• Structural Engineering and Mechanics
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• v.4 no.1
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• pp.49-59
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• 1996

This paper considers large deflection problem of a simply supported beam with variable are length subjected to a point load. The beam has one of its ends hinged and at a fixed distance from this end propped by a frictionless support over which the beam can slide freely. This highly nonlinear flexural problem is solved by elliptic-integral method and shooting-optimization technique, thereby providing independent checks on the new solutions. Because the beam can slide freely over the frictionless support, there is a maximum or critical load which the beam can carry and it is dependent on the position of the load. Interestingly, two possible equilibrium configurations can be obtained for a given load magnitude which is less than the critical value. The maximum arc-length was found to be equal to about 2.19 times the fixed distance between the supports and this value is independent of the load position.

• Computational Structural Engineering
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• v.10 no.4
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• pp.177-184
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• 1997

In this paper, numerical methods are developed for solving the elastica of simple beams with variable-arc-length subjected to a point loading. The beam model is based on Bernoulli-Euler beam theory. The Runge-Kutta and Regula-Falsi methods, respectively, are used to solve the governing differential equations and to compute the beam's rotation at the left end of the beams. Extensive numerical results of the elastica responses, including deflected shapes, rotations of cross-section and bending moments, are presented in non-dimensional forms. The possible maximum values of the end rotation, deflection and bending moment are determined by analyzing the numerical data obtained in this study.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.2
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• pp.129-138
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• 2012

This paper deals with geometrical non-linear analyses of the tapered variable-arc-length beam, subjected to the combined load with an end moment and a point load. The beam is supported by a hinged end and a frictionless sliding support so that the axial length of the deformed beam can be increased by its load. Cross sections of the beam whose flexural rigidities are functionally varied with the axial coordinate. The simultaneous differential equations governing the elastica of such beam are derived on the basis of the Bernoulli-Euler beam theory. These differential equations are numerically solved by the iteration technique for obtaining the elastica of the deformed beam. For validating theories developed herein, laboratory scaled experiments are conducted.

• Structural Engineering and Mechanics
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• v.19 no.4
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• pp.413-423
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• 2005

This paper presents the solution of large static deflection due to uniformly distributed self weight and the critical or maximum applied uniform loading that a simply supported beam with variable-arc-length can resist. Two analytical approaches are presented and validated experimentally. The first approach is a finite-element discretization of the span length based on the variational formulation, which gives the solution of large static sag deflections for the stable equilibrium case. The second approach is the shooting method based on an elastica theory formulation. This method gives the results of the stable and unstable equilibrium configurations, and the critical uniform loading. Experimental studies were conducted to complement the analytical results for the stable equilibrium case. The measured large static configurations are found to be in good agreement with the two analytical approaches, and the critical uniform self weight obtained experimentally also shows good correlation with the shooting method.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.04a
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• pp.146-153
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• 2001

In this paper, the governing differential equations for the non-linear behavior of shear deformable variable-arc-length beams subjected to an end moment are derived. The beam model is based on the Bernoulli-Euler beam theory. The Runge-Kutta and Regula-Falsi methods, respectively, are used to integrate the governing differential equations and to compute the beam's rotation at the left end of the beams. Numerical results are compared with existing closed-form and numerical solutions by other methods for cases in which they are available. The characteristic values of deflection curves for various load parameters are calculated and discussed.

• Structural Engineering and Mechanics
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• v.5 no.5
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• pp.529-539
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• 1997

This paper deals with the bending problem of a variable-are-length elastica under moment gradient. The variable are-length arises from the fact that one end of the elastica is hinged while the other end portion is allowed to slide on a frictionless support that is fixed at a given horizontal distance from the hinged end. Based on the elastica theory, exact closed-form solution in the form of elliptic integrals are derived. The bending results show that there exists a maximum or a critical moment for given moment gradient parameters; whereby if the applied moment is less than this critical value, two equilibrium configurations are possible. One of them is stable while the other is unstable because a small disturbance will lead to beam motion.

• Journal of Welding and Joining
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• v.23 no.1
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• pp.69-76
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• 2005

Recently, application of arc welding to galvanized carbon steel sheet is on the increasing Ould in the fields of automobile and construction industries. In arc welding process, zinc is evaporated in weld pool, even under the appropriate welding condition and produce blowhole and/or pit. Zinc gas cause instability of arc and increase spatter and fume. This research is purposed to minimize the heat-input and the formation of porosities in the welded joint of the galvanized carbon steel sheet using variable polarity AC wave pulse MIG welding system. An appropriate welding condition which showed low spatter and good bead appearance was acquired by applying the AC pulse MIG welding machine to DC duplicated MIG welding with the solid wire. When oxygen gas was added to shield gas of MIG welding for galvanized steel sheet, arc length was increased and arc stability was improved. In the AC duplicated welding, the loss of galvanized layer was decreased as the amount of heat-input was decreased when the EN ratio was increased under the condition that average welding current was evenly set.