtain more precise results and to consider several parameters influencing this factor which are neglected if the latter is constant.

• Earthquakes and Structures
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• v.13 no.1
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• pp.17-27
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• 2017

In this study, the characteristics of site amplification at seismic observation stations in Japan were estimated using the attenuation relationship of each station's response spectrum. Ground motion records observed after 32 earthquakes were employed to construct the attenuation relationship. The station correction factor at each KiK-net station was compared to the transfer functions between the base rock and the surface. For each station, the plot of the station correction factor versus the period was similar in shape to the graphs of the transfer function (amplitude ratio versus period). Therefore, the station correction factors are effective for evaluating site amplifications considering the period of ground shaking. In addition, the station correction factors were evaluated with respect to the average shear wave velocities using a geographic information system (GIS) dataset. Lastly, the site amplifications for specific periods were estimated throughout Japan.

• Smart Structures and Systems
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• v.1 no.3
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• pp.309-324
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• 2005

This paper presents an efficient and accurate coupled beam model for piezoelectric bimorphs based on improved first-order shear deformation theory (FSDT). The model combines the equivalent single layer approach for the mechanical displacements and a layerwise modeling for the electric potential. General electric field function is proposed to reasonably approximate the through-the-thickness distribution of the applied and induced electric potentials. Layerwise defined shear correction factor (k) accounting for nonlinear shear strain distribution is introduced into both the shear stress resultant and the electric displacement integration. Analytical solutions for free vibrations and forced response under electromechanical loads are obtained for the simply supported piezoelectric bimorphs with series or parallel arrangement, and the numerical results for various length-to-thickness ratios are compared with the exact two-dimensional piezoelasticity solution. Excellent predictions with low error estimates of local and global responses as well as the modal frequencies are observed.

• Coupled systems mechanics
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• v.12 no.3
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• pp.199-220
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• 2023

This article presents a new analytical model to study the effect of porosity on the shear correction factors (SCFs) of functionally graded porous beams (FGPB). For this analysis, uneven and logarithmic-uneven porosity functions are adopted to be distributed through the thickness of the FGP beams. Critical to the application of this theory is a determination of the correction factor, which appears as a coefficient in the expression for the transverse shear stress resultant; to compensate for the assumption that the shear strain is uniform through the depth of the cross-section. Using the energy equivalence principle, a general expression is derived from the static SCFs in FGPB. The resulting expression is consistent with the variationally derived results of Reissner's analysis when the latter are reduced from the two-dimensional case (plate) to the one-dimensional one (beam). A convenient algebraic form of the solution is presented and new study cases are given to illustrate the applicability of the present formulation. Numerical results are presented to illustrate the effect of the porosity distribution on the (SCFs) for various FGPBs. Further, the law of changing the mechanical properties of FG beams without porosity and the SCFare numerically validated by comparison with some available results.

• Structural Engineering and Mechanics
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• v.89 no.1
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• pp.1-11
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• 2024

This article introduces a novel analytical model for examining the impact of porosity on shear correction factors (SCFs) in functionally graded porous beams (FGPB). The study employs uneven and logarithmic-uneven modified porosity-dependent power-law functions, which are distributed throughout the thickness of the FGP beams. Additionally, a modified exponential-power law function is used to estimate the effective mechanical properties of functionally graded porous beams. The correction factor plays a crucial role in this analysis as it appears as a coefficient in the expression for the transverse shear stress resultant. It compensatesfor the assumption that the shear strain is uniform across the depth of the cross-section. By applying the energy equivalence principle, a general expression for static SCFs in FGPBs is derived. The resulting expression aligns with the findings obtained from Reissner's analysis, particularly when transitioning from the two-dimensional case (plate) to the one-dimensional case (beam). The article presents a convenient algebraic form of the solution and provides new case studies to demonstrate the practicality of the proposed formulation. Numerical results are also presented to illustrate the influence of porosity distribution on SCFs for different types of FGPBs. Furthermore, the article validates the numerical consistency of the mechanical property changesin FG beams without porosity and the SCF by comparing them with available results.

• Proceedings of the Korean Geotechical Society Conference
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• 2003.03a
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• pp.315-322
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• 2003

Cyclic simple shear tests were performed to find out the effect of preshear on dynamic strength of the sandy soil. Tests were performed for the specimens with 40% and 60% of relative density, under three different effective vertical stress of 50, 100 and 200kPa. For 50 and 100kPa, preshear ratios 0.00, 0.08, 0.12 and 0.16 were given, respectively, For low and high relative densities, two different results are shown in dynamic tests. Under the dense conditions, the maximum shear stress ratio($\tau$$\_$cyc//$\sigma$$\_$vo/) and the cyclic shear stress ratio($\tau$$\_$cyc//$\sigma$$\_$vo/) causing a certain shear strain increase with augmenting preshear ratio(${\alpha}$). However, the maximum shear stress ratio and the cyclic shear stress ratio increase or decrease with increasing preshear ratio under the loose conditions. Correction factor(K$\_$${\alpha}$/) for preshear increases at an early stage and then decreases with increasing preshear ratio at loose condition and increase with increasing preshear ratio at dense condition. Correction factor (K$\_$${\alpha}$,Max/) for preshear increases with the increasing preshear ratio irrespective of relative density, and the value of has same behavior as K$\_$${\alpha}$/.

• Steel and Composite Structures
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• v.33 no.5
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• pp.629-640
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• 2019

This paper presents a theoretical and finite element (FE) study on the stress intensity factors of double-edged cracked steel beams strengthened with carbon fiber reinforced polymer (CFRP) plates. By simplifying the tension flange of the steel beam using a steel plate in tension, the solutions obtained for the stress intensity factors of the double-edged cracked steel plate strengthened with CFRP plates were used to evaluate those of the steel beam specimens. The correction factor α₁ was modified based on the transformed section method, and an additional correction factor φ was introduced into the expressions. Three-dimensional FE modeling was conducted to calculate the stress intensity factors. Numerous combinations of the specimen geometry, crack length, CFRP thickness and Young's modulus, adhesive thickness and shear modulus were analyzed. The numerical results were used to investigate the variations in the stress intensity factor and the additional correction factor φ. The proposed expressions are a function of applied stress, crack length, the ratio between the crack length and half the width of the tension flange, the stiffness ratio between the CFRP plate and tension flange, adhesive shear modulus and thickness. Finally, the proposed expressions were verified by comparing the theoretical and numerical results.

• Structural Engineering and Mechanics
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• v.12 no.3
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• pp.249-266
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• 2001

Current seismic design provisions allow structures to deform into inelastic range during design level earthquakes since the chance to meet such event is quite rare. For this purpose, design base shear is defined in current seismic design provisions as the value of elastic seismic shear force divided by strength reduction factor, R (${\geq}1$). Strength reduction factor generally consists of four different factors, which can account for ductility capacity, overstrength, damping, and redundancy inherent in structures respectively. In this study, R factor is assumed to account for only the ductility rather than overstrength, damping, and redundancy. The R factor considering ductility is called "ductility factor" ($R_{\mu}$). This study proposes ductility factor with correction factor, C, which can account for dynamic P-${\Delta}$ effect. Correction factor, C is established as the functional form since it requires computational efforts and time for calculating this factor. From the statistical study using the results of nonlinear dynamic analysis for 40 earthquake ground motions (EQGM) it is shown that the dependence of C factor on structural period is weak, whereas C factor is strongly dependant on the change of ductility ratio and stability coefficient. To propose the functional form of C factor statistical study is carried out using 79,920 nonlinear dynamic analysis results for different combination of parameters and 40 EQGM.

• Proceedings of the Korea Concrete Institute Conference
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• 2005.05a
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• pp.399-402
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• 2005

This paper presents shear strength of concrete beam using FRP bars for flexure and shear reinforcements. Generally, the material properties of FRP bar are different from steel reinforcement. So, the shear strength correction factor is proposed through the experimental results.