• Structural Engineering and Mechanics
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• v.24 no.6
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• pp.647-664
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• 2006

In this study, an improved finite element formulation with a scheme of solution for the large deflection analysis of inextensible prismatic and nonprismatic slender beams is developed. For this purpose, a three-noded Lagrangian beam-element with two dependent degrees of freedom per node (i.e., the vertical displacement, y, and the actual slope, $dy/ds=sin{\theta}$, where s is the curved coordinate along the deflected beam) is used to derive the element stiffness matrix. The element stiffness matrix in the global xy-coordinate system is achieved by means of coordinate transformation of a highly nonlinear ($6{\times}6$) element matrix in the local sy-coordinate. Because of bending with large curvature, highly nonlinear expressions are developed within the global stiffness matrix. To achieve the solution after specifying the proper loading and boundary conditions, an iterative quasi-linearization technique with successive corrections are employed considering these nonlinear expressions to remain constant during all iterations of the solution. In order to verify the validity and the accuracy of this study, the vertical and the horizontal displacements of prismatic and nonprismatic beams subjected to various cases of loading and boundary conditions are evaluated and compared with analytic solutions and numerical results by available references and the results by ADINA, and excellent agreements were achieved. The main advantage of the present technique is that the solution is directly obtained, i.e., non-incremental approach, using few iterations (3 to 6 iterations) and without the need to split the stiffness matrix into elastic and geometric matrices.

• Structural Engineering and Mechanics
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• v.31 no.2
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• pp.163-180
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• 2009

In the design of tall reinforced concrete (R/C) buildings, the serviceability stiffness criteria in terms of maximum lateral displacement and inter-story drift must be satisfied to prevent large second-order P-delta effects. To accurately assess the lateral deflection and stiffness of tall R/C structures, cracked members in these structures need to be identified and their effective member flexural stiffness determined. In addition, the implementation of the geometric nonlinearity in the analysis can be significant for an accurate prediction of lateral deflection of the structure, particularly in the case of tall R/C building under lateral loading. It can therefore be important to consider the cracking effect together with the geometric nonlinearity in the analysis in order to obtain more accurate results. In the present study, a computer program based on the iterative procedure has been developed for the three dimensional analysis of reinforced concrete frames with cracked beam and column elements. Probability-based effective stiffness model is used for the effective flexural stiffness of a cracked member. In the analysis, the geometric nonlinearity due to the interaction of axial force and bending moment and the displacements of joints are also taken into account. The analytical procedure has been demonstrated through the application of R/C frame examples in which its accuracy and efficiency in comparison with experimental and other analytical results are verified. The effectiveness of the analytical procedure is also illustrated through a practical four story R/C frame example. The iterative procedure provides equally good and consistent prediction of lateral deflection and effective flexural member stiffness. The proposed analytical procedure is efficient from the viewpoints of computational effort and convergence rate.

• Journal of Korean Tunnelling and Underground Space Association
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• v.4 no.1
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• pp.79-90
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• 2002

The structural analysis such as rigid frame analysis has been used for the design of cut and cover tunnel due to its simplicity and convenience. This analysis, however, could not account for the geometrical factors such as interface elements, slope of excavation plane, distance between lining and excavation plane, etc. To develop the analysis technique and design technology for the cut and cover tunnel, in this study, the numerical analyses considering not only geometrical but geotechnical factors are conducted. Especially, the effects on the mechanical behaviors of cut and cover tunnel due to the slope of excavation plane and the distance between lining and excavation plane are mainly focused in this study.

• Bulletin of the Society of Naval Architects of Korea
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• v.17 no.1
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• pp.25-29
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• 1980

For the preliminary estimation of the vertical hull natural frequency, the Schlick's or Schlick-type formulae have been traditional ones and are still in common use today. Some investigators have made their efforts, based on statistical data of ships' system parameters, to extend the applicability of Schlick-type formulae to higher modes, or to utilize the Rayleigh method. For instance, the work done by Dinsenbacher et al.[5] belongs to the former and that of Nagamoto et al.[6] to the latter. In a part of his previous paper[7], the author, investigating the case of a cargo ship of medium size, suggested that provided statistically simplified curves such as trapezoid of system parameter distributions are available in hands, direct utlization of an ordinary computer program can be also an another convenient method by which we can obtain both natural frequencies and normal mode shapes. In this paper, to confirm the feasibility of the above suggestion, four high speed boats are investigated. The system parameters of them are originally given in [5]. The computer program used here is one confiled based on a calculation method derived from Myklestal-Prohl modeling of hull, transfer matrix formulation and an extended Gumbel's initial value method for solving frequency equation. The results of the investigation show that the direct calculation based on statistically oriented and reasonably assumed trapezoidal mean curves of system parameter distributions can give us natural frequencies within about 5% deviation up to several-noded modes and normal mode shapes serviceable at least up to 4- or 5-noded modes in comparision with those based on actual distributions of system parameters. For this simplified method the actual data required for input are only of ship length, displacement, total added mass, bending and shear rigidity at amidship. They are available at the early stage of design. By this method we can also easily trace variations of vibration characteristics in the course of ship design cycles.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.04a
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• pp.123-130
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• 2002

A general formulation for shape design sensitivity analysis over three dimensional beam structure is developed based on a variational formulation of the beam in linear elasticity. Sensitivity formula is derived based on variational equations in cartesian coordinates using the material derivative concept and adjoint variable method for the displacement and Von-Mises stress functionals. Shape variation is considered for the beam shape in general 3-dimensional direction as well as for the orientation angle of the beam cross section. In the sensitivity expression, the end points evaluation at each beam segment is added to the integral formula, which are summed over the entire structure. The sensitivity formula can be evaluated with generality and ease even by employing piecewise linear design velocity field despite the bending model is fourth order differential equation. For the numerical implementation, commercial software ANSYS is used as analysis tool for the primal and adjoint analysis. Once the design variable set is defined using ANSYS language, shape and orientation variation vector at each node is generated by making finite difference to the shape with respect to each design parameter, and is used for the computation of sensitivity formula. Several numerical examples are taken to show the advantage of the method, in which the accuracy of the sensitivity is evaluated. The results are found excellent even by employing a simple linear function for the design velocity evaluation. Shape optimization is carried out for the geometric design of an archgrid and tilted bridge, which is to minimize maximum stress over the structure while maintaining constant weight. In conclusion, the proposed formulation is a useful and easy tool in finding optimum shape in a variety of the spatial frame structures.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.23 no.1
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• pp.95-110
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• 2010

A numerical model to simulate bond-slip behavior of composite beam bridges is introduced in this paper. Assuming a linear bond stress-slip relation along the interface between the slab and girder, the slip behavior is implemented into a finite element formulation. Adopting the introduced model, the slip behavior can be taken account even in a beam element which is composed of both end nodes only. Governing equation of the slip behavior, based on the linear partial interaction theory, can be determined from the force equilibrium and a constant curvature distribution across the section of a composite beam. Since the governing equation for the slip behavior requires the moment values at both end nodes, the piecewise linear distribution of the constant bending moment in an element is assumed. Analysis results by the model are compared with numerical results and experimental values, and load-displacement relations of composite beams were then evaluated to verify the validity of the proposed model.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.21 no.1
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• pp.43-50
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• 2008

The analysis and results of flexural behavior for steel composite beam with built-up cross-section considering bolt deformation are presented in this paper. The bolt deformation and the restrict effect due to bolt-connection and friction are considered to investigate the flexural behavior of steel composite beam. Nonlinear spring element in ABAQUS is used to consider bolt deformation, also the results are compared with those in case bolt deformations are ignored. The displacement, bending stresses and shear stresses are calculated by F.E. model, and these results are compared with the analytical value of no interaction beam, partial interaction beam and full interaction beam. As a result of analysis, the behavior of composite beam is more dependant on the composite rate than the friction of the steel. When the composite rate is more than 50%, the behavior of composite beam considering the effects of bolt deformation is similar to that of fully composite beam.

• Structural Engineering and Mechanics
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• v.12 no.6
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• pp.657-668
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• 2001

Fiber reinforced cementitious composites are nowadays widely applied in civil engineering. The postcracking performance of this material depends on the interaction between a steel fiber, which is obliquely across a crack, and its surrounding matrix. While the partly debonded steel fiber is subjected to pulling out from the matrix and simultaneously subjected to transverse force, it may be modelled as a Bernoulli-Euler beam partly supported on an elastic foundation with non-linearly varying modulus. The fiber bridging the crack may be cut into two parts to simplify the problem (Leung and Li 1992). To obtain the transverse displacement at the cut end of the fiber (Fig. 1), it is convenient to directly solve the corresponding differential equation. At the first glance, it is a classical beam on foundation problem. However, the differential equation is not analytically solvable due to the non-linear distribution of the foundation stiffness. Moreover, since the second order deformation effect is included, the boundary conditions become complex and hence conventional numerical tools such as the spline or difference methods may not be sufficient. In this study, moment equilibrium is the basis for formulation of the fundamental differential equation for the beam (Timoshenko 1956). For the cantilever part of the beam, direct integration is performed. For the non-linearly supported part, a transformation is carried out to reduce the higher order differential equation into one order simultaneous equations. The Runge-Kutta technique is employed for the solution within the boundary domain. Finally, multi-dimensional optimization approaches are carefully tested and applied to find the boundary values that are of interest. The numerical solution procedure is demonstrated to be stable and convergent.

• Journal of the Korean Geotechnical Society
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• v.33 no.7
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• pp.17-28
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• 2017

This paper presents the investigation of dynamic behavior of a single pile in dry sand based on 1g shaking table tests. The natural frequency of soil-pile system was measured, and then a range of loading frequency was determined based on the natural frequency. Additionally, the studies were performed by controlling loading accelerations, pile head mass and connectivity conditions between pile and cap. Based on the results obtained, relatively larger pile head displacement and bending moment occur when the loading frequency is larger than the natural frequency of soil-pile system. However, the slope of the p-y curve is smaller in the similar loading frequency. Also, it was found that inertia force like input acceleration and pile head mass, and relation of the natural frequency of soil-pile system and input frequency have a great influence on the slope of dynamic p-y curve, while pile head conditions don't.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.4
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• pp.1263-1274
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• 1996

In this paper, as elastic-plastic fracture toughness test under mixed mode loading was proposed using a single edge-cracked specimen subjected to bending moment(M), shearing force(F), and twisting moment(T). The J-integral of a crack in the specimen is expressed in the form J=$J_I$+ $J_II$$J_III$, where $J_I$, $J_II$ and $J_III$ are the components of mode I, mode II and mode III deformation, respectively. $J_I$, $J_II$ and $J_III$ can be estimated from M-$\theta$ ($\theta$;crack opening angle), F-U(U; crack shear displacement) and T-$\alpha$ ($\alpha$;crack twisting angle). In order to obtain the the M<-TEX>$\theta$, F-U and T-$\alpha$ diagram inreal time, a new deformaiton gage for mixed mode loading was proposed using the optical position sensing device(PSD). The elastic-plastic fracture toughness test was carried out with an aluminum alloy. The loading apparatus was designed and manufactured for this experiment. For the loading condition of the crack initatio in the mixed mode, the MMT -3(mode I+ mode II+ mode III) has the lowest values out of the all specimens. This implies that MMT-3 is possible of the crackinitation at lower load, if the specimen acts on together with the torque under the same loading condition. An elastic-plastic fracture toughness test using the PSD brings a successful experimentation in measuring the crack deformation(mode I+ mode II+ mode III).