• Structural Engineering and Mechanics
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• v.54 no.3
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• pp.433-451
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• 2015

This paper focuses on large deflection static behavior of edge cracked simple supported beams subjected to a non-follower transversal point load at the midpoint of the beam by using the total Lagrangian Timoshenko beam element approximation. The cross section of the beam is circular. The cracked beam is modeled as an assembly of two sub-beams connected through a massless elastic rotational spring. It is known that large deflection problems are geometrically nonlinear problems. The considered highly nonlinear problem is solved considering full geometric non-linearity by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. There is no restriction on the magnitudes of deflections and rotations in contradistinction to von-Karman strain displacement relations of the beam. The beams considered in numerical examples are made of Aluminum. In the study, the effects of the location of crack and the depth of the crack on the non-linear static response of the beam are investigated in detail. The relationships between deflections, end rotational angles, end constraint forces, deflection configuration, Cauchy stresses of the edge-cracked beams and load rising are illustrated in detail in nonlinear case. Also, the difference between the geometrically linear and nonlinear analysis of edge-cracked beam is investigated in detail.

• Journal of KSNVE
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• v.9 no.6
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• pp.1193-1199
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• 1999

This paper deals with the free vibrations of circular curved beams with thin-walled cross-section. The differential equation for the coupled flexural-torsional vibrations of such beams with warping is solved numerically to obtain natural frequencies and mode shapes. The Runge-Kutta and determinant search methods, respectively, are used to solve the governing differential equation and to compute the eigenvalues. The lowest three natural frequencies and corresponding mode shapes are calculated for the thin-walled horizontally curved beams with hinged-hinged, hinged-clamped, and clamped-clamped end constraints. A wide range of opening angle of beam, warping parameter, and two different values of slenderness ratios are considered. Numerical results are compared with existing exact and numerical solutions by other methods.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2009.05a
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• pp.199-202
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• 2009

In roll forming process, a sheet metal is continuously progressively formed into a product with required cross-section and longitudinal shape, such as a circular tube with required diameter, wall-thickness and straightness, by passing through a series of forming rolls in arranged in tandem. Tn this process, each pair of forming rolls installed in a forming machine play a particular role in making up the required cross-section and longitudinal shape of the product. In recent years, that process is often applied to the bumper rail in the automotive industries. In this study, a optimal Front Bumper Beam manufacturing technology, model deign and proper roll-pass sequences can be suggested by forming number of roll-pass and bending angle. And also effects of the process parameters on the final shape formed by roll forming defects were evaluated.

• Journal of Korean Society of Steel Construction
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• v.10 no.3 s.36
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• pp.509-523
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• 1998

A consistent finite element formulation and analytic solutions are presented for stability of thin-walled circular arch. The total potential energy is derived by applying the principle of linearized virtual work and including second order terms of finite semitangential rotations. As a result, the energy functional corresponding to the semitangential moment is newly derived. Analytic solutions for the out-of-plane buckling of symmetric thin-walled curved beam subjected to pure bending or uniform compression with simply supported boundary conditions are obtained. For finite element analysis, the cubic Hermitian polynomials are utilized as shape functions and $16{\times}16$ stiffness matrix for curved beam elements and $14{\times}14$ stiffness matrix for straight beam elements are evaluated, respectively. In order to illustrate the accuracy of this study, analytical and numerical results for lateral buckling problems of circular arch are presented and compared with available analytical solutions.

• Structural Engineering and Mechanics
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• v.5 no.3
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• pp.257-268
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• 1997

The elastic deflections and Euler buckling loads are investigated for a class of tapered and initially curved cantilevered beams subjected to loading at the tip. The beam's width increases linearly and its depth decreases linearly with the distance from the fixed end to the tip. Unloaded, the beam forms a circular are perpendicular to the axis of bending. The beam's deflection responses, obtained by solving the differential equations in closed form, are presented in terms of four nondimensional system parameters: taper ratio ${\kappa}$, initial shape ratio ${\Delta}_0$, end load ratio f, and load angle ${\theta}$. Laboratory measurements of the Euler buckling loads for scale models of tapered initially straight, corrugated beams compared favorably with those computed from the present analysis. The results are applicable to future designs of the end structures of highway guardrails, which can be designed to give the appropriate balance between the capacity to deflect a nearly head-on vehicle back to its right-of-way and the capacity to buckle sufficiently that penetration of the vehicle may be averted.

• Journal of the Earthquake Engineering Society of Korea
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• v.11 no.1 s.53
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• pp.37-43
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• 2007

Experiments for circular unreinforced concrete beams confined by carbon fiber tubes (CFT) made of carbon fiber sheets were performed. Selected test parameter was thickness of carbon fiber tube: 1.5mm (3 layers), 2.0mm (4 layers), 2.5mm (5 layers), and 3.0mm (6 layers). Based on the test results, an equation for estimating moment capacity of the circular beams confined by carbon fiber tubes was proposed. Comparison results showed good agreement up to 2.5mm (5 sheets) of the CFT thickness.

• Journal of Korean Society of Steel Construction
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• v.22 no.6
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• pp.609-616
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• 2010

The objective of this study is to investigate the structural character of the buckling strength of 600MPa-class high-strength steel compression members. The buckling strength of circular hollow-section columns is evaluated by a numerical analysis of the stress-strain curves of the tension test results. The numerical analysis was based on the beam-column theory and the tangent modulus theory. It was considered possible to enlarge the nominal yield strength of the 600MPa-class steel.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1996.10a
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• pp.3-10
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• 1996

Numerical methods are developed for solving the buckling loads and the elastica of clamped- free columns of circular cross-section with constant volume. The column model is based rut the Timoshenko beam theory. The Runge-Kutta and Regula-Falsi methods, respectively, are used to solve the governing differential equations and to compute the eigenvalues. Extensive numerical results, including buckling loads, elastica of buckled shapes and effects of shear de-formation, are presented in non-dimensional form for elastic columns whose radius of circular cross-section varies both linearly and parabolically with column length.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2001.10a
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• pp.163-169
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• 2001

The solution of two-dimensional deflection of circular wavy reinforcing fiber elastics was obtained for one end clamped boundary under concentrated load condition. The fiber was regarded as a linear elastic material. Wavy shape was described as a combination of half-circular arc smoothly connected each other with constant curvature of all the same magnitude and alternative sign. Also load direction was taken into account. As a result, the solution was expressed in terms of a series of elliptic integrals. These elliptic integrals had two different transformed parameters involved with load value and initial radius of curvature. While we found the exact solutions and expressed them in terms of elliptic integrals, the recursive ignition formulae about the displacement and arc length at each segment of circular section were obtained. Algorithm of determining unknown parameters was established and the profile curve of deflected beam was shown in comparison with initial shape.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.10a
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• pp.341-348
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• 2000

The differential equations governing the free vibrations of stepped horizontally circular curved beams with circular cross-section are derived and solved numerically. In numerical method, the Runge-Kutta and Determinant Search methods are used for computing the natural frequencies and mode shapes. Frequencies and mode shapes are reported as the functions of non-dimensional system parameters. The numerical method developed herein for computing frequencies and mode shapes are efficient and reliable.