Rigid Beam Research Articles

The effect of roof systems on seismic performance of reinforced concrete frame-bent main building of large-scale thermal power plant

The roof systems of turbine hall in large-scale thermal power plant are often simulated by approximate rigid beam model. Wenchuan earthquake again revealed the frequent destruction of these roof systems. In this study, three kinds of general roof systems as space grid, trapezoid steel roof truss and reinforced concrete (RC) mansard roof truss were considered. Also, the numerical model of RC frame-bent main building in large-scale thermal power plant was established. Seismic performance of main building was compared with approximate rigid beam model, and the damage mechanism of roof systems was also investigated. The results indicate that the response calculation of frame part by rigid beam model is feasible, and roof systems give most contribution to the response of bent part. After considering roof systems, overall collaborative performance is enhanced, but bent part is still unable to become a second defence part after shear walls fail. The torsional irregularity of roof systems is very serious, and more attentions should be paid to the bearing shear failure of space grid and components strength failure of RC roof systems. Copyright © 2014 John Wiley & Sons, Ltd.

Research on the Calculation Method for Bending Rigidity of Recycled Concrete Beams

The comparison between the experimental results of bending rigidity of recycled concrete collected from the bending test carried out by domestic and overseas researchers and the calculated results by formulas from available codes is done. The results show that formulations of from available codes are not suitable for recycled concrete beams. Then, based on the factors that influence the bending rigidity of recycled concrete beams, the formulation of bending rigidity for recycled concrete beams is proposed by theory. The experimental results by this the formulation and the test results is very close, the mean value and variation coefficient of the ratio of experimental value and calculated value for recycled concrete beams is respectively 1.01 and 0.16.Keywords: recycled concrete beams;bending rigidity; deflection; formulation

Modeling of the dynamics of two coupled spherical pendula

We study the dynamics of the system of two spherical pendula mounted to the rigid beam which hang from the unmovable frame. Using Langrange’s multipliers the equations of motion have been derived. We identify two synchronous states in which pendula rotate in the same or different directions. The results of numerical simulations have been confirmed in the simple experiment.

A non-linear one-dimensional model of cross-deformable tubular beam

A direct non-linear one-dimensional model of an elastic, thin-walled, planar beam is formulated. The model accounts for changes in shape of the cross-section, in particular the ovalization (or flattening) occurring in tubular beams. The deformation of the cross-section is described in the spirit of the Generalized Beam Theory, as a linear combination of known deformation modes and unknown amplitude functions, said to be distortions. Kinematics calls for introducing distortional and bi-distortional strains, in addition to the usual strain measures of rigid cross-section beams. The balance equations are derived through the Virtual Power Principle, in which distortional and bi-distortional stresses, as well as distortional forces, are defined as conjugate quantities of distortional strain-rates and velocities, respectively. A non-linear, fully coupled, hyperelastic law is assumed. All the distortional quantities and the constitutive law are identified, via energy equalities, from a three-dimensional fiber-model of thin-walled beam where, for simplicity, just a distortion mode is considered. The model is specialized to a Euler–Bernoulli tubular beam, in which only constitutive non-linearities are retained, while kinematics is linearized. The relevant non-linear equations are solved, via a perturbation method, for several static loadings and for large-amplitude free vibrations. The interaction occurring between global bending and cross-section distortion is analyzed.

Effect of Rigidity of Plinth Beam on Soil Interaction of Modeled Building Frame Supported on Pile Groups

This paper presents the effect of rigidity of plinth beam on a model building frame supported by pile groups embedded in cohesionless soil (sand) through the results of static vertical load tests. The effect of rigidity of plinth beam on displacements and rotation at the column base and also shears and bending moments in the building frame were investigated. In the analytical model, soil nonlinearity in the axial direction is characterized by nonlinear vertical springs along the length of the pile (t-z curves) and at the tip of the pile (Q-z curves) while in the lateral direction by the p-y curves. Results revealed that, shear force and bending moment values which were back calculated from the experimental results, showed considerable reduction with the reduction of the rigidity of the plinth beam. The response of the frame from the experimental results is in good agreement with that obtained by the nonlinear finite element analysis.

Medición de frecuencias de resonancia, factor de pérdida y módulo de Young dinámico de varillas empotradas

En este trabajo se estudian teórica y experimentalmente las vibraciones forzadas de varillas rígidas y flexibles empotradas en un extremo. Las experiencias que se analizan, además de ilustrar el fenómeno de resonancia en una estructura diferente del clásico oscilador masa-resorte, permiten medir el módulo de Young del material. En el caso de la varilla flexible es fácil visualizar también el segundo y el tercer modo normal de vibración, lo cual nos permite comparar la forma que adopta la varilla, cuando vibra en sus diferentes modos, con las predicciones teóricas. En particular se pueden observar los "cuasi-nodos" (o nodos con pequeña amplitud) que se deben al flujo de energía a través de los mismos para compensar las pérdidas.

Snow Pressure on a Semiflexible Retaining Structure

AbstractSnow avalanche hazard is one of the most critical aspects in the urbanization of mountainous areas. The risk from these natural phenomena can be reduced if proper countermeasures for reducing the danger or preventing avalanche triggering are taken. For instance, in the avalanche initiation zone, devices able to withstand snowpack gliding and prevent crack propagation can be installed. These can be classified as rigid (snow bridges) or flexible (snow net) structures, depending on the mechanisms involved under snow loading. In recent years, a new kind of structure called a snow umbrella, based on a net panel supported by rigid beams, has been designed and installed in the northwestern Italian Alps. As the real behavior of these structures is far from being simple to understand because of the complex interaction with snowpack movements, an umbrella was instrumented and monitored during the winter season of 2010–2011. The recorded data are used for testing two possible pressure distributions and evalu...

Are Some Top-Heavy Structures More Stable?

AbstractThis technical note investigates the dynamic response and stability of a rocking frame that consists of two identical free-standing slender columns capped with a freely supported rigid beam. Part of the motivation for this study is the emerging seismic design concept of allowing framing systems to uplift and rock along their plane in order to limit bending moments and shear forces— together with the need to stress that the rocking frame is more stable the more heavy is its cap-beam, a finding that may have significant implications in the prefabricated bridge technology. In this technical note, a direct approach is followed after taking dynamic force and moment equilibrium of the components of the rocking frame, and the remarkable results obtained in the past with a variational formulation (by the same authors) is confirmed—that the dynamics response of the rocking frame is identical to the rocking response of a solitary, free-standing column with the same slenderness, yet with larger size, which p...

STRUCTURAL BEHAVIOUR OF FULLY COUPLED SPAR–MOORING SYSTEM UNDER EXTREME WAVE LOADING

Floating spar platform has been proven to be an economical and efficient type of offshore oil and gas exploration structure in deep and ultra-deep seas. Associated nonlinearities, coupled action, damping effect and extreme sea environments may modify its structural responses. In this study, fully coupled spar–mooring system is modelled integrating mooring lines with the cylindrical spar hull. Rigid beam element simulates large cylindrical spar hull and catenary mooring lines are configured by hybrid beam elements. Nonlinear finite element analysis is performed under extreme wave loading at severe deep sea. Morison's equation has been used to calculate the wave forces. Spar responses and mooring line tensions have been evaluated. Though the maximum mooring line tensions are larger at severe sea-state, it becomes regular after one hour of wave loading. The response time histories in surge, heave, pitch and the maximum mooring tension gradually decreases even after attaining steady state. It is because of damping due to heavier and longer mooring lines in coupled spar–mooring system under deep water conditions. The relatively lesser values of response time histories in surge, heave, pitch and the maximum mooring tension under extreme wave loading shows the suitability of a spar platform for deep water harsh and uncertain environmental conditions.

등가 기둥 모델을 이용한 철근콘크리트 전단벽-골조 구조물의 푸쉬오버 해석

RC shear wall sections which have irregular shapes such as T, ㄱ, ㄷ sections are typically used in low-rise buildings in Korea. Pushover analysis of building containing such members costs a lot of computation time and needs professional knowledge since it requires complicated modeling and, sometimes, fails to converge. In this study, a method using an equivalent column element for the shear wall is proposed. The equivalent column element consists of an elastic column, an inelastic rotational spring, and rigid beams. The inelastic properties of the rotational spring represent the nonlinear behavior of the shearwall and are obtained from the section analysis results and moment distribution for the member. The use of an axial force to compensate the difference in the axial deformation between the equivalent column element and the actual shear wall is also proposed. The proposed method is applied for the pushover analysis of a 5- story shear wall-frame building and the results are compared with ones using the fiber elements. The comparison shows that the inelastic behavior at the same drift was comparable. However, the performance points estimated using the pushover curves showed some deviations, which seem to be caused by the differences of estimated yield point and damping ratios.

Influence of Shape and Dimensions of Lamina on Shear and Bending Strength of Vertically Glue Laminated Bamboo Beam

The strength of the bamboo increases from innner surface layer (endodermis) to outer surface layer (exodermis). The strength of bamboo can be utilized optimally by making glue laminated bamboo beams. The curved bamboo lamina as part of the glue laminated beam may be made by peeling off slightly the outer surface layer that contains high strength of fibers. The lamina thickness is made by disposing inner layer of the bamboo. The bamboo used in this work belongs to the species of Bambusa Dendrocalamus asper (local name: bambu Petung). This research aims to improve the shear and flexural strength of the glue laminated bamboo beams by modifying the shape of the cross section of the lamina (curved) rather than ordinary rectangular shape of the lamina.The dimensions of the cross-section of the lamina were of 7/20mm and 9/20mm. The laminas were preserved by immersing them in a hot water having chemical solution namely “Natrium Tetrabonat or CCB4” with a concentration of 10%. Having dry air the laminas were glued using adhesive type PVAC and were staked under 2.5MPa. The cross section dimensions of the beam specimen in shear and bending were of 70/100-900mm and of 70/100-285mm, and of 750mm and 2700mm long respectively. The simply supported glue laminated beams were tested upon two point loads at a distance of 1/3 the length of the span.The results showed that the glue laminated bamboo beams having curved type of laminas are stronger, more rigid, and more ductile compared to rectangular lamina type. Likewise, the glue laminated bamboo beams having 7mm thick of lamina are stronger, stiffer, and ductile compared to the glue laminated beam with laminas of 9mm thick. The average flexural strength of BBR7 (rectangular, 7mm thick of lamina), BBR9 (rectangular, 9mm thick of lamina), BBC7 (curved, 7mm thick of lamina) and BBC9 (curved, 9mm thick of lamina) are respectively (68.80, 9.28, 63.28, 2.00) N/mm2. The flexural rigidity of related beams are respectively (68.36, 71.05, 75.06, 65.17) N/mm, and the ductility are respectively (2.35, 2.16, 1.87, 2.63). The related average shear strength of SBR7, SBR9, SBC7 and SBC9 are respectively (2.72, 2.61, 2.32, 2.64) N/mm2, while the shear rigidity are respectively (2,737.08, 3,029.77, 3,123.87, 2,794.82) N/mm.

Modeling the Boron-Doping Silicon Beam by a Multilayer Model

The boron-doping silicon beam commonly used in microdevices exhibits a nonuniform material property along its thickness or width because of the gradient of boron concentration induced by diffusion process. The constant of rigidity, one of the most important parameters of microbeam, needs to be accurately calculated and designed in the development of high precise sensors and actuators. Current design methods, mainly depending on the analytical solutions derived under the assumption of a uniform material property or some commercial software for a varied property, are not adequate and time consuming to calculate the constant of rigidity of boron-doping silicon beam. A multilayer model is proposed in this paper to replace the continuous solid model by dividing the beam into separated layers glued together. The finite element lamination method is utilized to acquire the equivalent Young modulus and moment of inertia of cross section of multilayer model. The equivalent values are calculated from double-layer structures to multilayer ones based on the small deformation theory and the material mechanics theory. The proposed method provides an effective method to design the stiffness or frequency of microdevice and its results are validated by COMSOL simulation.

An analytical model of a clamped sandwich beam under low-impulse mass impact

An analytical model is developed to examine a low impulsive projectile impact on a fully clamped sandwich beams by considering the coupled responses of the core and the face sheets. Firstly, based on the dynamic properties of foam cores, the sandwich beam is modeled as two rigid perfectly-plastic beams connected by rigid perfectly-plastic springs. Different from the previous sandwich beam model, the transverse compression and bending effects of the foam core are considered in the whole deformation process. Based on this model, different coupling mechanism of sandwich beams are constructed so that an analytical solution considering small deformation is derived. The coupled dynamic responses of sandwich beams with different core strengths are investigated. The results indicate that this model improves the prediction accuracy of the responses of the sandwich beams, and is available for the situation when the sandwich beam undergoes moderate global deformation.

Delaminated thin elastic inclusions inside elastic bodies

We propose a model for a two-dimensional elastic body with a thin elastic inclusion modeled by a beam equation. Moreover, we assume that a delamination of the inclusion may take place resulting in a crack. Nonlinear boundary conditions are imposed at the crack faces to prevent mutual penetration between the faces. Both variational and differential problem formulations are considered, and existence of solutions is established. Furthermore, we study the dependence of the solution on the rigidity of the embedded beam. It is proved that in the limit cases corresponding to infinite and zero rigidity, we obtain a rigid beam inclusion and cracks with nonpenetration conditions, respectively. Anisotropic behavior of the beam is also analyzed.

Wheel Slip Control of Vehicle ABS Using Piezoactuator-Based Valve System

This paper presents a novel piezoactuator-based valve for vehicle ABS. The piezoactuator located in one side of a rigid beam makes a displacement required to control the pressure at a flapper-nozzle of the pneumatic valve. In order to obtain the wide control range of the pressure, a pressure modulator comprised of dual-type cylinder and piston is proposed. The governing equation of the piezovalve system which consists of the proposed piezoactuator-based valve and the pressure modulator is obtained. The longitudinal vehicle dynamics and the wheel slip condition are then formulated. In order to evaluate the performance of the proposed piezovalve system from the viewpoint of the vehicle ABS, a sliding mode controller is designed for wheel slip control. The tracking control performances for the desired wheel slip rate are evaluated and the braking performances in terms of braking distance are then presented on different road conditions (dry asphalt, wet asphalt, and wet jennite). It is clearly shown that the desired wheel slip rate is well achieved and the braking distance and braking time can be significantly reduced by using the proposed piezovalve system associated with the slip rate controller.

A Numerical Study of the Flexural Behavior of Concrete Beams Reinforced with AFRP Bars

In this study, analytical and numerical investigations were extensively conducted to evaluate the flexural behavior of concrete beams reinforced with aramid fiber-reinforced polymer (AFRP) rebars. The AFRP-reinforced concrete beams were analyzed using the separated finite element method containing different elements for concrete and reinforcement. In addition, this study used two different effective moment of inertia expressions to estimate the load-deflection responses and the service-load deflections of the beams. The service-load deflections of the AFRP-reinforced concrete beams obtained from the finite element analysis were in close agreement with those from the effective moment of inertia expressions. The numerical ultimate moments also correlated well with the analytical values of concrete stress-strain models. Numerical analyses, which hardly predict the sudden reduction in the flexural rigidity of FRP-reinforced concrete beams due to the crushing of cover concrete, were shown to provide somewhat conservative deflection estimates.

MONOTONIC TEST AND CALCULATION METHOD OF CONCRETE FRAME WITH PRECAST BEAMS AND CAST-IN-PLACE COLUMNS

A six-story two-bay concrete plane frame with precast beams and cast-in-place columns was tested under monotonic loading, and the behavior of the specimen was evaluated based on failure modes, failure mechanism, displacement ductility, etc. The results indicated that the specimen attained the anticipated failure mechanism, i.e. a mixed mechanism. Plastic hinges firstly appeared in the beam-end, and the plastic hinge did not appear at the column-end until a number of plastic hinges formed at the second and third floor beam-ends during the test. The stirrups in the joint were elastic from beginning to end. The global displacement ductility factor of the specimen was 6.3, which suggested that it was a feasible method to design concrete frames with precast concrete beams and cast-in-place concrete columns in conformity with the current standard anti-seismic design of cast-in-place reinforced concrete structures. The internal force calculation method considering the reduced rigidity of precast beams and the internal force calculation method considering the reduced connection stiffness were investigated by MIDAS, and primary suggestions for calculating internal force of precast concrete frames were presented.

On the determination of natural frequencies of a cantilever beam in free bending vibration: a rigid multibody approach

A new approximate method for the determination of natural frequencies of a cantilever beam in free bending vibration by a rigid multibody system is proposed. Uniform Euler-Bernoulli cantilever beams with and without a lumped mass at the tips are considered. The modelling method consists of two steps. In the first step, the cantilever beam is replaced by lumped masses interconnected by massless flexible beams. In the second step, the massless flexible beams are replaced by massless rigid beams connected through revolute and prismatic joints with corresponding springs in them. Elastic properties of the massless flexible beams are modelled by the springs introduced. The method proposed is compared with similar ones in the literature.

Incorporating Residual Strains in the Flexural Rigidity of RC Members with Varying Degrees of Prestress and Cracking

The deformation of reinforced concrete columns and beams is controlled by the variation of the flexural rigidity (EI) both along the member and with applied loads and time. Currently, the moment-curvature (M/χ) approach is used to quantify EI. Prior to cracking, the M/χ approach provides a pure mechanics based solution for EI; that is, the only components of the model that have to be determined empirically are the material stress-strain relationships. However after cracking, the M/χ approach has to be semi-empirical, that is EI has to be determined empirically because the M/χ approach cannot simulate the mechanics of tension-stiffening. An alternative approach for quantifying EI using a moment-rotation (M/θ) approach is described in this paper. It is shown that the M/θ approach gives exactly the same results as the M/χ approach prior to cracking but after cracking has an advantage over the M/χ approach in that it can quantify the mechanics of tension-stiffening, that is allow for bond slip and its effect on crack spacing and crack widths. This paper deals with the mechanics of incorporating creep, shrinkage, prestress, relaxation and thermal gradients (broadly referred to as residual strains) on the flexural rigidity of RC beams and columns at all levels of loading prior to concrete softening.

Cable Force Optimization Method in Two Stages for Spatial Cables

To get the ideal cable forces of the arch bridge with spatial oblique cables,Rigid Support Continuous Beam Method and Rigid Suspender Method are discussed.The results show that the former is unsuitable for the spatial structure with smaller horizontal stiffness,and the latter does not consider the elastic deformations of the cables.An improved cable force optimization method is provided,which takes Rigid Suspender Method as the initial stage to obtain initial cable forces and takes Influence Matrix Method as the subsequent stage for cable force increments.The method by test is proved to be effective to spatial structure and nonlinear structure with spatial cables.