• Computational Structural Engineering
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• v.10 no.4
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• pp.131-142
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• 1997

In this paper the kinematics of damage for finite elastoplastic deformations is introduced using the fourth-order damage effect tensor through the concept of the effective stress within the framework of continuum damage mechanics. Unlike the approach of strain equivalence or energy equivalence, which is applicable only to small strains, the proposed kinematic description provides a relation between the effective strain and the damage elastoplastic strain in finite deformation. This is accomplished by directly considering the kinematics of the deformation field both real configuration. The proposed approach shows that it is equivalent to the hypothesis of energy equivalence at finite strains. The damage effect tensor in this work is explicitly characterized in terms of a kinematic measure of damage in the elastoplastic domain through a second-order damage tensor.

• Structural Engineering and Mechanics
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• v.17 no.5
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• pp.655-670
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• 2004

This paper aims to evaluate the effect of typhoons on fatigue damage accumulation in steel decks of long-span suspension bridges. The strain-time histories at critical locations of deck sections of long-span bridges during different typhoons passing the bridge area are investigated by using on-line strain data acquired from the structural health monitoring system installed on the bridge. The fatigue damage models based on Miner's Law and Continuum Damage Mechanics (CDM) are applied to calculate the increment of fatigue damage due to the action of a typhoon. Accumulated fatigue damage during the typhoon is also calculated and compared between Miner's Law and the CDM method. It is found that for the Tsing Ma Bridge case, the stress spectrum generated by a typhoon is significantly different than that generated by normal traffic and its histogram shapes can be described approximately as a Rayleigh distribution. The influence of typhoon loading on accumulative fatigue damage is more significant than that due to normal traffic loading. The increment of fatigue damage generated by hourly stress spectrum for the maximum typhoon loading may be much greater than those for normal traffic loading. It is, therefore, concluded that it is necessary to evaluate typhoon induced fatigue damage for the purpose of accurately evaluating accumulative fatigue damage for long-span bridges located within typhoon prone regions.

• Computers and Concrete
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• v.4 no.5
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• pp.377-402
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• 2007

The paper presents quasi-static plane strain FE-simulations of strain localization in reinforced concrete beams without stirrups. The material was modeled with two different isotropic continuum crack models: an elasto-plastic and a damage one. In case of elasto-plasticity, linear Drucker-Prager criterion with a non-associated flow rule was defined in the compressive regime and a Rankine criterion with an associated flow rule was adopted in the tensile regime. In the case of a damage model, the degradation of the material due to micro-cracking was described with a single scalar damage parameter. To ensure the mesh-independence and to capture size effects, both criteria were enhanced in a softening regime by nonlocal terms. Thus, a characteristic length of micro-structure was included. The effect of a characteristic length, reinforcement ratio, bond-slip stiffness, fracture energy and beam size on strain localization was investigated. The numerical results with reinforced concrete beams were quantitatively compared with corresponding laboratory tests by Walraven (1978).

• Steel and Composite Structures
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• v.2 no.1
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• pp.21-34
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• 2002

A model of the process of local buckling in tubular steel structural elements is presented. It is assumed that this degrading phenomenon can be lumped at plastic hinges. The model is therefore based on the concept of plastic hinge combined with the methods of continuum damage mechanics. The state of this new kind of inelastic hinge is characterized by two internal variables: the plastic rotation and the damage. The model is valid if only one local buckling appears in the plastic hinge region; for instance, in the case of framed structures subjected to monotonic loadings. Based on this damage model, a new finite element that can describe the development of local buckling is proposed. The element is the assemblage of an elastic beamcolumn and two inelastic hinges at its ends. The stiffness matrix, that depends on the level of damage, the yielding function and the damage evolution law of the two hinges define the new finite element. In order to verify model and finite element, several small-scale frames were tested in laboratory under monotonic loading. A lateral load at the top of the frame was applied in a stroke-controlled mode until local buckling appears and develops in several locations of the frame and its ultimate capacity was reached. These tests were simulated with the new finite element and comparison between model and test is presented and discussed.

• Proceedings of the Korean Society for Rock Mechanics Conference
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• 1995.03a
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• pp.1-26
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• 1995

Key aspects of the Norwegian Method of Tunnelling (NMT) are reviewed. These include a predictive method of support design using the six-parameter Q-system of rock mass characterisation. The rock mass rating or Q-value is updated during tunnel driving. The designed tunnel support generally consists of wet process, steel fibre reinforced shotcrete combined with fully grouted, untensioned rock bolts, Even in poor rock conditions S(fr) + B usually acts as the final rock reinforcement and tunnel lining. Since it is a drained lining, it is very economic compared to cast concrete with membranes. Light, free-standing steel liners are used to prevent water affecting the runnel environment. Rock mass conditions, and hence lining design and cost estimation can be assessed by careful use of seismic surveys. Relationships between the P-wave velocity, the rock mass deformation modulus and the Q-value have recently been established, where tunnel depth, rock porosity and the uniaxial compression strength of the rock are important variables. The rock mass modulus estimate, and simple index testing of the joints, provide the key input which joints are discretely represented (either in two dimensions with the UDEC code or in three dimensions with the 3DEC code) is generally favoured compared to continuum analysis. The latter may give a misleading impression of uniformity and deformations tend to be understimated. Q-system NMT designs of S(fr) + B (fibre reinforced shotcrete and bolting) are numerically checked and adjustments made to bolt capacities and shotcrete thickness if overloading is evident around the modelled profile.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2009.10a
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• pp.227-230
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• 2009

In order to predict failure behavior of advanced high-strength steel sheets (AHSS) in hole expansion tests, damage model was developed considering surface condition sensitivity (with specimens prepared by milling and punching: 340R, TRIP590, TWIP940). To account for the micro-damage initiation and evolution as well as macro-crack formation, the stress triaxiality dependent fracture criterion and rate-dependent hardening and ultimate softening behavior were characterized by performing numerical simulations and experiments for the simple tension and V-notch tests. The developed damage model and the characterized mechanical property were incorporated into the FE program ABAQUS/Explicit to perform hole expansion simulations, which showed good agreement with experiments.

• Structural Engineering and Mechanics
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• v.33 no.1
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• pp.95-107
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• 2009

A method for vibration analysis of asymmetric shear wall and Thin walled open section structures is presented in this paper. The whole structure is idealized as an equivalent bending-warping torsion beam in this method. The governing differential equations of equivalent bending-warping torsion beam are formulated using continuum approach and posed in the form of simple storey transfer matrix. By using the storey transfer matrices and point transfer matrices which consider the inertial forces, system transfer matrix is obtained. Natural frequencies can be calculated by applying the boundary conditions. The structural properties of building may change in the proposed method. A numerical example has been solved at the end of study by a program written in MATLAB to verify the presented method. The results of this example display the agreement between the proposed method and the other valid method given in literature.

• Structural Engineering and Mechanics
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• v.30 no.6
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• pp.665-678
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• 2008

The beams components subjected to the loading such as axial, bending and cyclic thermal loads were studied in this research. The used constitutive equations are those of elasto-plasticity coupled to ductile and/or creep damage. The nonlinear kinematic hardening behavior was considered in elastoplasticity modeling. The unified damage law proposed for ductile failure and fatigue by the author of Sermage et al. (2000) and Kachanov's creep damage model applied to cyclic creep and low cycle fatigue of beams. Based on the results of the analysis, the shakedown limit loads were determined through the calculation of the residual strains developed in the beam analysis. The iterative technique determines the shakedown limit load in an iterative manner by performing a series of full coupled elastic-plastic and continuum damage cyclic loading modeling. The maximum load carrying capacity of the beam can withstand, were determined and imposed on the Bree's interaction diagram. Comparison between the shakedown diagrams generated by or without creep and/or ductile damage for the loading patterns was presented.

• Structural Engineering and Mechanics
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• v.41 no.2
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• pp.299-312
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• 2012

Stiffened coupled shear walls (SCSW) are under axial load resulting from their weight and this axial load affects the behavior of walls because of their excessive height. In this paper, based on the continuum approach, the optimal position of the stiffening beam on the stiffened coupled shear walls is investigated considering the effect of uniformly distributed axial loads. Moreover, the effect of the height of stiffened coupled shear walls on the optimal position of the stiffening beam has been studied with and without considering the axial force effect. A computer program has been developed in MATLAB and numerical examples have been solved to demonstrate the reliability of this method. The effects of the various flexural rigidities of the stiffening beam on the internal forces and the lateral deflection of the structure considering axial force effect have also been investigated.

• Structural Engineering and Mechanics
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• v.66 no.5
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• pp.595-608
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• 2018

This paper deals with the lateral - torsional motion of bridges provided with external cables acting as dampers under the action of horizontal dynamic loads or of walking human crowd loads. A three dimensional analysis is performed for the solution of the bridge models. The theoretical formulation is based on a continuum approach, which has been widely used in the literature to analyze bridges. The resulting equations of the uncoupled motion are solved using the Laplace Transformation, while the case of the coupled motion is solved through the use of the potential energy. Finally, characteristic examples are presented and useful results are obtained.