• Structural Engineering and Mechanics
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• v.35 no.6
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• pp.677-697
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• 2010

This paper focuses on geometrically non-linear static analysis of a simply supported beam made of hyperelastic material subjected to a non-follower transversal uniformly distributed load. As it is known, the line of action of follower forces is affected by the deformation of the elastic system on which they act and therefore such forces are non-conservative. The material of the beam is assumed as isotropic and hyperelastic. Two types of simply supported beams are considered which have the following boundary conditions: 1) There is a pin at left end and a roller at right end of the beam (pinned-rolled beam). 2) Both ends of the beam are supported by pins (pinned-pinned beam). In this study, finite element model of the beam is constructed by using total Lagrangian finite element model of two dimensional continuum for a twelve-node quadratic element. The considered highly non-linear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. In order to use the solution procedures of Newton-Raphson type, there is need to linearized equilibrium equations, which can be achieved through the linearization of the principle of virtual work in its continuum form. In the study, the effect of the large deflections and rotations on the displacements and the normal stress and the shear stress distributions through the thickness of the beam is investigated in detail. It is known that in the failure analysis, the most important quantities are the principal normal stresses and the maximum shear stress. Therefore these stresses are investigated in detail. The convergence studies are performed for various numbers of finite elements. The effects of the geometric non-linearity and pinned-pinned and pinned-rolled support conditions on the displacements and on the stresses are investigated. By using a twelve-node quadratic element, the free boundary conditions are satisfied and very good stress diagrams are obtained. Also, some of the results of the total Lagrangian finite element model of two dimensional continuum for a twelve-node quadratic element are compared with the results of SAP2000 packet program. Numerical results show that geometrical nonlinearity plays very important role in the static responses of the beam.

• Steel and Composite Structures
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• v.46 no.4
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• pp.539-551
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• 2023

In order to study the fire resistance of castellated composite beams with ortho-hexagonal holes and different beam-end restraints, temperature rise tests with constant load were conducted on full-scale castellated composite beams with ortho-hexagonal holes and hinge or rigid joint constraints to investigate the temperature distribution, displacement changes and failure patterns of castellated composite beams with two different beam-end constraints during the whole course of fire. The results show that (1) During the fire, the axial pressure and horizontal expansion deformation generated in the rigid joint constrained composite beam were larger than those in the hinge joint constrained castellated composite beam, and their maximum horizontal expansion displacements were 30.2 mm and 17.8 mm, respectively. (2) After the fire, the cracks on the slab surface of the castellated composite beam with rigid joint constraint were more complicated than hinge restraint, and the failure more serious; the lower flange and web at the ends of the castellated steal beams with hinge and rigid joint constraint produced serious local buckling, and the angles of the ortho-hexagonal holes at the support cracked; the welds at both ends of the castellated composite beam with rigid joint constraint cracked. (3) Based on the simplified calculation method of solid-web composite beam, considering the effect of holes on the web, this paper calculated the axial force and displacement of the beam-end constrained castellated composite beams under fire. The calculation results agreed well with the test results.

• Journal of Korean Society of Steel Construction
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• v.20 no.3
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• pp.445-454
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• 2008

Based on previous research on steel moment connections, experimental and analytical results showed that the deformation capacity was poor in specimens using RHS columns and with conventional weld access holes and strain concentration at the end of beam is influenced by the efficiency in transmitting the moment in the web of beam through the beam-to-column joint. This paper is focused on the retrofitting of pre-Kobe steel moment frame connections using a stiffened RBS and a welded horizontal stiffener. These retrofitting methods were considered only in beam bottom flange. A parametric study was performed using nonlinear finite element analysis to elucidate and improve the retrofit methods of connections.

• Advances in aircraft and spacecraft science
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• v.2 no.1
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• pp.57-76
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• 2015

We investigated complex damped modes in beams in the presence of a viscoelastic layer sandwiched between two elastic layers. The problem was solved using two approaches, (1) Rayleigh beam theory and analyzed using the Ritz method, and (2) by using 2D plane stress elasticity based finite-element method. The damping in the layers was modeled using the complex modulus. Simply-supported, cantilever, and viscously supported boundary conditions were considered in this study. Simple trigonometric functions were used as admissible functions in the Ritz method. The key idea behind sandwich structure is to increase damping in a beam as affected by the presence of a highly-damped core layer vibrating mainly in shear. Different assumptions are utilized in the literature, to model shear deformation in the core layer. In this manuscript, we used FEM without any kinematic assumptions for the transverse shear in both the core and elastic layers. Moreover, numerical examples were studied, where the base and constraining layers were also damped. The loss factor was calculated by modal strain energy method, and by solving a complex eigenvalue problem. The efficiency of the modal strain energy method was tested for different loss factors in the core layer. Complex mode shapes of the beam were also examined in the study, and a comparison was made between viscoelastically and viscously damped structures. The numerical results were compared with those available in the literature, and the results were found to be satisfactory.

• Steel and Composite Structures
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• v.9 no.3
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• pp.191-208
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• 2009

Observations from experiments and real fire indicate that restrained steel beams have better fire-resistant capability than isolated beams. Due to the effects of restraints, a steel beam in fire condition can undergo very large deflections and the run away damage may be avoided. However disgusting damages may occur in the beam-to-column connections, which is considered to be mainly caused by the enormous axial tensile forces in steel beams resulted from temperature decreasing after fire dies out. Over the past ten years, the behaviour of restrained steel beams subjected to fire during heating has been experimentally and theoretically investigated in detail, and some simplified analytical approaches have been proposed. While the performance of restrained steel beams during cooling has not been so deeply studied. For the safety evaluation and repair of steel structures against fire, more detailed investigation on the behaviour of restrained steel beams subjected to fire during cooling is necessary. When the temperature decreases, the elastic modulus and yield strength of steel recover, and the contraction force in restrained steel beams will be produced. In this paper, an incremental method is proposed for analyzing the behaviour of restrained steel beams subjected to cooling. In each temperature decrement, the development of deformation and internal forces of a restrained beam is divided into four steps, in order to consider the effect of the recovery of the elastic modulus and strength of steel and the contraction force generated by temperature decrease in the beam respectively. At last, the proposed approach is validated by FE method.

• Steel and Composite Structures
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• v.22 no.1
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• pp.45-61
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• 2016

The domestic and foreign scholars conducted many studies on mechanical properties of wave web steel beam and high-strength spiral stirrups confined concrete columns. Based on the previous research work, studies were conducted on the anti-seismic property of the end plate bolt connected wave web steel beam and high-strength spiral stirrups confined concrete column nodes applied with pre-tightening force. Four full-size node test models in two groups were designed for low-cycle repeated loading quasi-static test. Through observation of the stress, distortion, failure process and failure mode of node models, analysis was made on its load-carrying capacity, deformation performance and energy dissipation capacity, and the reliability of the new node was verified. The results showed that: under action of the beam-end stiffener, the plastic hinges on the end of wave web steel beam are displaced outward and played its role of energy dissipation capacity. The study results provided reliable theoretical basis for the engineering application of the new types of nodes.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.11
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• pp.2762-2772
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• 1993

The paper deals with the flutter of a cantilevered beam subjected to a rocket thrust generated by a solid rocket motor. It is saaumed that the rocket thrust is to be a constant follower thrust, and produced by the installation of a solid rocket motor to the tip end of the cantilevered beam. The rocket motor is considered to be a rigid body having finite sizes, but not a mass point as it has been assumed so far. Governing equations are derived through the extended Hamilton's principle, and finite element method is applied to obtain the theoretical prediction for critical follower thrust. The maximum follower thrust is also calculated through the change of shear deformation parameter of the beam in the numerical simulation. The theoretical prediction for flutter or stability is verified by experiment. The experimental results show that critical follower thrust in theory agrees well with the experimental value taking account of the magnitude, rotary inertia of the rocket motor and the distance from the tip end of the beam to the center of gravity of the rocket motor.

• The korean journal of orthodontics
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• v.26 no.3
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• pp.281-290
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• 1996

Determination of force system and prediction of side effects from unbent straight wire engaged in edgewise bracket is clinically very difficult because it is statically indeterminate system. This study is to develop a linear beam theory that explains the force system for straight wire engaged in edgewise bracket regardless of geometry(a/b), material, cross section of wire, and interbracket distance. 1. Formula for force system of bilateral fixed end beam was derived. 2. It is possible to calculate force system of each tooth engaged in continuous straight wire. 3. The possibility and location of permanent deformation can be predicted.

• Journal of Korean Society of Steel Construction
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• v.14 no.5 s.60
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• pp.577-591
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• 2002

This study presented a composite beam element for modeling the inelastic behavior of the steel beam, which has composite slabs in steel moment frames that are subjected to earthquake ground motions. The effects of composite slabs on the seismic behavior of steel moment frames were investigated. The element can be considered as a single-component series hinge type model whose predicted analytical results were consistent with the experimental results. Likewise, the element showed a significantly better performance than the bare steel beam elements. The composite model can also predict more accurately the local deformation demands and overall response of structural systems under earthquake loading compared with the bare steel models. Therefore, composite stabs can significantly affect locally and globally predicted responses of steel moment frames.

• Steel and Composite Structures
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• v.1 no.1
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• pp.145-158
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• 2001

An experimental study was conducted to evaluate the effects of loading sequence and lateral bracing on the behavior of reduced beam section (RBS) steel moment frame connections. Four full-scale moment connections were cyclically tested-two with a standard loading history and the other two with a near-fault loading history. All specimens reached at least 0.03 radian of plastic rotation without brittle fracture of the beam flange groove welds. Two specimens tested with the nearfault loading protocol reached at least 0.05 radian of plastic rotation, and both experienced smaller buckling amplitudes at comparable drift levels. Energy dissipation capacities were insensitive to the types of loading protocol used. Adding a lateral bracing near the RBS region produced a higher plastic rotation; the strength degradation and buckling amplitude were reduced. A non-linear finite element analysis of a one-and-a-half-bay beam-column subassembly was also conducted to study the system restraint effect. The study showed that the axial restraint of the beam could significantly reduce the strength degradation and buckling amplitude at higher deformation levels.