• Computers and Concrete
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• v.1 no.2
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• pp.115-130
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• 2004

The flexural ductility of solid rectangular reinforced concrete beams has been studied quite extensively. However, many reinforced concrete beams are neither solid nor rectangular; examples include T-, ${\Gamma}$-, ${\Pi}$- and box-shaped beams. There have been few studies on the flexural ductility of non-rectangular reinforced concrete beams and as a result little is known about the possible effect of sectional shape on flexural ductility. Herein, the effect of sectional shape on the post-peak flexural behaviour of reinforced normal and high-strength concrete beams has been studied using a newly developed analysis method that employs the actual stress-strain curves of the constitutive materials and takes into account the stress-path dependence of the stress-strain curve of the steel reinforcement. It was revealed that the sectional shape could have significant effect on the flexural ductility of a concrete beam and that the flexural ductility of a T-, ${\Gamma}$-, ${\Pi}$- or box-shaped beam is generally lower than that of a solid rectangular beam with the same overall dimensions and the same amount of reinforcement provided. Based on the numerical results obtained, a simple method of ensuring the provision of a certain minimum level of flexural ductility to non-rectangular concrete beams has been developed.

• 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.

• Steel and Composite Structures
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• v.31 no.6
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• pp.559-573
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• 2019

Spiral spacing effect on axial compressive behavior of reinforced concrete filled steel tube (RCFST) stub column is experimentally investigated in this paper. A total of twenty specimens including sixteen square RCFST columns and four benchmarked conventional square concrete filled steel tube (CFST) columns are fabricated and tested. Test variables include spiral spacing (spiral ratio) and concrete strength. The failure modes, load versus displacement curves, compressive rigidity, axial compressive strength, and ductility of the specimens are obtained and analyzed. Especially, the effect of spiral spacing on axial compressive strength and ductility is investigated and discussed in detail. Test results show that heavily arranged spirals considerably increase the ultimate compressive strength but lightly arranged spirals have no obvious effect on the ultimate strength. In practical design, the effect of spirals on RCFST column strength should be considered only when spirals are heavily arranged. Spiral spacing has a considerable effect on increasing the post-peak ductility of RCFST columns. Decreasing of the spiral spacing considerably increases the post-peak ductility of the RCFSTs. When the concrete strength increases, ultimate strength increases but the ductility decreases, due to the brittleness of the higher strength concrete. Arranging spirals, even with a rather small amount of spirals, is an economical and easy solution for improving the ductility of RCFST columns with high-strength concrete. Ultimate compressive strengths of the columns are calculated according to the codes EC4 (2004), GB 50936 (2014), AIJ (2008), and ACI 318 (2014). The ultimate strength of RCFST stub columns can be most precisely evaluated using standard GB 50936 (2014) considering the effect of spiral confinement on core concrete.

• Transactions of Materials Processing
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• v.27 no.2
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• pp.93-99
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• 2018

An analytical solution for the tensile ductility in porous ductile materials was derived based on an Irwin's approach of the elastic-plastic deformation in fracture mechanics. This was in good agreement with the experimental results of a tensile ductility in a sintered pure Al, and could solve the discrepancies in the Brown and Embury, or the McClintock models. This model was also offered as an advanced analytical solution considering the effect of stress triaxiality of pore tip in addition to pore interactions, material properties of matrix, and local deformation effect around pore. The evaluation of an analytical solution in the sintered pure Al powder compacts showed that the tensile ductility depends not only on the volume fraction of pores, but also on the pore size and on the mechanical properties of the matrix. The tensile ductility of the sintered pure Al compacts decreased rapidly with the increasing of a pore volume fraction, despite of the excellent tensile ductility of the matrix. This significant decrease in the tensile ductility was mainly attributed to the low yield strength of the matrix and small pore size. Particularly, the effects of the large radius and high volume fraction of the pore on the tensile ductility in Al-Form, were thus reasonably predicted by this analytical equation.

• Transactions of Materials Processing
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• v.13 no.8
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• pp.710-715
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• 2004

The effect of microstructural features on ductility of cold drawn pearlitic steels containing 0.52 ～ 0.92 wt%C was investigated. During wire drawing, reduction of area (Rh) increased initially with the progressive realignment of randomly oriented cementite, showed a maximum peak due to the completion of the alignment of most cementite, and decreased with thinning or fragmentation of the aligned cementite. Among factors on ductility, cementite thickness was found to be the most dominant microstructural feature for Rh of drawn pearlitic wires, regardless of transformation temperature and carbon content in steels.

• Journal of the Korea Concrete Institute
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• v.14 no.1
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• pp.8-15
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• 2002

This paper presents a study carried out for the seismic capacity in reinforced concrete(RC) piers by the confinement effect of transverse reinforcement as such a hooked-tied, welded-tied and spiral reinforcement. In order to assess the seismic capacity with transverse reinforcement, experiment리 and analytical methods were adopted. A RC column survey was conducted based on eight one-fourth scale single circular column specimens designed and tested under slow horizontal cyclic loads. Two cases were analyzed. The confinement effect of concrete by transverse reinforcement is considered not in Case 1 but in Case 2. Also, we studied the propriety of making use of the method in which a carbon fiber rod replace spiral reinforcement in RC piers. In experimental tests, a welded-tied and spiral reinforcement has a good seismic capacity, but a carbon fiber rod presents low ductility in comparison with a hooked-tied reinforcement. In an analytical study, displacement ductility is approximate to the experimental result because of considering the confinement effect of the transverse reinforcement. Even if the confinement effect of the transverse reinforcement is considered, the analytical results for ductility of the specimens with welded-tied and spiral reinforcement show an excessive underestimation of the experimental results.

• Earthquakes and Structures
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• v.10 no.5
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• pp.989-1012
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• 2016

The structural dynamic behavior and yield strength considering both ductility and strain rate effects are analyzed in this article. For the single-degree-of-freedom (SDOF) system, the relationship between the relative velocity and the strain rate response is deduced and the strain rate spectrum is presented. The ductility factor can be incorporated into the strain rate spectrum conveniently based on the constant-ductility velocity response spectrum. With the application of strain rate spectrum, it is convenient to consider the ductility and strain rate effects in engineering practice. The modal combination method, i.e., square root of the sum of the squares (SRSS) method, is employed to calculate the maximum strain rate of the elastoplastic multiple-degree-of-freedom (MDOF) system under uniform excitation. Considering the spatially varying ground motions, a new response spectrum method is developed by incorporating the ductility factor and strain rate into the conventional response spectrum method. In order to further analyze the effects of strain rate and ductility on structural dynamic behavior and yield strength, the cantilever beam (one-dimensional) and the triangular element (two-dimensional) are taken as numerical examples to calculate their seismic responses in time domain. Numerical results show that the permanent displacements with and without considering the strain rate effect are significantly different from each other. It is not only necessary in theory but also significant in engineering practice to take the ductility and strain rate effects into consideration.

• Computers and Concrete
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• v.20 no.2
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• pp.129-143
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• 2017

Seismic design of reinforced concrete (RC) structures requires a certain minimum level of flexural ductility. For example, Eurocode EN1998-1 directly specifies a minimum flexural ductility for RC beams, while Chinese code GB50011 limits the equivalent rectangular stress block depth ratio at peak resisting moment to achieve a certain nominal minimum flexural ductility indirectly. Although confinement is effective in improving the ductility of RC beams, most design codes do not provide any guidelines due to the lack of a suitable theory. In this study, the confinement for desirable flexural ductility performance of both normal- and high-strength concrete beams is evaluated based on a rigorous full-range moment-curvature analysis. An effective strategy is proposed for flexural ductility design of RC beams taking into account confinement. The key parameters considered include the maximum difference of tension and compression reinforcement ratios, and maximum neutral axis depth ratio at peak resisting moment. Empirical formulae and tables are then developed to provide guidelines accordingly.

• Computers and Concrete
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• v.15 no.4
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• pp.607-642
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• 2015

The stress-strain relationship of concrete in flexure is one of the essential parameters in assessing the flexural strength and ductility of reinforced concrete (RC) columns. An overview of previous research studies revealed that the presence of strain gradient would affect the maximum concrete stress developed in flexure. However, no quantitative model was available to evaluate the strain gradient effect on concrete under flexure. Previously, the authors have conducted experimental studies to investigate the strain gradient effect on maximum concrete stress and respective strain and developed two strain-gradient-dependent factors k3 and ko for modifying the flexural concrete stress-strain curve. As a continued study, the authors herein will extend the investigation of strain gradient effects on flexural strength and ductility of RC columns to concrete strength up to 100 MPa by employing the strain-gradient-dependent concrete stress-strain curve using nonlinear moment-curvature analysis. It was evident from the results that both the flexural strength and ductility of RC columns are improved under strain gradient effect. Lastly, for practical engineering design purpose, a new equivalent rectangular concrete stress block incorporating the combined effects of strain gradient and concrete strength was proposed and validated. Design formulas and charts have also been presented for flexural strength and ductility of RC columns.

• International Journal of Concrete Structures and Materials
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• v.2 no.2
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• pp.115-122
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• 2008

Ductility is important in the design of reinforced concrete structures. In seismic design of reinforced concrete members, it is necessary to allow for relatively large ductility so that the seismic energy is absorbed to avoid shear failure or significant degradation of strength even after yielding of reinforcing steels in the concrete member occurs. Therefore, prediction of the ductility should be as accurate as possible. The principal aim of this paper is to present the basic data for the ductility evaluation of reinforced high-strength concrete beams. Accordingly, 23 flexural tests were conducted on full-scale structural concrete beam specimens having concrete compressive strength of 40, 60, and 70MPa. The test results were then reviewed in terms of flexural capacity and ductility. The effect of concrete compressive strength, web reinforcement ratio, tension steel ratio, and shear span to beam depth ratio on ductility were investigated experimentally.