• Structural Engineering and Mechanics
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• v.43 no.2
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• pp.147-161
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• 2012

This paper presents a curvature method for analysis of beam-columns with different materials and arbitrary cross-section shapes and subjected to combined biaxial moments and axial load. Both material and geometric nonlinearities (the p-delta effect in this case) were incorporated. The proposed method considers biaxial curvatures and uniform normal strains of discrete cross-sections of beam-columns as basic unknowns, and seeks for a solution of the column deflection curve that satisfies force equilibrium conditions. A piecewise representation of the beam-column deflection curve is constructed based on the curvatures and angles of rotation of the segmented cross-sections. The resulting bending moments were evaluated based on the deformed column shape and the axial load. The moment curvature relationship and the beam-column deflection calculation are presented in matrix form and the Newton-Raphson method is employed to ensure fast and stable convergence. Comparison with results of analytic solutions and eccentric compression tests of wood beam-columns implies that this method is reliable and effective for beam-columns subjected to eccentric compression load, lateral bracings and complex boundary conditions.

• 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.

• Structural Engineering and Mechanics
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• v.61 no.1
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• pp.117-124
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• 2017

Load testing is one of the important tests to determine if the structural elements can be used at the intended locations for which they have been designed. It is nothing but gradually applying the loads and measuring the deflections and other parameters. It is usually carried out to determine the behaviour of the system under service/ultimate loads. It helps to identify the maximum load that the structural element can withstand without much deflection/deformation. It will also help find out which part of the element causes failure first. The load-deflection behaviour of the road bridge girder has been studied by carrying out the load test after simulating the field conditions to the extent possible. The actual vertical displacement of the beam at mid span due to the imposed load was compared with the theoretical deflection of the beam. Further, the recovery of deflection at mid span was also observed on removal of the test load. Finally, the beam was checked for any cracks to assert if the beam was capable of carrying the intended live loads and that it could be used with confidence.

• Steel and Composite Structures
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• v.12 no.3
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• pp.249-260
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• 2012

In this study, stress and deflection behaviours of T-type welding joint applied to HE200M steel beam and column were investigated in finite element method (FEM) under different distributed loads. In the 3D-FEM modelling, glue option was used to contact between steel materials and weld nuggets. Geometrical model was designed as 3-dimensional solid in ANSYS software program. After that, homogeneous, linear and isotropic properties were used to design to materials of model. Solid-92 having 3-dimensional, 4 faced and 10-noded was selected as element type. In consequence of mesh operation, elements of 13285 and nodes of 28086 were occurred. Load distribution was applied to top surface of steel beam to determine behaviours of stress and deflection. As a result of FEM analysis applied with the loads of 55,000 N, 110,000 N and 220,000 N, maximum values were obtained as 116 N/$mm^2$, 232 N/$mm^2$ and 465 N/$mm^2$ for stress and obtainedas 1,083 mm, 2,166 mm and 4.332 mm for deflection, respectively. When modelling results and classical calculation values were compared, it was obtained difference of 10 % for stress values and 2.5% for deflection values.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.11a
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• pp.471-475
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• 2007

Design equations of coupling plates, which connects floor beam of the upper modular unit and overhead beam of the lower one in order to improve serviceability in vibration, are proposed. End conditions of the coupled beams is semi-rigid and the optimal location of the coupling plates are assumed. Rotational constraints for both ends of the coupling plate modeled with beam elements are released and flexibility method is applied to obtain deflection equations of the coupled beam. Proposed equations are defined using the flexibility of the coupling plate, of which size can be determined inversely. Based on numerical analysis, coefficients of the design equations are calibrated and the revised equations are verified to be useful in the design of the coupled beam.

• Structural Engineering and Mechanics
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• v.80 no.5
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• pp.585-594
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• 2021

Ductility is very important parameter in seismic design of RC members such as beams where it allows RC beams to dissipate the seismic energy. In this field, the curvature ductility has taken a large part of interest compared to the deflection ductility. For this reason, the present paper aims to propose a general formula for predicting the deflection ductility factor of RC beams under mid-span load. Firstly, the moment area theorem is used to develop a model in order to calculate the yield and the ultimate deflections; then this model is validated by using some results extracted from previous researches. Secondly, a general formula of deflection ductility factor is written based on the developed deflection expressions. The new formula is depended on curvature ductility factor, beam length, and plastic hinge length. To facilitate the use of this formula, a parametric study on the curvature ductility factor is conducted in order to write it in simple manner without the need for curvature calculations. Therefore, the deflection ductility factor can be directly calculated based on beam length, plastic hinge length, concrete strength, reinforcement ratios, and yield strength of steel reinforcement. Finally, the new formula of deflection ductility factor is compared with the model previously developed based on the moment area theorem. The results show the good performance of the new formula.

• Journal of Mechanical Science and Technology
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• v.20 no.10
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• pp.1646-1652
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• 2006

A model of mechanical behavior of microcantilever due to intrinsic strain during deposition of MEMS structures is derived. A linear ordinary differential equation is derived for the beam deflection as a function of the thickness of the deposited layer. Closed-form solutions are not possible, but numerical solutions are plotted for various dimensionless ratios of the beam stiffness, the intrinsic strain, and the elastic moduli of the substrate and deposited layer. This model predicts the deflection of the cantilever as a function of the deposited layer thickness and the residual stress distribution during deposition. The usefulness of these equations is that they are indicative of the real time behavior of the structures, i.e. it predicts the deflection of the beam continuously during deposition process.

• Journal of the korean Society of Automotive Engineers
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• v.3 no.1
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• pp.54-60
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• 1981

This paper presents the dynamic behaviour of a simple beam subjected to moving loads and prebending moments. The velocity of the moving loads is assumed constant, and the prebending moment is assumed to be M. The fundamental equation of motion of the beam is derived from the principle of virtual works and solved by using Duhamel's Integral. In this paper we found that the dimensionless deflection at the middle of beam was related with prebending moment(M), velocity(V) and magnitude of the moving load(F) ; that is y/y$_{0}$=1/1-.betha.$^{2}$-.pi.M/Fl The faster the velocity becomes, the deeper the maximum deflection becomes. And the maximum deflection at the middle of beam was occurred after the moving load passed the midpoint of beam.

• Smart Structures and Systems
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• v.19 no.4
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• pp.431-439
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• 2017

This investigation is aimed to develop a model of experimental-computation determination of a support moment of a cantilever beam loaded with concentrated force at its end including the optimal choice of coordinates of deflection data points and parameters of transformation of deflection data in case of insufficient accuracy of the assignment of initial parameters (support settlement, angle of rotation of the bearing section) and cantilever beam length. The influence of distribution and characteristics of sensors on the cantilever beam on the accuracy of determining the support moment which improves in the course of transition from the uniform distribution of sensors to optimal non-uniform distribution is shown. On the basis of the theory of inverse problems the method of transformation reduction at numerical differentiation of deflection functions has been studied. For engineering evaluation formulae of uncertainty estimate to determine a support moment of a cantilever beam at predetermined uncertainty of measurements using sensors have been obtained.

• 한국기계연구소 소보
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• s.18
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• pp.131-136
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• 1988

A small-deflected beam can be easily solved by assuming a linear system. But a large-deflected beam can not be solved by superposition of the displacements, because the system is nonlinear. The solutions for the large-deflection problems can not be obtained directly from elementary beam theory for linearized systems since the basic assumptions are no longer valid. Specifically, elementary theory neglects the square of the first derivative in the beam curvature formula and provides no correction for the shortening of the moment-arm cause by transverse deflection. These two effects must be considered to analyze the large deflection. Through the correction of deflected geometry and internal axial force, the proposed new approach is developed from the linearized beam theory. The solutions from the proposed approach are compared with exact solutions.