• Journal of Korean Tunnelling and Underground Space Association
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• v.16 no.2
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• pp.173-180
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• 2014

In the design of tunnel segment structure, axial and moment forces are considered as significant forces. Since axial force is much greater than moment force, the whole section of segment remains in compression. Therefore crack width can be reduced. But the axial force is not considered in criteria for serviceability check. This fact leads service condition more severe compared to ultimate condition and makes the required steel reinforcement increase to meet the serviceability criteria. In this study, the effect of axial force on serviceability of tunnel segment is evaluated, experimentally and analytically. Mock-up tests on segments with actual size were performed and investigated in terms of initial crack resistance. The evaluation proves that more comprehensive design could be achieved when the axial force is considered in the procedure for the serviceability check in design of tunnel segment.

• Steel and Composite Structures
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• v.34 no.2
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• pp.241-260
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• 2020

This article presented a comprehensive model to study static buckling stability and associated mode-shapes of higher shear deformation theories of sandwich laminated composite beam under the compression of varying axial load function. Four higher order shear deformation beam theories are considered in formulation and analysis. So, the model can consider the influence of both thick and thin beams without needing to shear correction factor. The compression force can be described through axial direction by uniform constant, linear and parabolic distribution functions. The Hamilton's principle is exploited to derive equilibrium governing equations of unified sandwich laminated beams. The governing equilibrium differential equations are transformed to algebraic system of equations by using numerical differential quadrature method (DQM). The system of equations is solved as an eigenvalue problem to get critical buckling loads and their corresponding mode-shapes. The stability of DQM in determining of buckling loads of sandwich structure is performed. The validation studies are achieved and the obtained results are matched with those. Parametric studies are presented to figure out effects of in-plane load type, sandwich thickness, fiber orientation and boundary conditions on buckling loads and mode-shapes. The present model is important in designing process of aircraft, naval structural components, and naval structural when non-uniform in-plane compressive loading is dominated.

• Steel and Composite Structures
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• v.23 no.5
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• pp.501-516
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• 2017

Numerical simulations are prevalently used to evaluate the seismic behaviour of structures. The accuracy of the simulation results depends directly on the accuracy of the modelling techniques employed to simulate the behaviour of individual structural members. An empirical modelling technique is employed in this paper to simulate the behaviour of column members under cyclic and seismic loading. Despite the common modelling techniques, this technique is capable of simulating two important aspects of the cyclic and seismic behaviour of columns simultaneously. The proposed fiber-based modelling technique captures explicitly the interaction between the bending moment and the axial force in columns, and the cyclic deterioration of the hysteretic behaviour of these members is implicitly taken into account. The fiber-based model is calibrated based on the cyclic behaviour of square hollow steel sections. The behaviour of several column archetypes is investigated under a dual cyclic loading protocol to develop a benchmark database before the calibration procedure. The dual loading protocol used in this study consists of both axial and lateral loading cycles with varying amplitudes. After the calibration procedure, a regression analysis is conducted to derive an equation for predicting a varying calibrated modelling parameter. Finally, several nonlinear time-history analyses are conducted on a 6-story steel special moment frame in order to investigate how the results of numerical simulations can be affected by employing the intended modelling technique for columns instead of other common modelling techniques.

• Wind and Structures
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• v.21 no.2
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• pp.119-158
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• 2015

The characteristics of the coherence functions of X axial, Y axial, and RZ axial (i.e., body axis) wind forces on the Shanghai World Trade Centre - a 492 m super-tall building with section varying along height are studied via a synchronous multi-pressure measurement of the rigid model in wind tunnel simulating of the turbulent, and the corresponding mathematical expressions are proposed there from. The investigations show that the mathematical expressions of coherence functions in across-wind and torsional-wind directions can be constructed by superimposition of a modified exponential decay function and a peak function caused by turbulent flow and vortex shedding respectively, while that in along-wind direction need only be constructed by the former, similar to that of wind speed. Moreover, an inductive analysis method is proposed to summarize the fitted parameters of the wind force coherence functions of every two measurement levels of altitudes. The comparisons of the first three order generalized force spectra show that the proposed mathematical expressions accord with the experimental results well. Later, the influences of coherence functions on wind-induced dynamic responses are analyzed in detail based on the proposed mathematical expressions and the frequency-domain method of random vibration theory.

• Advances in Computational Design
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• v.5 no.4
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• pp.397-416
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• 2020

Functionally graded material (FGM) illustrates a novel class of composites that consists of a graded pattern of material composition. FGM is engineered to have a continuously varying spatial composition profile. Current work focused on buckling analysis of beam made of stepwise linear and quadratic graded material in axial direction subjected to axial span-load with piecewise function and rested on shear layer based on classical beam theory. The various boundary and natural conditions including simply supported (S-S), pinned - clamped (P-C), axial hinge - pinned (AH-P), axial hinge - clamped (AH-C), pinned - shear hinge (P-SHH), pinned - shear force released (P-SHR), axial hinge - shear force released (AH-SHR) and axial hinge - shear hinge (AH-SHH) are considered. To the best of the author's knowledge, buckling behavior of this kind of Euler-Bernoulli beams has not been studied yet. The equilibrium differential equation is derived by minimizing total potential energy via variational calculus and solved analytically. The boundary conditions, natural conditions and deformation continuity at concentrated load insertion point are expressed in matrix form and nontrivial solution is employed to calculate first buckling loads and corresponding mode shapes. By increasing truncation order, the relative error reduction and convergence of solution are observed. Fast convergence and good compatibility with various conditions are advantages of the proposed method. A MATLAB code is provided in appendix to employ the numerical procedure based on proposed method.

• Steel and Composite Structures
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• v.45 no.4
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• pp.547-554
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• 2022

This paper studies the static stability of an axially graded column with the power-law gradient varying along the axial direction. For a nonhomogeneous column with one end linked to a rotational spring and loaded by a compressive force, respectively, an Euler problem is analyzed by solving a boundary value problem of an ordinary differential equation with varying coefficients. Buckling loads through the characteristic equation with the aid of the Bessel functions are exactly given. An alternative way to approximately determine buckling loads through the integral equation method is also presented. By comparing approximate buckling loads with the exact ones, the approximate solution is simple in form and enough accurate for varying power-law gradients. The influences of the gradient index and the rotational spring stiffness on the critical forces are elucidated. The critical force and mode shapes at buckling are presented in graph. The critical force given here may be used as a benchmark to check the accuracy and effectiveness of numerical solutions. The approximate solution provides a feasible approach to calculating the buckling loads and to assessing the loss of stability of columns in engineering.

• Steel and Composite Structures
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• v.28 no.2
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• pp.179-194
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• 2018

Reliable and accurate method of computationally aided design processes of advanced thin walled structures in automotive industries are much essential for the efficient usage of smart materials, that possess higher energy absorption in dynamic compression loading. In this paper, most versatile components i.e., thin walled crash tubes with different geometrical profiles are introduced in view of mitigating the impact of varying cross section in crash behavior and energy absorption characteristics. Apart from the geometrical parameters such as length, diameter and thickness, the non-dimensionalized parameters of average forces which control the plastic bending moment for varying thickness has explored in view of quantifying its impact on the crashworthiness of the structure. The explicit finite element code ABAQUS is utilized to conduct the numerical studies to examine the effect of parametric modifications in crash behavior and energy absorption. Also the simulation results are experimentally validated. It is evident that the circular cross-sectional tubes are preferable as high collision impact shock absorbers due to their ability in withstanding axial and oblique impact loads effectively. Furthermore, the specific energy absorption (SEA), crash force efficiency (CFE), plastic bending moment, peak force responses and its impact for optimally tailoring a design to cater the crashworthiness requirements are investigated. The primary outcome of the study is to provide sufficient information on circular tubes for the use of energy absorbers where impact oblique loading is expected.

• Journal of KSNVE
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• v.2 no.3
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• pp.203-211
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• 1992

The main purpose of this paper is to present both the natural frequencies and the first critical loads of tapered columns. The ordinary differential equation governing the free vibration for tapered columns under compressive axial force is derived. Three kinds of cross sectional shape are considered in the governing equation. The Runge-Kutta method and determinant search method are used to perform the integration of the differential equation and to determine the natural frequencies, respectively. Additionally, the bisection method is used to determine the critical loads. In numerical examples, the effects of compressive axial force on the natural frequencies of tapered columns are investigated varying the end conditions. The first critical loads of tapered columns are determined on the basis of dynamic concepts. The first critical loads of tapered columns are determined on the basis of dynamic concept. The effects of cross sectional shapes are shown and some typical mode shapes are also presented.

• Steel and Composite Structures
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• v.34 no.1
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• pp.75-89
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• 2020

The current paper illustrates the effect of in-plane varying compressive force on critical buckling loads and buckling modes of sandwich composite laminated beam rested on elastic foundation. To generalize a proposed model, unified higher order shear deformation beam theories are exploited through analysis; those satisfy the parabolic variation of shear across the thickness. Therefore, there is no need for shear correction factor. Winkler and Pasternak elastic foundations are presented to consider the effect of any elastic medium surrounding beam structure. The Hamilton's principle is proposed to derive the equilibrium equations of unified sandwich composite laminated beams. Differential quadrature numerical method (DQNM) is used to discretize the differential equilibrium equations in spatial direction. After that, eigenvalue problem is solved to obtain the buckling loads and associated mode shapes. The proposed model is validated with previous published works and good matching is observed. The numerical results are carried out to show effects of axial load functions, lamination thicknesses, orthotropy and elastic foundation constants on the buckling loads and mode shapes of sandwich composite beam. This model is important in designing of aircrafts and ships when non-uniform compressive load and shear loading is dominated.

• Earthquakes and Structures
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• v.7 no.3
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• pp.251-269
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• 2014

To investigate the seismic performance and to obtain quantitative parameters for the requirement of performance-based bridge seismic design approach, 12 reinforced concrete (RC) hollow rectangular bridge column specimens were tested under constant axial load and cyclic bending. Parametric study is carried out on axial load ratio, aspect ratio, longitudinal reinforcement ratio and transverse reinforcement ratio. The damage states of these column specimens were related to engineering limit states to determine the quantitative criteria of performance-based bridge seismic design. The hysteretic behavior of bridge column specimens was simulated based on the fiber model in OpenSees program and the results of the force-displacement hysteretic curves were well agreed with the experimental results. The damage states of residual cracking, cover spalling, and core crushing could be well related to engineering limit states, such as longitudinal tensile strains of reinforcement or compressive strains of concrete, etc. using cumulative probability curves. The ductility coefficient varying from 3.71 to 8.29, and the equivalent viscous damping ratio varying from 0.19 to 0.31 could meet the requirements of seismic design.