• Structural Engineering and Mechanics
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• v.53 no.4
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• pp.781-790
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• 2015

We apply higher-order beam theory to analyze the deflections and stresses of a cantilevered single leaf flexure in bending. Our equations include shear deformation and the warping effect in bending. The results are compared with Euler-Bernoulli and Timoshenko beam theory, and are verified by finite element analysis (FEA). The results show that the higher-order beam theory is in a good agreement with the FEA results, with errors of less than 10%. These results indicate that the analysis of the deflections and stresses of a single leaf flexure should consider the shear and warping effects in bending to ensure high precision mechanism design.

• Journal of Korean Society of Steel Construction
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• v.18 no.3
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• pp.349-359
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• 2006

This paper presents a new block stiffness matrix for the analysis an orthogonal Cartesian coordinate system. The displacement fields are defined using the first order shear deformable beam theory. The longitudinal displacement can be expressed as the sum of the projected plane deformation of the cross-section due to Timoshenko's beam theory and axial warping deformation due to modified Vlasov's thin-waled beam theory. The derived element takes into account flexural shear deformation and torsional warping deformation. Three different types of beam elements, namely, the two-noded, three-noded, and four-noded beam elements, are developed. The quadratic and cubic elements are found to be very efficient for the flexural analysis of laminated composite beams. The versatility and accuracy of the new element are demonstrated by comparing the numerical results available in the literature.

• 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.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.20 no.6
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• pp.583-592
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• 2010

Equations of motion of thin-walled composite H-type cross-section beams exposed to concentrated harmonic and non-harmonic time-dependent external excitations, incorporating a number of nonclassical effects of transverse shear, primary and secondary warping, and anisotropy of constituent materials are derived. The forced vibration response characteristics of a composite H-type cross-section beam exhibiting the circumferentially asymmetric stiffness(CAS) configuration are exploited in connection with the structural bending-torsion coupling resulting from directional properties of fiber reinforced composite materials.

• The Bulletin of The Korean Astronomical Society
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• v.39 no.2
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• pp.74.1-74.1
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• 2014

We study a wraping instability of a geometrically thin, non-self-gravitating disk surrounding binary supermassive black holes on a circular orbit. Such a circumbinay disk is subject to not only tidal torques due Line 8 to the binary gravitational potential but also radiative rorques due to radiation emitted from each accretion disk. We find tat a circumbinary disk initially aligned with the binary orbital plane is unstable to radiation-driven warping beyond the marginally stable warping radius, which is sensitive to both the ratio of vertical to horizontal shear viscosities and the mass-to-energy conversion efficiency. As expected, the tidal torques give no contribution to the growth of warping modes but tend to align the circumbinary disk with the orbital plane. Since the tidal torques can suppress the warping modes in the inner part of circumbinary disk, the circumbinaary disk starts to be warped at the radii larger than the marginally stable warping radius. If the warping radius is of the order of 0.1 pc, a resultant semi-major axis is estimated to be of the order of 10-2 pc to 10-4 pc for 107 Msun black hole. We also discuss the posibility that the central objects of observed warped maser disks in active galactic nuclei are binary supermassive black holes with a triple disk: two accretion disks around the individual black holes and one circumbinary disk surrounding them.

• Journal of Korean Society of Steel Construction
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• v.18 no.2
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• pp.203-211
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• 2006

This paper presents a new, effective torsional constant for thin-waled open beams under concentrated and uniformly distributed torques. The proposed constant can be used directly, instead of the St. Venant torsional constant, for any generic comemrcial finite-element program, without modifying the algorithm. The derived torsional constant accounts for both the pure torsion and the warping torsion, and is equal to the St. Venant torsion constant times a correction factor. It is also shown, in the case of the St. Venant torsion, that the derived constant is identical to the torsional constant. The derived effective torsional constant is different from the one given by Elhelbawey et al. The pure torsional shear stress, the warping shear stress, and the warping normal stress were also determine d, using the maximum twisting angle. The accuracy of the proposed torsional constant was validated by comparing the numerical results with the closed-form solutions or other numerical results available in the literature.

• Composites Research
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• v.30 no.6
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• pp.343-349
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• 2017

A multifield variational formulation is developed for the finite element (FE) cross-sectional analysis of composite beams. The cross-sectional warping displacements and sectional stresses are considered to be the primary variables through the application of Reissner's partially mixed principle. The warping displacements are modeled using generic FE shape functions with nonlinear distribution over the beam section. A generalized Timoshenko level stiffness matrix is derived which incorporates the effects of elastic couplings, transverse shear, and Poisson's deformations. The accuracy of the present analysis is validated for the stiffness constants and elastostatic responses of composite box beams which correlate well with the experimental data and other state-of-the-art approaches.

• Journal of Mechanical Science and Technology
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• v.19 no.2
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• pp.589-604
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• 2005

To overcome the drawback of currently available curved beam theories having non-symmetric thin-walled cross sections, a curved beam theory based on centroid-shear center formulation is presented for the spatially coupled free vibration and elastic analysis. For this, the displacement field is expressed by introducing displacement parameters defined at the centroid and shear center axes, respectively. Next the elastic strain and kinetic energies considering the thickness-curvature effect and the rotary inertia of curved beam are rigorously derived by degenerating the energies of the elastic continuum to those of curved beam. And then the equilibrium equations and the boundary conditions are consistently derived for curved beams having non-symmetric thin-walled cross section. It is emphasized that for curved beams with L- or T-shaped sections, this thin-walled curved beam theory can be easily reduced to the solid beam theory by simply putting the sectional properties associated with warping to zero. In order to illustrate the validity and the accuracy of this study, FE solutions using the Hermitian curved beam elements are presented and compared with the results by previous research and ABAQUS's shell elements.

• Structural Engineering and Mechanics
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• v.68 no.1
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• pp.67-80
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• 2018

Recently, U-section decks have been more and more used in metro and light rail bridges as an innovative concept in bridge deck design and a successful alternative to conventional box girders because of their potential advantages. U-section may be viewed as a single vent box girder eliminating the top slab connecting the webs, with the moving vehicles travelling on the lower deck. U-section bridges thus solve many problems like limited vertical clearance underneath the bridge lowest point, besides providing built-in noise barriers. Beam theory in mechanics assumes that plane section remains plane after bending, but it was found that shearing forces produce shear deformations and the plane section does not remain plane. This phenomenon leads to distortion of the cross section. For a box or a U section, this distortion makes the central part of the slab lagging behind those parts closer to the webs and this is known as shear lag effect. A sample real-world double-track U-section metro bridge is modelled in this paper using a commercial finite element analysis program and is analysed under various loading conditions and for different geometric variations. The three-dimensional finite element analysis is used to demonstrate variations in the transverse bending moments in the deck as well as variations in the longitudinal normal stresses induced in the cross section along the U-girder's span thus capturing warping and shear lag effects which are then compared to the stresses calculated using conventional beam theory. This comparison is performed not only to locate the distortion, warping and shear lag effects typically induced in U-section bridges but also to assess the main parameters influencing them the most.

• Ocean Systems Engineering
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• v.1 no.1
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• pp.73-93
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• 2011

Large deck openings of ultra large container ships reduce their torsional stiffness considerably and hydroelastic analysis for reliable structural design becomes an imperative. In the early design stage the beam model coupled with 3D hydrodynamic model is a rational choice. The modal superposition method is ordinary used for solving this complex problem. The advanced thin-walled girder theory, with shear influence on both bending and torsion, is applied for calculation of dry natural modes. It is shown that relatively short engine room structure of large container ships behaves as the open hold structure with increased torsional stiffness due to deck effect. Warping discontinuity at the joint of the closed and open segments is compensated by induced distortion. The effective torsional stiffness parameters based on an energy balance approach are determined. Estimation of distortion of transverse bulkheads, as a result of torsion and warping, is given. The procedure is illustrated in the case of a ship-like pontoon and checked by 3D FEM analysis. The obtained results encourage incorporation of the modified beam model of the short engine room structure in general beam model of ship hull for the need of hydroelastic analysis, where only the first few natural modes are of interest.