• Structural Engineering and Mechanics
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• v.70 no.3
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• pp.257-267
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• 2019

Expressions for the calculation of ductility index for concrete girders with different ratios of prestressed and classical reinforcement were proposed using load-displacement, load-strain and load-curvature relation. The results of previous experimental static tests of several large-scale concrete girders with different ratio of prestressed and classical reinforcement are briefly presented. Using the proposed expressions, various ductility index of tested girders were calculated and discussed. It was concluded that the ductility of girders decreases approximately linearly by increasing the degree of prestressing. The study presents an expression for the calculation of the average ductility index of classical and prestressed reinforced concrete girders, which are similar to the analysed experimental test girders.

• Proceedings of the Korea Concrete Institute Conference
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• 1998.10a
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• pp.501-506
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• 1998

This paper is an experimental study on the flexural strength and ductility capacity of reinforced high performance concrete beams with the concrete which has compressive strength of 600~700kg/$\textrm{cm}^2$, slump value of 20~25cm and slump-flow value of 60~70cm. Total 8 beams with different tensile reinforcement ratio and pattern of loading were tested. Form the results of reinforced high performance concrete beams, the equivalent stress block parameters proposed by MacGregor et al. or New Zealand code are recommended to use. Also, an extreme fiber concrete compressive strain of reinforced high performance concrete beams are distributed 0.0033~0.0048. In reinforced high performance concrete beams, reinforcement ratio in order to insure curvature ductility index 2 and 4 propose by ACI code should be less than those of reinforced normal strength concrete beams.

• Journal of the Korea Concrete Institute
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• v.13 no.6
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• pp.553-560
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• 2001

The ductility capacity should be estimated for inelastic analysis and design of reinforced concrete flexural members. Therefore, to estimate the ductility capacity, the model of moment-curvature relationship of reinforced concrete flexural member is assumed in this study. The curvature, rotation, and displacement(deflection) of reinforced concrete cantilever beams are analyzed and tested. The analytical results are compared with the test results. According to the analytical and test results, the assumed model of moment-curvature relationship in this study is adequate in flexural analysis of reinforced concrete members because the analytical results are well agreed with the test results, and it is resonable to express the ductility capacity in the rotation or displacement ductility, Because the curvature ductility is the limited index in a certain section. It is investigated that the ductility capacity is proportional to lateral reinforcement and compression reinforcement and inversely proportional to tension reinforcement.

• Journal of the Korea Concrete Institute
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• v.11 no.4
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• pp.147-156
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• 1999

Current design code states that the strength reduction factor shall be permitted to be increased linearly from that for axial compression to that for flexure as the design axial load strength $\Phi$cPn decrease from 0.1fckAg to zero. Since this empirically adopted axial load level of $\Phi$cPn=0.1fckAg considers only sectional area and concrete strength, the other variables such as steel ratio, steel yielding strength, and steel arrangement can not be considered. This research is performed to investigate the consistency and the rationality of the code requirement for determination of column design strength. A nonlinear axial force-moment-curvature analysis was conducted in order to investigate the ductility of reinforced concrete column sections. As the result of ductility analysis, it was found that the ductility at the axial force of $\Phi$cPn=0.1fckAg represented a lock of consistency for the various variable contained sections. Therefore, a more reasonable application method of strength reduction factor is proposed, that is based on the strain ductility index.

• Structural Engineering and Mechanics
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• v.43 no.2
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• pp.225-237
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• 2012

This paper presents an experimental investigation of the flexural behavior of square hollow steel section (HSS) beams subjected to pure bending. Totally six unfilled and nine ultra high performance concrete (UHPC)-filled HSS beams were tested under four-point bending until failure. The effects of the steel tube thickness, the yield strength of the steel tube and the strength of concrete on moment capacity, curvature, and ductility of UHPC-filled HSS beams were examined. The performance indices named relative ductility index (RDI) and strength increasing factor (SIF) were investigated with regard to different height-to-thickness ratio of the specimens. The flexural strengths obtained from the tests were compared with the values predicted by Eurocode 4, AISC-LRFD and CIDECT design codes. The results showed that the increase in the moment capacity and the corresponding curvature is much greater for thinner HSS beams than thicker ones. Eurocode 4 and AISC-LRFD predict the ultimate moment capacity of the all UHPC-filled HSS beams conservatively.

• Journal of the Korea Concrete Institute
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• v.26 no.2
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• pp.159-169
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• 2014

This study generalizes the lateral load-displacement relationship of reinforced concrete shear walls from the section analysis for moment-curvature response to straightforwardly evaluate the flexural capacity and ductility of such members. Moment and curvature at different selected points including the first flexural crack, yielding of tensile reinforcing bar, maximum strength, 80% of the maximum strength at descending branch, and fracture of tensile reinforcing bar are calculated based on the strain compatibility and equilibrium of internal forces. The strain at extreme compressive fiber to determine the curvature at the descending branch is formulated as a function of reduction factor of maximum stress of concrete and volumetric index of lateral reinforcement using the stress-strain model of confined concrete proposed by Razvi and Saatcioglu. The moment prediction models are simply formulated as a function of tensile reinforcement index, vertical reinforcement index, and axial load index from an extensive parametric study. Lateral displacement is calculated by using the moment area method of idealized curvature distribution along the wall height. The generalized lateral load-displacement relationship is in good agreement with test result, even at the descending branch after ultimate strength of shear walls.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.14 no.3
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• pp.391-402
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• 1994

One of the most important design concept for reinforced concrete structures is to achieve a ductile failure mode, and also moment redistribution for economic design is possible in case that adequate ductility is provided. Flexural ductility index is, therefore, used as a reference for possibility of moment redistribution as well as for prediction of flexural behavior of designed R.C. structures. Ductility index equations, however, provide approximate values due to the linear concrete compressive stress assumption at the tension steel yielding state. Theoretically more exact ductility index is calculated by a numerical analysis with the realistic stress-strain curves for concrete and steel to be compared with the result from tire ductility index equations. Variation of ductility index for the selected variables and the reasonable maximum tension steel ratio for doubly reinforced section are investigated. A moment-curvature curve model is also proposed for future research on moment redistribution.

• Journal of the Korea Concrete Institute
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• v.27 no.3
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• pp.207-214
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• 2015

This study examined the feasibility of wire ropes as lateral reinforcement at the boundary element of heavyweight concrete shear walls. The spacing of the wire ropes varied from 60 mm to 120 mm at an interval of 30 mm, which produces the volumetric index of the lateral reinforcement of 0.126~0.234. The wire ropes were applied as a external hoop and/or internal cross-tie. Five shear wall specimens were tested to failure under constant axial load and cyclic lateral loads. Test results showed that with the increase of the volumetric index of the lateral reinforcement, the ductility of shear walls tended to increase, whereas the variation of flexural capacity of walls was minimal. The flexural capacity of shear walls tested was slightly higher than predictions determined from ACI 318-11 procedure. The displacement ductility ratio of shear walls with wire ropes was higher than that of shear wall with the conventional mild bar at the same the volumetric index of the lateral reinforcement. In particular, the shear walls with wire rope index of 0.233 achieved the curvature ductility ratio of more than 16 required for high-ductility design.

• Structural Engineering and Mechanics
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• v.55 no.6
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• pp.1099-1120
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• 2015

External prestressing has been applied to both new construction and retrofitting of existing reinforced and prestressed concrete structures. Continuous beams are preferred to simply supported beams because of economy, fewer movement joints and possible benefits from moment redistribution. However, this paper argues that continuous prestressed concrete beams with external unbonded tendons demonstrate different full-range behaviour compared to reinforced concrete (RC) beams. Applying the same design approach for RC to external prestressing may lead to design with a lower safety margin. To better understand the behaviour of continuous prestressed concrete beams with unbonded tendons, an experimental investigation is performed in which nine such specimens are tested to failure. The full-range behaviour is investigated with reference to moment-curvature relationship and moment redistribution. The amounts of moment redistribution measured in the experiments are compared with those allowed by BS 8110, EC2 and ACI 318. Design equations are also proposed to estimate the curvature ductility index of unbonded prestressed concrete beams.

• Journal of the Korea Concrete Institute
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• v.28 no.3
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• pp.279-288
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• 2016

The present study simplified the moment-curvature relationship to straightforwardly determine the flexural behavior of reinforced concrete (RC) columns. For the idealized column section, moments and neutral axis depths at different stages(first flexural crack, yielding of tensile reinforcing bar, maximum strength, and 80% of the maximum strength at the descending branch) were derived on the basis of the equilibrium condition of forces and compatibility condition. Concrete strains at the extreme compression fiber beyond the maximum strength were determined using the stress-strain relationship of confined concrete, proposed by Kim et al. The lateral load-displacement curves converted from the simplified moment-curvature relationship of columns are well consistent with test results obtained from column specimens under various parameters. The moments and the corresponding neutral axis depth at different stages were formulated as a function of longitudinal reinforcement and transverse reinforcement indices and/or applied axial load index. Overall, curvature ductility of columns was significantly affected by the axial load level as well as concrete compressive strength and the amount of longitudinal and transverse reinforcing bars.