• Earthquakes and Structures
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• v.5 no.2
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• pp.239-259
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• 2013

Typically, beams that form part of structural systems are subjected to vertical distributed loading along their length. Distributed loading affects moment and shear distribution, and consequently spread of inelasticity, along the beam length. However, the finite element models developed so far for seismic analysis of frame structures either ignore the effect of vertical distributed loading on spread of inelasticity or consider it in an approximate manner. In this paper, a beam-type finite element is developed, which is capable of considering accurately the effect of uniform distributed loading on spreading of inelastic deformations along the beam length. The proposed model consists of two gradual spread inelasticity sub-elements accounting explicitly for inelastic flexural and shear response. Following this approach, the effect of distributed loading on spreading of inelastic flexural and shear deformations is properly taken into account. The finite element is implemented in the seismic analysis of plane frame structures with beam members controlled either by flexure or shear. It is shown that to obtain accurate results the influence of distributed beam loading on spreading of inelastic deformations should be taken into account in the inelastic seismic analysis of frame structures.

• Steel and Composite Structures
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• v.22 no.3
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• pp.627-645
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• 2016

When an eccentrically braced frame (EBF) is subjected to severe earthquakes, the links experience inelastic deformations while beams outside of the link, braces and columns are designed to remain elastic. To perform reliable inelastic analyses of EBFs sufficient analytical model which can accurately predict the inelastic performance of the links is needed. It is said in the literature that available analytical models for shear links generally predict very well the maximum shear forces and deformations from experiments on shear links, but may underestimate the intermediary values. In this study it is shown that available analytical models do not predict very well the maximum shear forces and deformations too. In this study an analytical model which can accurately predict both maximum and intermediary values of shear force and deformation is proposed. The model parameters are established based on test results from several experiments on shear links. Comparison of available test results with the hysteresis curves obtained using the proposed analytical model established the accuracy of the model. The proposed model is recommended to be used to perform inelastic analyses of EBFs.

• Structural Engineering and Mechanics
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• v.10 no.4
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• pp.405-426
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• 2000

Two approximate methods based on mechanism analysis suitable for seismic assessment/design of structural concrete are reviewed. The methods involve use of equal energy concept or equal displacement concept along with appropriate patterns of inelastic deformations to relate structure's maximum lateral displacement to member and plastic deformations. One of these methods (Clough's method), defined here as a ductility-based approach, is examined in detail and a modification for its improvement is suggested. The modification is based on estimation of maximum inelastic displacement using inelastic design response spectra (IDRS) as an alternative to using equal energy concept. The IDRS for demand displacement ductilities are developed for a single degree of freedom model subjected to several accelerograms as functions of response modification factor (R), damping ratios, and strain hardening. The suggested revised methodology involves estimation of R as the ratio of elastic strength demand to code level demand, and determination of design base shear using $R_{design}{\leq}R$ and maximum displacement, determination of plastic displacement using IDRS and subsequent local plastic deformations. The methodology is demonstrated for the case of a 10-story precast wall panel building.

• Computers and Concrete
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• v.20 no.1
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• pp.11-22
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• 2017

There are two methods to model the plastification of members comprising lumped and distributed plasticity. When a reinforced concrete member experiences inelastic deformations, cracks tend to spread from the joint interface resulting in a curvature distribution; therefore, the lumped plasticity methods assuming plasticity is concentrated at a zero-length plastic hinge section at the ends of the elements, cannot model the actual behavior of reinforced concrete members. Some spread plasticity models including uniform, linear and recently power have been developed to take extended inelastic zone into account. In the aforementioned models, the extended inelastic zones in proximity of critical sections assumed close to connections are considered. Although the mentioned assumption is proper for the buildings simply imposed lateral loads, it is not appropriate for the gravity load effects. The gravity load effects can influence the inelastic zones in structural elements; therefore, the plasticity models presenting the flexibility distribution along the member merely based on lateral loads apart from the gravity load effects can bring about incorrect stiffness matrix for structure. In this study, the linear flexibility distribution model is improved to account for the distributed plasticity of members subjected to both gravity and lateral load effects. To do so, a new model in which, each member is taken as one structural element into account is proposed. Some numerical examples from previous studies are assessed and outcomes confirm the accuracy of proposed model. Also comparing the results of the proposed model with other spread plasticity models illustrates glaring error produced due to neglecting the gravity load effects.

• Journal of the Korean Society of Safety
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• v.29 no.3
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• pp.64-71
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• 2014

The generalized tangential stiffness matrix of semi-rigid frame element with shear deformations based on Haringx's shear theory is newly derived and compared with the previous study based on Engesser's shear theory. Also, linearized elastic and geometric stiffness matrices are newly presented from the exact tangential stiffness matrix. In oder to obtain the inelastic system buckling load of shear flexible semi-rigid frame structure, the Ef method by tangential modulus theory is adopted and the FE analysis programs are developed. Finally, the shear and semi-rigid effects of system bucking are investigated by two numerical examples.

• Journal of the Korean Society of Safety
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• v.8 no.1
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• pp.47-53
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• 1993

Residual Deformation Analysis(RDA) is a new method for ratings of the continuous bridges. The RDA makes it possible to expand the inelastic steel girder bridge design method set forth in the American Association of State Highway Officals'(AASHTO) Guide Specifications for Alternate Load Factor Design Procedures for Steel Beam Bridges Using Braced Compact Sections(1986) into an inelastic rating method. It is a method to assess the residual moments and deformations that are set up in a beam that has been loaded into the post-elastic range This method combines classical elastic conjugate beam theory with linear moment-rotation relationships for midspan inelastic positive moment. The limit state is inelastic serviceability limit. which is defined as the ratio of the span to midspan inelastic deflection(C=L/D).

• Steel and Composite Structures
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• v.17 no.6
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• pp.951-965
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• 2014

Point bending is commonly used for cambering and curving steel girders to large radii. In this system, a hydraulic ram or press is used to apply concentrated loads at selected points to obtain the required vertical (cambering) or horizontal (curving) curved profile from induced permanent deformations. This paper derives closed form solutions that relate loads to permanent deformations for horizontally curving wide flange steel beams based on their post-yield response. These solutions are presented in a parametric form to identify the relationship between key variables and their impact on the accuracy of the curving operation. It is shown that point bending could yield parabolic curved profiles that are within 1% of a desired circular curve if the span length to radius of curvature ratio (L / R) is less than 1.5 and the point loads are spaced at one third the beam length. Safe limits are then established on loads, strains and curvatures to avoid damaging the steel section. This leads to optimization of the point bending operation for inducing a circular profile in wide flange steel beams of any size.

• Structural Engineering and Mechanics
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• v.5 no.6
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• pp.817-837
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• 1997

In the present contribution an interface crack model is introduced which is capable of modelling crack initialisation and growth in aluminium as well as in Fibre Metal Laminates. Interface elements are inserted in a finite element mesh with a yield function which bounds all states of stress in the interface. Hardening occurs after a state of stress exceeds the yield stress of the material. The hardening branch is bounded by the ultimate stress of the material. Thereafter, the state of stress is reduced to zero while the inelastic deformations grow. The energy dissipated by the inelastic deformations in this process equals the fracture energy of the material. The model is applied to calculate the onset and growth of cracking in centre cracked plates made of aluminium and GLARE$^{(R)}$. The impact of the model parameters on the performance of the crack model is studied by comparisons of the numerical results with experimental data.

• Structural Engineering and Mechanics
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• v.5 no.6
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• pp.755-765
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• 1997

Within the framework of anisotropic combined viscoplastic hardening formulation, accounting macroscopically for residual stress as well as texture development at finite deformations of metals, simple shear analyses for the simulation of fixed-end torsion experiments for ${\alpha}$-Fe, Al and Cu at different strain rates are reviewed with an emphasis on the role of constitutive spins. Complicated responses of the axial stresses with monotonically increasing shear deformations can be successfully described by the capacity of orthotropic hardening part, featuring tensile axial stresses either smooth or oscillatory. Temperature effect on the responses of axial stresses for Cu is investigated in relation to the distortion and orientation of yield surface. The flexibility of this combined hardening model in the simulation of finite inelastic strains is discussed with reference to the variations of constitutive spins depending upon strain rates and temperatures.

• Smart Structures and Systems
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• v.2 no.4
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• pp.339-355
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• 2006

A procedure to retrofit existing essential facilities subjected to seismic excitation is proposed. The main features of this procedure are to reduce maximum acceleration and associated forces in buildings subjected to seismic excitation by reducing their strength (weakening). The weakening retrofit, which is an opposite strategy to strengthening, is particularly suitable for buildings having overstressed components and foundation supports or having weak brittle components. However, by weakening the structure large deformations are expected. Supplementaldamping devices however can control the deformations within desirable limits. The structure retrofitted with this strategy will have, therefore, a reduction in the acceleration response and a reduction in the deformations, depending on the amount of additional damping introduced in the structure. An illustration of the above strategy is presented here through an evaluation of the inelastic response of the structure through a nonlinear dynamic analysis. The results are compared with different retrofit techniques. A parametric analysis has also been carried out to evaluate the effectiveness of the retrofitting method using different combination of the performance thresholds in accelerations and displacements through fragility analysis.