• Structural Engineering and Mechanics
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• v.53 no.5
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• pp.997-1016
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• 2015

The contribution of tensioned concrete between cracks (tension-stiffening) cannot be ignored when analysing deformation of reinforced concrete elements. The tension-stiffening effect is crucial when it comes to adequately estimating the load-deformation response of steel reinforced concrete and the more recently appeared fibre reinforced polymer (FRP) reinforced concrete. This paper presents a unified methodology for numerical modelling of the tension-stiffening effect in steel as well as FRP reinforced flexural members using the concept of equivalent deformation modulus and the smeared crack approach to obtain a modified stress-strain relation of the reinforcement. A closed-form solution for the equivalent secant modulus of deformation of the tensioned reinforcement is proposed for rectangular sections taking the Eurocode 2 curvature prediction technique as the reference. Using equations based on general principles of structural mechanics, the main influencing parameters are obtained. It is found that the ratio between the equivalent stiffness and the initial stiffness basically depends on the product of the modular ratio and reinforcement ratio ($n{\rho}$), the effective-to-total depth ratio (d/h), and the level of loading. The proposed methodology is adequate for numerical modelling of tension-stiffening for different FRP and steel reinforcement, under both service and ultimate conditions. Comparison of the predicted and experimental data obtained by the authors indicates that the proposed methodology is capable to adequately model the tension-stiffening effect in beams reinforced with FRP or steel bars within wide range of loading.

• Steel and Composite Structures
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• v.29 no.5
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• pp.623-633
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• 2018

A robust element is essential for successful design of steel frames with Direct analysis (DA) method. To this end, an innovative and efficient curved-quartic-function (CQF) beam-column element using the fourth-order polynomial shape function with end-springs in series is proposed for practical applications of DA. The member initial imperfection is explicitly integrated into the element formulation, and, therefore, the P-${\delta}$ effect can be directly captured in the analysis. The series of zero-length springs are placed at the element ends to model the effects of semi-rigid joints and material yielding. One-element-per-member model is adopted for design bringing considerable savings in computer expense. The incremental secant stiffness method allowing for large deflections is used to describe the kinematic motion. Finally, several problems are studied in this paper for examining and validating the accuracy of the present formulations. The proposed element is believed to make DA simpler to use than existing elements, which is essential for its successful and widespread adoption by engineers.

• Journal of the Earthquake Engineering Society of Korea
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• v.11 no.2 s.54
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• pp.105-113
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• 2007

In the current research, an algorithm of performance-based seismic retrofit design of reinforced concrete columns using FRP jacket has been proposed. For exact prediction of the nonlinear flexural analysis or FRP composite RC members, multiaxial constitutive laws of concrete and composite materials have been presented. For seismic retrofit design, an algorithm of direct displacement-based design method (DDM) proposed by Chopra and Goel (2001) has been newly applied to determine the design thickness of FRP jacket in seismic retrofit of reinforced concrete columns. To compare with the displacement coefficient method (DCM), the DDM gives an accurate prediction of the target displacement in highly nonlinear region, since the DCM uses the elastic stiffness before reaching the yield load as the effective stiffness but the DDM uses the secant stiffness.

• Steel and Composite Structures
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• v.49 no.4
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• pp.441-456
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• 2023

Aiming at the development trend of light weight and high strength of engineering structures, this paper experimentally investigated the seismic performance of circular-in-square high-strength concrete-filled double skin steel tubular (HCFDST) stub columns with out-of-code width-to-thickness (B/t) ratios. Typical failure mode of HCFDST stub columns appeared with the infill material crushing, steel fracture and local buckling of outer tubes as well as the inner buckling of inner tubes. Subsequently, the detailed analysis on hysteretic curves, skeleton curves and ductility, energy dissipation, stiffness degradation and lateral force reduction was conducted to reflect the influences of hollow ratios, axial compression ratios and infill types, e.g., increasing hollow ratio from 0.54 to 0.68 and 0.82 made a slight effect on bearing capacity compared to the ductility coefficients; the higher axial compression ratio (e.g., 0.3 versus 0.1) significantly reduced the average bearing capacity and ductility; the HCFDST column SCFST-6 filled with concrete obviously displayed the larger initial secant stiffness with a percentage 34.20% than the column SCFST-2 using engineered cementitious composite (ECC); increasing hollow ratios, axial compression ratios could accelerate the drop speed of stiffness degradation. The out-of-code HCFDST stub columns with reasonable design could behave favorable hysteretic performance. A theoretical model considering the tensile strength effect of ECC was thereafter established and verified to predict the moment-resisting capacity of HCFDST columns using ECC. The reported research on circular-in-square HCFDST stub columns can provide significant references to the structural application and design.

• Journal of Korean Society of Steel Construction
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• v.15 no.3
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• pp.281-290
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• 2003

A series of connection tests of portal frames which were composed of cold-formed steel studs and rafters was carried out to study the moment-rotation relation, the rotational rigidity, and the yield and the ultimate moment of the connections. The main factors of the tests were the thickness, the shape of the connecting members which were made of mild steel, and the torsional restraints of the test specimens. The test results were compared with those obtained through the non-linear analysis, for verification. The secant stiffness estimated from the experimental moment-rotation curve was proposed for the rotational rigidity of semi-rigid connections, and its validity was verified in the structural frame analysis.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.16 no.4 s.109
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• pp.394-403
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• 2006

A new equivalent linearization technique is proposed for a friction damper-brace system (FDBS) idealized as a elastoplastic system. The equivalent linearization technique utilizes secant stiffness and dissipated energy defined by the probability distribution of the extremal displacement of the FDBS. In addition, a conversion scheme is proposed so that an equivalent linear system is designed first and converted to the FDBS. For comparative study, an existing model update technique based on system identification is modified in a form appropriate to update single element. For the purpose of verification, shaking table tests of a small scale three-story shear building model, in which a rotational FDBS is installed, are conducted and equivalent linear systems are obtained using the proposed technique and the model update technique. Complex eigenvalue analysis is conducted for those equivalent linear systems, and the natural frequencies and modal damping ratios are compared with those obtained from system identification. Additionally, RMS and peak responses obtained from time history analysis of the equivalent linear systems are compared with measured ones.

• Journal of the Earthquake Engineering Society of Korea
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• v.14 no.5
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• pp.1-12
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• 2010

This study presents a finite element analysis method that can accurately evaluate the nonlinear behaviour of structures affected by shallow soft subsoils and the soil-structure interaction. A two-dimensional finite element model that consists of a structure and shallow soft subsoil was used. The finite element model was used for a nonlinear time domain analysis of the OpenSees program. A parametric study was performed to investigate the effects of soil shear velocities, earthquake input motions, soft soil depth, and soil-structure interaction. The result of the proposed nonlinear finite element analysis method was compared with the result of an existing frequency domain analysis method, which is frequently used for addressing nonlinear soil behavior. The result showed that the frequency domain analysis, which uses equivalent secant soil stiffness and does not address the soil-structure interaction, significantly overestimated the response of the structures with short dynamic periods. The effect of the soil-structure interaction on the response spectrum did not significantly vary with the foundation dimensions and structure mass.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.28 no.6A
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• pp.789-798
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• 2008

The stiffness method provides a framework to calculate the structural deformations directly from solving the equilibrium state. However, to use the displacement shape functions leads to approximate estimation of stiffness matrix and resisting forces, and accordingly results in a low accuracy. The conventional flexibility method uses the relation between sectional forces and nodal forces in which the equilibrium is always satisfied over all sections along the element. However, the determination of the element resisting forces is not so straightforward. In this study, a new fiber finite element mixed method has been developed for nonlinear anaysis of steel-concrete composite structures in the context of a standard finite element analysis program. The proposed method applies the Newton method based on the load control and uses the incremental secant stiffness method which is computationally efficient and stable. Also, the method is employed to analyze the steel-concrete composite structures, and the analysis results are compared with those obtained by ABAQUS. The comparison shows that the proposed method consistently well predicts the nonlinear behavior of the composite structures, and gives good efficiency.

• International Journal of Concrete Structures and Materials
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• v.11 no.1
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• pp.135-149
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• 2017

The prediction of the actual ultimate capacity of confined concrete columns requires partial confinement utilization under eccentric loading. This is attributed to the reduction in compression zone compared to columns under pure axial compression. Modern codes and standards are introducing the need to perform extreme event analysis under static loads. There has been a number of studies that focused on the analysis and testing of concentric columns. On the other hand, the augmentation of compressive strength due to partial confinement has not been treated before. The higher eccentricity causes smaller confined concrete region in compression yielding smaller increase in strength of concrete. Accordingly, the ultimate eccentric confined strength is gradually reduced from the fully confined value $f_{cc}$ (at zero eccentricity) to the unconfined value $f^{\prime}_c$ (at infinite eccentricity) as a function of the ratio of compression area to total area of each eccentricity. This approach is used to implement an adaptive Mander model for analyzing eccentrically loaded columns. Generalization of the 3D moment of area approach is implemented based on proportional loading, fiber model and the secant stiffness approach, in an incremental-iterative numerical procedure to achieve the equilibrium path of $P-{\varepsilon}$ and $M-{\varphi}$ response up to failure. This numerical analysis is adapted to assess the confining effect in rectangular columns confined with conventional lateral steel. This analysis is validated against experimental data found in the literature showing good correlation to the partial confinement model while rendering the full confinement treatment unsafe.

• Journal of Korean Society of Steel Construction
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• v.17 no.1 s.74
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• pp.103-113
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• 2005

In the present study, the Direct Inelastic Design (DID) for steel structures developed in the previous study was improved to expand it applicability. The proposed design method can perform inelastic designs that address the design characteristics of steel structures: Group member design, discrete member sizes, variation of moment-carrying capacity according to axial force, connection types, and multiple design criteria and load conditions. The design procedure for the proposed method was established, and a computer program incorporating the design procedure was developed. The design results from the conventional elastic method and the DID were compared and verified by the existing computer program for nonlinear analysis. Compared with the conventional elastic design, the DID addressing the inelastic behavior reduced the total weight of steel members and enhanced the deformability of the structure. The proposed design method is convenient because it can directly perform inelastic design by using linear analysis for secant stiffness. Also, it can achieve structural safety and economical design by controlling deformations of the plastic hinges.