Bending Moment Distribution Research Articles

Smooth Hysteretic Model of H‐shaped Steel Beams

ABSTRACTSteel frame structures are generally designed with a beam‐collapse mechanism in mind. Beam members are important earthquake‐resistant elements that dominate the behavior of an entire structure during an earthquake. In order to improve the structural design of such beams, it is important to clarify their performance during cyclic loading, because beams are subjected to a cyclic bending moment under the influence of seismic forces. Hysteretic models have been proposed for each slenderness ratio of lateral buckling for H‐shaped steel beams with lateral buckling. However, this provides inconsistent results and a lack of continuity. Since lateral buckling is a continuous process, it is more reasonable to use a hysteretic model containing continuous parameters.In the present study, we develop a simple smooth hysteretic model that is valid for all lateral buckling slenderness ratios. We applied the that proposed hysteretic model for the reinforced concrete structure to H‐shaped steel beams. In the proposed hysteretic model, which involves an H‐shaped steel simple beam undergoing bending at one‐end, the behavior of the weakened area when the maximum loading capacity has been exceeded can be expressed using two parameters: the lateral buckling slenderness ratio and the standardized width thickness ratio. In addition, we also propose a hysteretic model that can be adapted for a uniformly distributed bending moment and an antisymmetric bending moment. We expect that simple smooth hysteretic model can be applied to a wide range of H‐shaped steel beams.

Lateral impact behavior of double-skin steel tubular (DST) members with ultra-high performance fiber-reinforced concrete (UHPFRC)

This study investigates the lateral impact behavior of double-skin steel tubular (DST) members with ultra-high performance fiber-reinforced concrete (UHPFRC). A total of six specimens were prepared and tested under lateral impact loading. In addition to UHPFRC filled DST members, normal strength concrete (NSC) filled DST member was also tested for comparison. Other investigated parameters in this study include the impact energy, the outer steel tube thickness, the inner steel tube thickness, and the presence of axial force. The test results demonstrate that the UHPFRC filled DST members exhibit significantly higher lateral impact resistance capacity than the NSC filled DST member. The impact energy and the outer steel tube thickness significantly affect the lateral impact behavior of UHPFRC filled DST members, while the influence of inner steel tube thickness is insignificant. With the applied axial force in this study, the influence of axial force is also insignificant. Afterwards, numerical model was developed and validated by the present test results. Based on the validated numerical model, the mid-span bending moment distributions and the stress wave propagations were investigated. Finally, parametric analyses were carried out to investigate the influences of different parameters on the lateral impact behavior of UHPFRC filled DST members.

Efficient FORM-based extreme value prediction of nonlinear ship loads with an application of reduced-order model for coupled CFD and FEA

In this paper, a method for predicting the extreme value distribution of the vertical bending moment (VBM) in a ship under a given short-term sea state is presented. To predict the extreme value distribution of the VBM, the first-order reliability method (FORM), by which the most probable wave episodes (MPWEs) leading to given VBMs are identified, is introduced. The coupled computational fluid dynamics (CFD) and finite-element analysis (FEA) are used to provide the high-fidelity numerical solutions for the wave-induced and whipping components of the VBM. Then, a Reduced-Order Model (ROM) which can yield the predictions equivalent to the coupled CFD–FEA results in a relatively short time is developed. The ROM is incorporated into FORM to identify the MPWEs, in lieu of the coupled CFD–FEA. The accuracy of the ROM is verified by comparing with the coupled CFD–FEA results under identified MPWEs, in terms of both the wave-induced and whipping VBM. Then, a series of tank tests using a scaled container ship is conducted. In the first series of the tests, the VBM measurements under the MPWEs identified from the FORM-based approach using the ROM are made, to validate the accuracy of the ROM. The extreme value distribution of the combined wave-induced and whipping VBM is also measured by performing the second series of the tests, in random waves. The validity of the FORM-based extreme value prediction using the ROM is investigated by comparing with the second series of the tests.

Live Load Distribution Factor for Tank Loading on Slab-Girder Bridges

The aim of this research is to obtain the bending moment and shear live load distribution factors (LLDFs) for interior girders of simply supported slab-girder bridges subjected to continuous loading, such as military tanks. The effective parameters considered in calculating the live load distribution factor were: Girders’ number and spacing, span length, slab thickness and the longitudinal to transverse ratio of deck stiffness. Over fifty 3D finite element models were created based on the existing information of bridges in the USA. An equation was obtained for the distribution factor and its validity was assessed against the numerical results. The proposed equation was compared with the AASHTO-LRFD equation for one lane of standard truck loading and also with the equation proposed by the US army corps of engineers for military vehicles. The accuracy of the equation was also verified by performing several sensitivity analyses for the parameters involved. It is concluded that the proposed LLDF equation predicts the distribution factor more accurately than the above mentioned specifications.

Using a two-stage approach to improving accuracy of resonance fatigue tests for large-scale wind turbine blades

The increasing size and complexity of wind turbine blade designs challenge the ability of traditional fatigue testing methods to accurately and efficiently reproduce load distributions representative of real world conditions. A new two-stage approach is proposed. In the first stage, the blade is subjected to a dual-axis resonance test, where additional masses are mounted to the blade to control the bending moment distribution. In the second stage, part of the blade is removed, allowing it to be exercised at a higher frequency and for more damage to be applied to the root and transitional sections. The results of the proposed method were compared with those of traditional testing methods for 38 m and 60 m blades. The results indicate that the new methods have the potential to significantly improve accuracy, but the testing duration will increase.

Analysis of Deck Slab of Reinforced Concrete Gerber-Girder Bridge Widened by Addition of Continuous Steel-Concrete Composite Girders

Many Gerber-girder bridges have become obsolete in terms of deck width and load carrying capacity. If bridge replacement is not necessary, additional girders are installed. Sometimes, due to erection convenience, the added girders do not replicate the static scheme of the refurbished structure. Such an arrangement requires special attention to preserve structural durability. An example of the inappropriate arrangement of the widening of a Reinforced Concrete Gerber-girder road bridge is presented together with an alternative concept of refurbishment based on the addition of the continuous steel-concrete girders as the outermost ones. The added deck slab connects the added and the existing parts of the structure. Attention is drawn the static analysis of the added deck slab and the influence of the added outermost girders that do not replicate the static scheme of the existing ones. Due to different static schemes of the existing and the added girders, the traditional method of the deck slab analysis is inappropriate. The Finite Element 3D model is to be applied to access bending moments in the deck slab spans correctly. It is shown that: a) the analysis of the distribution of the bending moments in the existing and the added slab spans, especially near Gerber-hinges, should be based on the Finite Element 3D modelling; b) the analysis should consider live loads acting on the whole width of the Gerber-hinge span; c) the bending moment distribution in the widened deck slab is sensitive to the distance to the Gerber hinge.

Mechanical behavior of high-strength bolts in T-stubs based on moment distribution

A T-stub is a component comprising a T-section with two bolts attached to its flange. It can be used to analyze the mechanical behavior of high-strength bolts in tension. In this study, the mechanical behavior of bolts was assessed via six static tests and 17 finite element analysis models. The effects of the thickness of the flange, the length of the inner and outer flange, and the diameter of the bolt were studied. With the exception of outer flange length, the parameters significantly affected the bolt bending moment, yielding load, and T-stub failure mode. Both the tests and the finite element analyses indicated that when the bolts yielded, the bending stress could reach 13% to 45% of the total tensile stress in the samples. It is not advisable to design bolts without considering the effect of the bending moment. A stable bending moment distribution relationship was also found between the bolt and the outer flange. The bending moment of the joint, the bending moment ratio of the bolt to the joint, and the distance from the contact force center to the bolt center are also discussed. Lastly, a new T-stub connector model and calculation method were proposed and proven to be reliable. This method is based on the theory of moment distribution and does not require the prying force to be calculated.

Behavior of ultra-high performance fiber-reinforced concrete (UHPFRC) filled steel tubular members under lateral impact loading

This study investigates the behavior of ultra-high performance fiber-reinforced concrete (UHPFRC) filled steel tubular (UHPFRCFST) members under lateral impact loading. A total of five specimens were prepared and tested under lateral impact loading. All specimens were 168 mm in diameter and 2000 mm in length. In addition to UHPFRCFST members, normal strength concrete (NSC) filled steel tubular (NSCFST) members were also tested for comparison purpose. Other investigated parameters in this study include the impact energy and the presence of an inner void. The test results show that as compared to the NSCFST members, the UHPFRCFST members exhibit higher lateral impact resistance with higher peak and plateau impact forces, smaller deflection, and less local indentation. With the increase of impact energy, the peak impact force, the impact duration, and the deflection of the UHPFRCFST members are increased, while the plateau impact force is almost kept constant. Moreover, the presence of an inner void does not deteriorate the lateral impact resistance of the UHPFRCFST members. Finite element (FE) model was then developed and validated by the test results in this study. Afterwards, full-range analysis was performed to investigate the damage evolution, sectional bending moment distribution, and the interactions between the steel tube and the concrete during the impact process. Finally, detailed parametric analyses were carried out to investigate the influences of different parameters on the lateral impact behavior of UHPFRCFST members.

A Simplified Algorithm for Designing Tunnel Composite Support System in Discontinuous Rock Media

Since the introduction of the primary support systems in tunnels, many researchers tried to enhance their composite-like behavior by improving the behavior of structural elements. In this study, the behavior of composite lining with three elements (mesh + frame + shotcrete) was investigated based on the share of each structural element from section’s internal forces using equations derived from shell theory. Then, the result was compared to results of composite section consisting of two elements (frame + shotcrete) in order to determine the role of mesh in bending and axial capacities of composite section. The results showed that mesh element helps the section’s composite-like behavior and increases the bending and axial capacities. Based on this comparison, an algorithm was presented for determining frame spacing as a critical parameter with technical and economical points of view. In this algorithm, an iterative process was introduced to determine lining equivalent section’s properties, inputs for universal distinct element numerical model, based on structural elements, frame spacing and structural analysis methods. The outputs of the numerical method (bending moment distribution, axial force and shear force in the equivalent section) were returned to theoretical model and were compared to structural elements’ capacity diagrams. This process continued until the internal forces reached the range within that of the capacity diagrams. Results indicate that the addition of mesh element reduces the shotcrete’s and steel frame’s share of section’s internal forces. Thus, the steel frame spacing could be increased and the costs of primary support system per meter could be reduced.

CALCULATION OF STRETCHING AND BENDING STRESS IN A CASING STRING INSTALLED IN A WELL WITH A COMPLEX PROFILE

The casing column in the curvilinear well is represented as a long solid elastic rod. It has a vertically actingweight, which is evenly distributed along the length and creates variable axial tensile forces in the column body. At the same time, it is influenced by the reaction forces of the borehole walls, which, together with the weight, bend the column of initially straight pipes. It is assumed that the casing axis replicates the axis of the bent borehole, and the walls reaction is continuously distributed along the length according to a certain law, which, together with the weight, bends the column of the initially straight pipes. A system of differential equilibrium equations of internal and external forces and moments was composed. This system was supplemented to a closed form with the differential equation of curvature. This system describes large deformations of a long elastic rod in one plane. The introduction of the distributed weight, wall reactions and resistance forces into the calculation makes it non-uniform. Its feature is the need to solve the inverse problem. In this case the external load and rod deformations defined by the well shape in the form of an inclinometric data table are known. The unknown internal forces and the function of the walls reaction which creates its predetermined shape must be determined. It is established that this function depends on the distribution of axial forces caused by weight and resistance forces. As a result the system was reduced to a linear inhomogeneous differential equation with variable coefficients of the first order as to the axialforce and its solution was obtained as a sum of integrals. It is shown that one of them can be found in quadratures only in the case of a constant radius of curvature of the well. This necessitated the use of numerical integration methods. Formulas for the distribution of axial forces and bending moments in the body of the column, as well as the reactions of the walls leading the column to the actual well profile are obtained from the solution of the basic equation. To calculate these force factors, a method for numerical integration of inclinometric measurements data and software for numerical analysis of a real well are developed. This technique allows to detect the areas of local increase of the curvature and difficult passage of the curvilinear wellbore and to calculate the main parameters of the stress-strain state of the casing column in it.

Unstrained length-based methods determining an optimized initial shape of 3-dimensional self-anchored suspension bridges

Two robust methods, a Generalized Target Configuration Under Dead Loads (GTCUD) method and a simplified analytical method are developed for 3D analysis of suspension bridges. These methods provide an optimized initial state for 3D suspension bridges under dead loads. The current study makes application to 3D self-anchored suspension bridges with spatially curved main cables and initial cambers of the main girder. Furthermore, the unstrained length method (ULM) based on the unstrained lengths is applied to the bridge structure using two procedures. Finally, it is demonstrated through a bridge example having vertical cambers that the proposed analysis methods can indeed provide an optimized initial solution by showing that both schemes lead to practically identical initial configuration with localized small bending moment distributions.

Seismic response of tunnel lining structure in a thick expansive soil stratum

The seismic response of a tunnel lining structure is essential for its safety design and construction. The objective of this study is to investigate the seismic response of a tunnel lining structure embedded in a thick expansive soil stratum. First, the deformation and internal force characteristics of tunnel lining structure under seismic action are evaluated from a theoretical perspective. Second, a finite element (FE) analysis is carried out of the seismic responses of the tunnel lining structure and ground stratum. In the FE analysis, the bolted connections in the tunnel lining structure are simulated using the local stiffness reduction method (LSRM). The LSRM reduces the stiffness of the lining segments affected directly by the bolted connections using a stiffness reduction coefficient (SRC), while leaves the stiffness of the rest of the lining segments to remain to be unchanged. The results indicate that under the effect of transversal waves propagating in the direction perpendicular to tunnel axis, the transversal displacement characteristics of the tunnel lining structure are almost identical to that of the surrounding soil stratum. They both decrease with an increase in buried depth. The circumferential distributions of shear force, bending moment, and axial force in lining segments are varied, but the magnitudes of them increase with an increase in SRC.

Finite Element Analysis of Square-Shaped Compensator for Overhead Pipeline with Thermal Fluid-Solid Coupling

In the present study, the square-shaped compensator for the overhead pipeline in a chemical industrial park was selected as the research object. The pipeline gallery had 10 sets of support columns, 4-layer pipe racks and 27 pipes to transport the flow mediums in different temperatures and pressures. By taking into account the factors such as gravity, medium temperature, flow force acted on the pipeline, etc, the ANSYS finite element model was established sophisticatedly to perform the thermal fluid-solid coupling computation. The distributions of displacement, axial force, shear force, bending moment and stress of the square-shaped compensator were obtained. The maximum values and the corresponding positions in these distributions were found and analyzed. The reliability of the square-shaped compensator was judged by checking the secondary stresses. The study aims to explore a safety assessment method for the application of complex overhead pipelines, and to provide solid technical support for the safety operation of overhead pipelines.

Estimating the local and global effects of infills on steel frames by an improved macro-model

Masonry infill panels change the seismic behavior and internal forces of surrounding frames and should be considered in analysis and design phases. Single equivalent strut model, the most common strut model, does not address the internal forces and therefore the multi-strut models are preferred. In this paper, the previously proposed three-strut model (model PD) has been improved to represent a more reliable prediction of both local and global infill effects. For this, an in-depth finite element sensitivity analysis is performed. It is shown that the new model estimates the bending moment and shear force distribution and predicts the stiffness and strength of the infilled steel frames more accurately than previously proposed models in the literature. Properties of the nonlinear hysteretic behavior of infilled frames including stiffness degradation and strength deterioration can also be determined precisely. Finally, the macro-model is further developed to capture the global seismic response and element force distribution of frames with a soft first story.

Curvature-based, time delayed feedback as a means for self-propelled swimming

The development of bio-inspired robotics has led to an increasing need to understand the strongly coupled fluid–structure and control problem presented by swimming. Usually, the mechanical forcing of muscles is modeled with an imposed distribution of bending moments along the swimmer’s body. A simple way to exploit this idea is to define a central pattern forcing for this active driving, but this approach is not completely satisfactory because locomotion results from the interaction of the organism and its surroundings. Gazzola et al. (2015) have proposed that a curvature-based feedback with a time delay can trigger self-propulsion for a swimmer without necessitating such a pre-defined forcing. In the present work, we implement this feedback within a numerical model. We represent the swimmer as a thin elastic beam using a finite element representation which is coupled to an unsteady boundary element method for the resolution of the fluid domain. The model is first benchmarked on a flexible foil in forced leading edge heave.To recover previous findings, an imposed traveling bending moment wave is then used to drive the swimmer which yields peaks in the mean forward velocity when the driving frequency corresponds to the natural frequencies of the elastic structure. Delayed, curvature-based feedback is then applied to the swimmer and produces peaks in the velocity for delays that differ from the natural periods, associated to its deformations modes. Finally, a simplified model is shown to qualitatively describe the origin of the peaks observed in the feedback swimmer.

Predicting the Extreme Loads in Power Production of Large Wind Turbines Using an Improved PSO Algorithm

Predicting the extreme loads in power production for the preliminary-design of large-scale wind turbine blade is both important and time consuming. In this paper, a simplified method, called Particle Swarm Optimization-Extreme Load Prediction Model (PSO-ELPM), is developed to quickly assess the extreme loads. This method considers the extreme loads solution as an optimal problem. The rotor speed, wind speed, pitch angle, yaw angle, and azimuth angle are selected as design variables. The constraint conditions are obtained by considering the influence of the aeroelastic property and control system of the wind turbine. An improved PSO algorithm is applied. A 1.5 MW and a 2.0 MW wind turbine are chosen to validate the method. The results show that the extreme root load errors between PSO-ELPM and FOCUS are less than 10%, while PSO-ELPM needs much less computational cost than FOCUS. The distribution of flapwise bending moments are close to the results of FOCUS. By analyzing the loads, we find that the extreme flapwise bending moment of the blade root in chord coordinate (CMF_ROOT) is largely reduced because of the control system, with the extreme edgewise bending moment of the blade root in chord coordinate (CME_ROOT) almost unchanged. Furthermore, higher rotor speed and smaller pitch angle will generate larger extreme bending moments at the blade root.

Impact force profile and failure classification of reinforced concrete bridge columns against vehicle impact

Numerical simulations are utilized in this study to define the impact force profile generated by vehicle collisions on reinforced concrete bridge columns (RCBCs) and classify the dynamic responses and failure of the columns under collision events. The results indicate that both the column properties (i.e. dimension of the cross-section and concrete strength) and initial conditions of vehicles (i.e. vehicle velocity, engine mass, and vehicle mass) play a crucial role in determining the impact force profile from the vehicle collision. A new vehicle impact force model is proposed for engineers to use in design of RCBCs under vehicle collisions in which the influence of shear failure of the column on impact force is considered. Based on the shear mechanism of RCBCs under impact events, the maximum dynamic shear capacity of a column is defined. Furthermore, the bending moment and shear force distributions, as well as the failure mode of RCBCs have been classified into two categories, i.e. flexural response and shear response governed failure with respect to the peak impact force (PIF) on the column. For the flexural response governed failure mode, flexural cracks at the intermediate sections are formed in the positive side of the column, while the diagonal shear or punching shear failure at the impact area together with negative flexural-shear cracks occur in the column if the shear failure mode dominant the column responses.

Complex bend of multilayered concrete rods

The problem of complex bend of multilayered rods based on concrete is considered. It is assumed that the rod of constant cross-section is of arbitrary shape and different brands of concrete are used in the cross-section of the rod layer by layer. The solution is sought by the small parameter method. The case of a complex bend of the rod pinched at both ends is considered as an example of this solution method. The distribution of bending moments and longitudinal forces in the zero and first approximations is determined.

Bending by explosion of a multilayered concrete beam on a visco-elastic basis

In this work, the problem of bending of a multilayered concrete beam of arbitrary cross-section by explosive loading on a visco-elastic basis is considered. It is assumed that different grades of concrete can be realized in layers in the cross-section. The property of concrete resistance to tension and compression is considered in work. It is assumed that the dynamic loading is caused by consecutive explosion of two charges over the middle of the span of beam. The distribution of bending moments and deflections of the beam at each time is determined. The time of the end of motion and the residual deflection of beam are found.

Evaluation of the reliability of reinforced concrete beams on a stochastically inhomogeneous elastic foundation under the action of a non-stationary random load

The results of the evaluation of the reliability of reinforced concrete beams lying on an elastic foundation are presented. The load on the beam is considered as a non-stationary random function, the elastic properties of the foundation are described as a stationary random function. Beam stiffness is considered as a random variable depending on the cubic strength of concrete. To solve the beam bending equation on an elastic foundation with random properties and a loaded non-stationary random load, the small parameter method and the method of spectral representations are used. The obtained probability characteristics of the probability density distribution of bending moments allow us to find the probability of failure of a reinforced concrete beam on an elastic stochastically inhomogeneous foundation.