Simply-supported Beam Research Articles

A state of the art review on transverse web opening for reinforced concrete beams with and without strengthening method

To erect modern constructions needs many ducts and pipes to accommodate essential services such as telephone, electricity, air conditioning, and computer network. Transverse web openings throughout the Reinforced Concrete (RC) beams enable the installation of these services. In recent decades, the researchers suggested several strategies for improving the structural behavior for deep, continuous, and simply-supported beams; involving transverse web-holes underwent shear forces, bending, torsion, and cyclic loads by utilizing supplementary internal steel reinforcing bars, Fiber Reinforced Polymer (FRP) rods or plates, steel fiber, and Carbon Fiber Reinforced Polymer (CFRP) sheets. The current paper presents the previous investigations on the structural action of the RC-beams with the transverse web-openings. The effect of the shape, size, position of the opening, and type of strengthening on the structural performance of RC beams highlight and discussed in this paper. It found when the diameter of circle opening equal or greater than 40% of the depth of beam attributed by reducing in beam strength and earlier cracks occurred. Besides, the deflection of beams was rose when the openings settled below the centroid of the section. Finally, this study proves that the few previous studies discussed the RC beam’s behavior with openings under cyclic loading. However, this paper aims to develop insights for future studies about assessing and strengthening methods for the RC beams with the transverse web opening.

A simplified method to account for vertical human-structure interaction

To account for vertical human-structure interaction (HSI) in the vibration serviceability analysis, the contact force between the pedestrian and the structure can be modelled as the superposition of the force induced by the pedestrian on a rigid surface and the force resulting from the mechanical interaction between the structure and the human body. For the case of large crowds, this approach leads to (time-variant) models with a very high number of degrees of freedom (DOFs). To simplify analysis, this paper investigates the performance of an equivalent single-degree-of-freedom approach whereby the effect of HSI is translated into an effective natural frequency and modal damping ratio for each mode of the supporting structure. First, the numerical study considers a footbridge structure that is modelled as a simply-supported beam for which only the fundamental vertical bending mode is taken into account. For a relevant range of structure and crowd parameters, the comparison is made between the structural response predicted by the simplified model and the more accurate reference model that accounts for all DOFs of the coupled crowd-structure model. Where the simplified model is found to underestimate the structural response, although to a limited extent, this is compensated for by introducing a correction factor for the effective damping ratio. Second, the performance of the simplified method is evaluated through the application on a real footbridge. The results show that the simplified method allows for a good and mildly conservative estimate of the structural acceleration response that is within 10–20% of the predictions of the reference crowd-structure model.

Energy harvesting analysis in railway bridges: An approach based on modal decomposition

In this paper the authors investigate the energy harvesting in railway bridges and analyse the performance under different operational conditions. An approximation based on modal superposition is proposed for the computation of the energy harvested from train-induced bridge vibration. This approach is consistent with the analytical modal solutions of the simply-supported Bernouilli-Euler beam transverse response under moving loads. The influence of the bridge maximum dynamic response and cancellation phenomena, the tuning effect of the harvester device and the relevance of different modal contributions on the harvested energy are studied using a single-degree of freedom system as a simplistic mechanical approach. Later, a piezoelectrically coupled lumped parameter model is used to investigate the available energy due to High-Speed train passages at different circulating speeds. Finally, the feasibility of energy harvesting is evaluated from the experimental data measured by the authors in a railway bridge from the Madrid-Sevilla High-Speed line. The obtained results allow quantifying the harvested energy in a time window of three and a half hours and twenty train passages.

Seismic isolation design for simply-supported beam bridges based on the energy balance method under near-fault ground motions

The seismically isolated simply-supported beam bridge (SISBB) with the seismic isolation bearing (SIB) is converted into an equivalent bilinear single-degree-of-freedom system. Then, by inputting the 139 near-fault ground motion (GM) records into the equivalent system, the parametric study on the near-fault seismic input energy spectra (SEI) of the SISBB is conducted by considering the equivalent system parameters and the near-fault GM characteristics. So, it can be found that: the increase of post-yield stiffness ratio (ηe) can slightly increase the peak values of the near-fault SEI, and ηe = 0.2 can be used to calculate the near-fault SEI design spectra of the SISBB; with the increase of the damping ratio (ξe) (or ductility ratio (μe)), the spectral values of the near-fault SEI increases, the hysteretic energy dissipation capacity of the SIB decreases, and the damping energy dissipation capacity of the equivalent system increases; when μe ≥ 10, the effect of μe on the near-fault SEI can be ignored; the softer the site soil or the smaller the Joyner-Boore distance to rupture plane (Rjb) is, the greater the near-fault SEI is; if the near-fault SEI with a standard peak ground acceleration (PGA) is known, the near-fault SEI with other PGAs can be obtained by multiplying the (PGAOther/PGAStandard)2 by the spectral values of the near-fault SEI with a standard PGA. Finally, the near-fault SEI design spectra of the SISBB are obtained, and the seismic isolation design for SISBB based on the energy balance method is proposed, the feasibility of which is verified by a case study.

Study on the influence of trains on the seismic response of high-speed railway structure under lateral uncertain earthquakes

At present, specific earthquake motion is often used for analyzing the influence of trains on high-speed railway structure; however, the uncertainty of earthquake motion is rarely taken into consideration. In this study, on the basis of considering the uncertainty of earthquake motion, and taking a simply-supported beam with CRTS II track system and CRH2 high-speed train in China as the research objects, a finite element analysis model of vehicle-bridge coupled model was established and verified by tests. The influencing mechanism of the trains on structural response under the action of uncertain earthquake was analyzed, and the range of the influence levels of trains on seismic response of structure was calculated. The research findings show that under the effect of earthquake, the presence of trains decreases the responses of piers and bearings, while increases the response of track structure. With increasing peak ground acceleration, the effect of trains on the track structure deformation increases, while that on the bending moment of piers, shearing force, and bearing deformation all decrease. The increase in train speed will not significantly affect the seismic response of structures. The ratio of seismic response between the operating conditions with and without vehicles was kept within a certain range, so that the demand range for seismic response under the operating condition with vehicles can be approximately simplified.

An equivalent single-layer theory for free vibration analysis of steel-concrete composite beams

An equivalent single-layer theory (EST) is put forward for analyzing free vibrations of steel-concrete composite beams (SCCB) based on a higher-order beam theory. In the EST, the effect of partial interaction between sub-beams and the transverse shear deformation are taken into account. After using the interlaminar shear force continuity condition and the shear stress free conditions at the top and bottom surface, the displacement function of the EST does not contain the first derivatives of transverse displacement. Therefore, the C0 interpolation functions are just demanded during its finite element implementation. Finally, the EST is validated by comparing the results of two simply-supported steel-concrete composite beams which are tested in laboratory and calculated by ANSYS software. Then, the influencing factors for free vibrations of SCCB are analyzed, such as, different boundary conditions, depth to span ratio, high-order shear terms, and interfacial shear connector stiffness.

Bending analysis of simply-supported sandwich beam using Chebyshev quadrature element method

Based on the higher-order sandwich beam theory, the Chebyshev quadrature sandwich beam element is established for the bending analysis of the simply-supported sandwich beam. Gauss Lobatto sampling is adopted as element nodes. The discrete governing equation of the sandwich beam is obtained by the principle of minimum potential energy. A series of numerical examples are carried out on simply-supported sandwich beams under sinusoidal loading. The results are compared with the finite element method, showing that the proposed method can yield very accurate displacements and stresses. This method is suitable for the static analysis of simply-supported sandwich beams with different materials and different geometric parameters.

Time-dependent behavior of porous curved nanobeam

This work provides a comparative analysis of the effect of nanovoids distribution associated with trigonometric functions on forced mechanical characteristics of functionally graded curved nanobeams. A geometrically exact model is developed for the simply-supported beam utilizing a higher-order beam theory including thickness stretching effect. In order to capture the small-scale effects, the governing motion equations are integrated with the general strain gradient theory. The virtual work statement of Hamilton principle is adopted to gain the governing equation as well as boundary conditions. Then, Navier solving procedure-based Fourier series is exerted for stating the reference surface displacements of the nanobeam. The numerical examples are expanded to know the behave of transverse deflection, axial, normal, and shear stresses which are highlighted by time under the influence of material composition, porosity coefficient and its distribution patterns, small-scale coefficients as well as geometrical parameters. It is manifested that in a periodic domain, the oscillation amplitudes grow smaller extremely by raising the excitation frequency, while the repetition of them increases.

Experiments and numerical modelling of cold-formed steel beams under bending and torsion

Cold-formed steel C- and Z-section beams are widely used in light gauge steel building systems as flexural members. In their applications as flexural members, mono-symmetric C-sections and point-symmetric Z-sections are often subjected to transverse loads eccentric to the shear centre, leading to combined bending and torsion actions. However, research and design methods for cold-formed steel beams subjected to combined bending and torsion are limited. Hence this research has investigated the structural behaviour, strength and design of cold-formed steel C- and Z-section beams under the action of combined bending and torsion. Twenty-four tests were conducted on simply-supported beams subjected to a mid-span eccentric load. Two C-sections and two Z-sections were used in the tests with two different spans, each with three loading-eccentricities. A special test set-up was developed and used to simulate the different loading-eccentricities and to provide accurate boundary conditions. Numerical models of tested beams were then developed using ANSYS and nonlinear finite element analyses including the effects of large deformation and material yielding were performed. The numerical results agreed well with the test results in terms of ultimate strengths, failures modes and load-displacement curves. Finally the results from tests were compared with predictions from the current design equation for bending and torsion. This paper presents this investigation of cold-formed steel beams subjected to combined bending and torsion, and the results.

Research on load bearing performance recovery method of a RC simply-supported beam bridge

The load-bearing performance of a RC simply supported beam bridge was comprehensively detected and evaluated. The appearance detection results show that there is a large area of damaged and exposed reinforcement in the main girder and diaphragm plate of the bridge. The detecting results of material condition and state parameters show that the durability of the bridge is insufficient, the risk of steel corrosion is large, and the strength condition of concrete material is poor. The load test results show that the bearing capacity of the bridge does not meet the requirements. In view of the current situation of the bridge, a comprehensive reinforcement treatment scheme was proposed, in which modified epoxy mortar is used to repair the main beam and diaphragm of the whole bridge, steel plate is pasted to reinforce the main beam of the whole bridge, and anticorrosive coating is applied on the main beam and diaphragm.

Damage Identification of Simply-Supported Beam Bridge Based on Deflection Influence Line

In order to extend the service life of the bridge and reduce the occurrence of catastrophic accidents, it is necessary to monitor and identify the damaged parts of the bridge in time. In this paper, the author firstly proposes a basic theory of deflection influence line, then analyzes the calculation basis and proposes a method of deflection influence line of simple supported structure. Finally, according to displacement-time curve of simply-supported beam structure under different load-moving speed can be obtained by using MIDAS, the mid span, damage degree and load-moving speed of structure model can be set to carry out the simulation calculation. The results show that: when the load moving speed is 10km/h, 30km/h, 60km/h and 100km/h, the influence line of deflection difference has no obvious change pattern, and there are different peak values, which cannot be used for damage identification. Under the static load condition, the influence lines of deflection difference at 1/2L position, 3/4L position and end part at 10% and 25% damage degree basically show linear change, while the deflection difference value at 1/2L position appears peak value, and the maximum deflection difference value at different damage positions shows nonlinear change. It indicates that the damage degree can be judged according to the deflection differences at the damage positions identified above.

Stochastic dynamic analysis of vehicle-bridge coupled systems with nonlinear Hertz contacts by explicit time-domain method

ABSTRACT Vibration analysis of vehicle-bridge coupled systems has received considerable attentions over the past two decades. This work is dedicated to the stochastic dynamic analysis of vehicle-bridge coupled systems with nonlinear Hertz wheel-rail contacts subjected to random track irregularities. An explicit time-domain method (ETDM) is proposed for efficient nonlinear dynamic analysis of vehicle-bridge coupled systems with a dimension-reduced iteration scheme focusing on the nonlinear wheel-rail contact forces. The high-efficient ETDM is further utilised to implement the numerous nonlinear dynamic analyses required in the Monte-Carlo simulation (MCS) for obtaining the response statistics of the vehicle-bridge coupled systems. A numerical example involving a single-wheel vehicle traversing a simply-supported beam with nonlinear Hertz wheel-rail contacts considering random track irregularities is presented to demonstrate the computational accuracy and efficiency of the proposed method, and an engineering application involving a four-wheel vehicle moving across the Egongyan suspension bridge is further analysed to indicate the effectiveness of the proposed method for large-scale engineering problems.

Localizing gradient damage model coupled to extended microprestress-solidification theory for long-term nonlinear time-dependent behaviors of concrete structures

A nonlocal damage-based model is proposed to predict the nonlinear long-term deformation of concrete structures, which couples the localizing gradient-enhanced damage (LGED) model for crack nucleation and propagation to the extended microprestress-solidification (XMPS) theory for creep and shrinkage deformations. The proposed LGED-XMPS model circumvents damage localization by incorporating higher-order deformation gradients, and connects creep and shrinkage to inherent moisture transport and heat transfer processes. For creep part, a solidifying Kelvin chain is adopted for the rate-type formulation, which greatly reduces computational burdens of the conventional integral-type formulation. The LGED-XMPS model regularizes mesh-sensitivity of creep deformation intertwined with damage and cracking, which is rarely reported elsewhere. Furthermore, the model are validated with several tests reported in literatures. Specifically, the time-to-failure of concrete specimens subject to high level stresses is well predicted, along with the long-term deflections of simply-supported beams affected by crack growths. It is highlighted that the model is competitive for predicting nonlinear long-term deformation of creep- and crack-sensitive structures.

Loading Condition Estimation Using Long-Period Fiber Grating Array

To ensure the safety and durability of structures, the constant monitoring of their structural health has been used by engineers to manage these structures. Optical fiber sensors have the advantage of long transducer-to-processing distances, the capacity to work in harsh environments, immunity to electromagnetic noise, and reliability. Therefore, optical fiber sensors are great candidates to monitor structures in-service. Here, we propose the use of a long-period fiber grating (LPG) array to monitor the loading condition of a structure. The identification method was tested in a simply-supported beam model and the estimated loading conditions were compared to the loading conditions applied to the beam. By analyzing different combinations of force intensity and position along the beam length, the results showed the force position could be estimated with 0.901% accuracy and force intensity with 2.51% accuracy using a four-LPG strain sensor array.

Thermal-induced snap-through buckling of simply-supported functionally graded beams

The instability of functionally graded material (FGM) structures is one of major threats to their service safety in widely engineering applications. This paper aims to clarify a long-standing controversy on the type of thermal instability of simply-supported FGM beams. Firstbased on the Euler-Bernoulli beam theory and von Karman geometric nonlinearitya nonlinear governing equation of simply-supported FGM beams under uniform thermal loads by Zhang’s two-variable method is formulated. Secondan approximate analytic solution to the nonlinear integro-differential boundary value problem with a thermal-induced inhomogeneous force boundary condition is obtained by using a semi-inverse method when the coordinate axis is relocated to the bending axis (physical neutral plane), and then the analytical predictions are verified by the differential quadrature method (DQM). Finallybased on the free energy theoremit is revealed that the symmetry breaking caused by the material inhomogeneity can make the simply-supported FGM beam under uniform thermal loads occur snap-through postbuckling only in odd modes; furthermorethe nonlinear critical load of thermal buckling varies non-monotonically with the functional gradient index due to the stretching-bending coupling effect. These results are expected to provide new ideas and references for the design and regulation of FGM structures.

Time-dependent pounding probability analysis between adjacent decks of bridges under non-stationary stochastic seismic excitations

This paper proposes a time-dependent probability method to predict the time-variant pounding risk, owing to this reason that the required separation gap width fails to accommodate the relative movement between two adjacent decks, of bridge systems subjected to non-stationary stochastic seismic excitations. Firstly the pseudo excitation method in random theory is utilized to transform the motion equation of system under the non-stationary stochastic seismic excitations into the transient response equation under deterministic external loads. And then the high precision direct integration method (HPDIM) is also employed to reduce the large number of transient analysis into two times for overcoming the challenges of strenuous computing effort. The time-dependent pounding system probability of bridges is derived by the combination of extreme value distribution theory and matrix-based system probability theory. Finally based on the proposed time-dependent probability method the numerical analysis of a real two span simply-supported beam bridge subjected to spatial and non-stationary ground motions is conducted herein for the pounding risk assessment. The results of this study provides in-depth insight into the time-dependent pounding probability of bridge systems subjected to spatially varying and non-stationary ground motions.

Experimental Studies on Blast-Resistance of HFR-LWC Beams Enhanced with Membrane Action

Support-induced membrane action can enhance the resistance, while altering the failure pattern, of reinforced concrete (RC) members under static/dynamic loadings. Nevertheless, the membrane effect on the load-response is regarded as a safety factor in current design guides, hence, a thorough understanding of the resistance capability of RC members in the presence of membrane actions is considered essential. To quantitatively depict the membrane behavior and its influence on the blast-resistance and failure pattern of Hybrid Fiber Reinforced-Lightweight Aggregate Concrete (HFR-LWC) beams, a specially built end-constraint clamp is developed to provide membrane actions on the structural component subjected to the blast load simultaneously. A series of field tests are conducted to investigate the dynamic behaviors of the HFR-LWC beams under close-range detonations. Overpressure-time histories of shock waves induced by the close-range explosive charge are captured. Then the deflection-responses and failure modes of the HFR-LWC beams are further investigated. The responses of the clamped HFR-LWC beam under blast loadings can be well simulated, and the blast-resistances of the beam-type members with membrane action are evaluated reasonably. The results show that membrane action is beneficial for the bridging effects of hybrid fibers and the interlocking effects of coarse aggregate, thereby giving rise to the ductile failures of HFR-LWC beam. The maximum deflections of the clamped HFR-LWC beam decrease by about 60% compared with simply-supported HFR-LWC beam in this paper, illustrating that the blast-resistance may be seriously underestimated if the membrane effects are ignored in structural design.

Existence and location of solutions to fourth-order Lidstone coupled systems with dependence on odd derivatives

This paper addresses the existence and location results for coupled system with two fourth-order differential equations with dependence on all derivatives in nonlinearities and subject to Lidstone-type boundary conditions. To guarantee the existence and location of the solutions, we applied lower and upper solutions technique and degree theory. In this context, we highlight a new type of Nagumo condition to control the growth of the third derivatives and increases the number of applications, as well as a new type of definitions of upper and lower solutions for such coupled systems. Last section contains an application to a coupled system composed by two fourth order equations, which models the estimated bending of simply-supported beam with torsional solitons.

A simplified theory of FG curved beams

The FG (functionally graded) curved beams are investigated in this paper. Starting from the general mode, the higher-order circumferential displacement is re-expressed in an orthogonal form by virtue of the assumptions and the shear stress free condition. On this basis, generalized stresses and strains are defined, and the uncoupled constitutive relationships are built for an FG curved beam as if the beam were homogeneous. According to the principle of virtual work, the higher-order beam theory is established, including equilibrium equations and corresponding boundary conditions. The lower-order beam theory is then established by ignoring the contributions of higher-order moment and higher-order shear force to the virtual wok, and hence it is correlated with the higher-order beam theory. A procedure is suggested to analytically solve FG curved beam problems with the lower-order theory. The results for the clamped-free and clamped-clamped curved beams validate the present theory and the results for the simply-supported beam shed light on the nature of the Navier's solution.

Three alternative versions of the theory for a Timoshenko–Ehrenfest beam on a Winkler–Pasternak foundation

This paper analyzes the free vibration frequencies of a beam on a Winkler–Pasternak foundation via the original Timoshenko–Ehrenfest theory, a truncated version of the Timoshenko–Ehrenfest equation, and a new model based on slope inertia. We give a detailed comparison between the three models in the context of six different sets of boundary conditions. In particular, we analyze the most common combinations of boundary conditions deriving from three typical end constraints, namely the simply supported end, clamped end, and free end. An interesting intermingling phenomenon is presented for a simply-supported (S-S) beam together with proof of the ‘non-existence’ of zero frequencies for free-free (F-F) and simply supported-free (S-F) beams on a Winkler–Pasternak foundation.