Equivalent bending stiffness of simply supported preflex beam bridge with variable cross-section

In order to understand mechanical characters and find out a calculating method for preflex beams used in particular bridge engineering projects, two types of simply supported preflex beams with variable crosssection, preflex beam with alterative web depth and preflex beam with aherative steel flange thickness, are dis- cussed on how to achieve the equivalent moment of inertia and Young＇ s modulus. Additionally, methods of cal- culating the equivalent bending stiffness and post-cracking deflection are proposed. Results of the experiments on 6 beams agree well with the theoretical analysis, which proves the correctness of the proposed formulas.

Analysis of Stress Concentration Factors due to in-Plane Bending and out-of-Plane Bending Loads on Tubular TY-Joints of Offshore Structures

The aim of this work is to study the stress distributions and the location of hot spots stress in the vicinity of the intersection lines of the tubular elements of the tubular TY-joints.Using the finite element models,we analyze the effects of geometrical parameters on the stress concentration factor in the case of in-plane bending and out-of-plane bending loads,around the weld toe of the tubular joints.Our results reveal the location of the maximum stress concentration factor at the heel or toe in the case of in-plane bending loads and at the saddle point in the case of out-of-plane bending loads.Six parametric equations are established and used to calculate the stress concentration factor at critical locations using the non-linear regression method.The results obtained from the finite element analysis are close to the results of the parametric equations and the experimental data from the previous work.

Theoretical Prediction of the Bending Stiffness of Reinforced Thermoplastic Pipes Using a Homogenization Method

The accurate prediction of bending stiffness is important to analyze the buckling and vibration behavior of reinforced thermoplastic pipes(RTPs)in practical ocean engineering.In this study,a theoretical method in which the constitutive relationships between orthotropic and isotropic materials are unified under the global cylindrical coordinate system is proposed to predict the bending stiffness of RTPs.Then,the homogenization assumption is used to replace the multilayered cross-sections of RTPs with homogenized ones.Different from present studies,the pure bending case of homogenized RTPs is analyzed,considering homogenized RTPs as hollow cylindrical beams instead of using the stress functions proposed by Lekhnitskii.Therefore,the bending stiffness of RTPs can be determined by solving the homogenized axial elastic moduli and moment of inertia of cross sections.Compared with the existing theoretical method,the homogenization method is more practical,universal,and computationally stable.Meanwhile,the pure bending case of RTPs was simulated to verify the homogenization method via conducting ABAQUS Explicit quasi-static analyses.Compared with the numerical and existing theoretical methods,the homogenization method more accurately predicts the bending stiffness and stress field.The stress field of RTPs and the effect of winding angles are also discussed.

Analytical solution of rectangular plate with in-plane variable stiffness

The bending problem of a thin rectangular plate with in-plane variable stiffness is studied. The basic equation is formulated for the two-opposite-edge simply supported rectangular plate under the distributed loads. The formulation is based on the assumption that the flexural rigidity of the plate varies in the plane following a power form, and Poisson＇s ratio is constant. A fourth-order partial differential equation with variable coefficients is derived by assuming a Levy-type form for the transverse displacement. The governing equation can be transformed into a Whittaker equation, and an analytical solution is obtained for a thin rectangular plate subjected to the distributed loads. The validity of the present solution is shown by comparing the present results with those of the classical solution. The influence of in-plane variable stiffness on the deflection and bending moment is studied by numerical examples. The analytical solution presented here is useful in the design of rectangular plates with in-plane variable stiffness.

Flexural behavior of in-plane bending glass structures for design method

Experimental study was carried out on the in-plane bending behavior of glass plates without lateral supports, and the effects of the factors, such as height-to-span ratio, on the stability of glass panels were studied. Results show that the in-plane bending glass plates with both ends simply supported and their upper edge free lose overall stability under loads, which belongs to the limit-point type of instability. It is found that the buckling load increases linearly with the increase of height-to-span ratio of the glass plates. The lateral stress of in-plane bending glass plates without lateral supports increases linearly under loads; while the large-area stress increases nonlinearly and the lateral stress is not the controlling factor of instability. In finite element analysis, the first buckling mode is regarded as the initial imperfection and imposed on the model as 1/1000 of the span of the components. The numerical buckling load according to the theory of large deflection is less than the experiment result, which is more conservative and can provide some reference for design. For the design method, when the in-plane load is imposed on the glass plate, its lateral strength and the deflection should be verified. Considering the stability of the in-plane bending glass plate without reliable lateral support, buckling is another possible failure mode and calls for verification.

Assessment of Existing Bridge’s Beam Bending Stiffness Using Crack Characteristics

At present, the bearing capacity evaluation is mainly based on load detection, which requires closed traffic and has certain risks. With the increase of service time, the cracks of reinforced concrete beam bridge will gradually develop and the stiffness will reduce, resulting in the decrease of bearing capacity. Therefore, in this paper, the calculation of stiffness reduction coefficient by using crack characteristic parameters, which provides basic data for bearing capacity evaluation, has been studied. In this paper, using regression analysis through fracture characteristics of four model beam observation and test load-displacement curve characteristic parameters, crack flexural rigidity of the beam bridge relationship has been set up. The qualitative assessment based appearance of cracks in the structure of checks has been converted to quantitative assessment. And compared with the test results of a real bridge, comparative results show that the assessment is objective and reliable. It makes the assessment more objective and scientific. A new way of Quantitative assessment of the structural performance has been provided for a large number of existing reinforced concrete beam bridge.

Research of Elastic and Elastic-Plastic Deformation on Bending Problems of Variable Stiffness Beams

A novel variable stiffness model was proposed for analyzing elastic-plastic bending problems with arbitrary variable stiffness in detail.First,it was assumed that the material of a rectangular beam is an ideal isotropic elastic-plastic material,whose elastic modulus,yield strength,and section height are functions of the axial coordinates of the beam respectively.Considering the effect of shear on the deformation of the beam,the elastic and elastic-plastic bending problems of the axially variable stiffness beam were studied.Then,the analytical solutions of the elastic and elastic-plastic deformation of the beam were derived when the cross-section height and the elastic modulus of the material were varied by special function along the length of the beam respectively.The elastic and elastic-plastic analysis of the variable stiffness beam was carried out using Differential Quadrature Method(DQM)when the bending stiffness varied arbitrarily.The influence of the axial variation of the bending stiffness on the elastic and elastic-plastic deformation of the beam was analyzed by numerical simulation,DQM,and finite element method(FEM).Simulation results verified the practicability of the proposed mechanical model,and the comparison between the results of the solutions of DQM and FEM showed that DQM is accurate and effective in elastic and elastic-plastic analysis of variable stiffness beams.

Tunable Bending Stiffness, Buckling Force, and Natural Frequency of Nanowires and Nanoplates

This paper aims to obtain the simple closed-form results for the combined effects of surface elasticity, initial stress/ strain, and material Poisson ratio on the bending stiffness, natural frequency and buckling force of nanowires and nano-plates. The results demonstrate that all these properties of nanowires or nanoplates can be designed either very sensitive or not sensitive at all to the amplitude of an applied electric potential;show how much of those properties can be controlled to vary;and thus provide a reliable guide to the measurement of the Young’s modulus of nanowires/nanoplates and to the design of nano-devices, such as nano-sensors or the cantilever of an AFM.

Bending Stiffness of Truss-Reinforced Steel-Concrete Composite Beams

This paper is concerned with a special steel-concrete composite beam in which the resisting system is a truss structure whose bottom chord is made of a steel plate supporting the precast floor system. This system works in two distinct phases with two different resisting mechanisms: during the construction phase, the truss structure bears the precast floor system and the resisting system is that of a simply supported steel truss;once the concrete has hardened, the truss structure becomes the reinforcing element of a steel-concrete composite beam, where it is also in a pre-stressed condition due to the loads carried before the hardening of concrete. Within this framework, the effects of the diagonal bars on the bending stiffness of this composite beam are investigated. First, a closed-form solution for the evaluation of the equivalent bending stiffness is derived. Subsequently, the influence of geometrical and mechanical characteristics of shear reinforcement is studied. Finally, results obtained from parametric and numerical analyses are discussed.

The Effects of the Longitudinal Axis of Loading upon Bending, Shear and Torsion of a Thin-Walled Cantilever Channel Beam

Three aluminium channel sections of US standard extruded dimension are mounted as cantilevers with x-axis symmetry. The flexural bending and shear that arise with applied axial torsion are each considered theoretically and numerically in terms of two longitudinal axes of loading not coincident with the shear centre. In particular, the warping displacements, stiffness and stress distributions are calculated for torsion applied to longitudinal axes passing through the section’s centroid and its web centre. The stress conversions derived from each action are superimposed to reveal a net sectional stress distribution. Therein, the influence of the axis position upon the net axial and shear stress distributions is established compared to previous results for each beam when loading is referred to a flexural axis through the shear centre. Within the net stress analysis is, it is shown how the constraint to free warping presented by the end fixing modifies the axial stress. The latter can be identified with the action of a ‘bimoment’ upon each thin-walled section.

Evaluation of reclaimed asphalt pavement binder stiffness without extraction and recovery

A new testing procedure to estimate the low-temperature stiffness of the reclaimed asphalt pavement （RAP） binder was developed. In the testing procedure, the SuperpaveTM Bending Beam Rheometer （BBR） with special modifications and binder blending charts by Asphalt Institute were utilized. Modifications involved the development of a new kind of sample mold and different testing parameters were made to BBR testing procedure to capture the theological properties of bitumen mortars produced by mixing fresh binder with fine RAP materials or RAP aggregate. The stiffness relationship between binder and bitumen mortar was established based on the BBR test results. The blended binder stiffness in bitumen RAP mortar was estimated from the RAP mortar stiffness based on the binder-mortar relationship. And finally, the RAP binder stiffness was estimated from the blended binder and fresh binder stiffness based on the blending charts by Asphalt Institute. The results indicate that the new procedure can capture the rheological properties of bitumen mortar and can be used to estimate the low temperature stiffness of RAP binder without binder extraction and/or any chemical treatments.

Plate reinforced square hollow section X-joints subjected to in-plane moment

The static test of 13 square hollow section(SHS) X-joints with different β and different types of plate reinforcement under in-plane moment in brace was carried out. Experimental test schemes, failure modes of specimens, moment-vertical displacement curves, moment-deformation of the chord, and strain strength distribution curves were presented. The effect of β and plate reinforcement types on in-plane flexural property of SHS X-joints was studied. Results show that punching shear of chord face disappears, brace material fracture appears and concave and convex deformation of chord decrease when either collar plates or doubler plates were welded on chord face. Moment-vertical displacement curves of all specimens have obvious elastic, elastic-plastic and plastic stages. As β increases, the in-plane flexural ultimate capacity and initial stiffness of joints of the same plate reinforcement type increase, but ductility of joints decreases. With the same β, the in-plane flexural initial stiffness and ultimate capacity of doubler plate reinforced joints, collar plate reinforced joints, and unreinforced joints decrease progressively. Thickness of reinforcement plate has no obvious effect on in-plane flexural initial stiffness and ultimate capacity of joints. As thickness of reinforcement plate increases, the ductility of reinforced X-joints decreases. The concave and convex deformation of every specimen has good symmetry;as β increases, the yield and ultimate deformation of chord decrease.

BENDING AND VIBRATION OF COMPOSITE LAMINATED PLATES

Hybrid-stress finite element method is applied for analysis of bending and vibration ofcomposite laminated plates in this paper.Firstly,based on the modified-complementaryprinciple,a reciangular hybrid-stress plate bending element is presented which applies toanalysis of laminates.Inside the element,different stress parameters are assumedaccording to different layers.The boundary displacements are determined by means of theassumption of YNS theory on the boundary of elements.The element formed in this way notonly can take effects of transverse shear deformation and local warping into account,butalso has less degrees of freedom.Then.problems of bending and vibration of laminates aresolved by using this element.and the numerical results are compared with the exactsolutions.This shows that the results obtained in the paper are very close to the exactresults.

Bending Resistance Covalent Organic Framework Superlattice:“Nano‑Hourglass”‑Induced Charge Accumulation for Flexible In‑Plane Micro‑Supercapacitors

Covalent organic framework(COF)film with highly exposed active sites is considered as the promising flexible selfsupported electrode for in-plane microsupercapacitor(MSC).Superlattice configuration assembled alternately by different nanofilms based on van der Waals force can integrate the advantages of each isolated layer to exhibit unexpected performances as MSC film electrodes,which may be a novel option to ensure energy output.Herein,a mesoporous free-standing A-COF nanofilm(pore size is 3.9 nm,averaged thickness is 4.1 nm)with imine bond linkage and a microporous B-COF nanofilm(pore size is 1.5 nm,averaged thickness is 9.3 nm)withβ-keto-enamine-linkages are prepared,and for the first time,we assembly the two lattice matching films into sandwich-type superlattices via layer-by-layer transfer,in which ABA–COF superlattice stacking into a“nano-hourglass”steric configuration that can accelerate the dynamic charge transportation/accumulation and promote the sufficient redox reactions to energy storage.The fabricated flexible MSC–ABA–COF exhibits the highest intrinsic CV of 927.9 F cm^(−3) at 10 mV s^(−1) than reported two-dimensional alloy,graphite-like carbon and undoped COF-based MSC devices so far,and shows a bending-resistant energy density of 63.2 mWh cm^(−3) even after high-angle and repeat arbitrary bending from 0 to 180°.This work provides a feasible way to meet the demand for future miniaturization and wearable electronics.

Experimental study on centrifugal concrete-filled steel tubes under bending and torsion

A real-size experiment on 11 tubes was done to study the performance o f centrifugal concrete-filled steel tubes under bending and torsion. This pape r first introduces the relevant operating method,equipment,subjects and process es. The factors that affect deformation and stiffness and the break mechanism un der different loading were studied. Experimental stress analysis showed that the values of practical critical stress of steel tubes accorded well with the MISES Yielding Rule. The correlative equation (on the bearing capacity of a structura l member under bending and torsion) deduced in this study may provide valuable reference for the design of this structural member.

A Research on Effect of Finishing Applications on Fabric Stiffness and Prediction of Fabric Stiffness

In this study fabric stiffness/softness is examined which is an important element of applications on finishing processes of fabric.It is also studied the prediction of the fabric stiffness/softness with help of different parameters.Specific to this aim three different weft densitoes(30 tel/cm),3 different yarn numbers(20/1,24/1,30/1 Nm)and 3 different weaving patterns were used and 27 different fabrics were weaved.During the weaving process warp yarn is 100%polyester and weft yarn is 67-33%cotton/polyester.Three different finishing processes are applied to the 27 different fabrics(softness finishing treatment,crosslinking finishing and antipilling finishing)in 3 different concentrations and at the end there are 243 sample fabrics gathered.Stiffness test was applied to the samples according to the ASTM(American Society for Testing and Materials)D 4032-94 the Circular Bending Method.Test results were evaluated statistically.It was seen that the established model was related with p<0.0001 also,Artificial Neural Network(ANN)model was formed in order to predict the fabric softness using the test results.MATLAB packet model was used in forming the model.ANN was formed with 5 inputs(fabric plait,weft yarn no,weft density,weft type,finishing concentration)and 1 output(stiffness).ANN model was established using feed forward-back propagation network.There were many trials in forming the ANN and the best results were gathered at the values established with 0.97317 regression value,2 hidden layers and 10 neurons.

Buckling Response of Pipe-in-Pipe Systems Subjected to Bending

The buckling response of pipe-in-pipe(PIP)systems subjected to bending is investigated in this paper. A set of parameterized models are established to explore the bending characteristics of the PIP systems through eigenvalue buckling analysis and nonlinear post-buckling analysis. The results show that the length of PIP systems and the height of centralizers are the most significant factors that influence the buckling moment, ultimate bending moment and buckling mode; the other geometric characteristics, such as initial geometric imperfection and friction between centralizers and outer pipes, evidently influence the post-buckling path and ductility of PIPs; the equivalent bending stiffness is dependent on the length and centralizers. Moreover, the range of equivalent bending stiffness is also discussed.

Preparation of textile preform with sewing machines and bending properties of stitched woven glass fibre fabrics

With the increasing demand of light structure composite in industry, carbon and glass fibres are more and more used, because of their light mass, high strength, high temperature endurance and erosion resistance. This paper focuses on the process of forming a preform. Up to the finished preform, the multilayer reinforced fabrics are subjected to the following procedures: pattern design, cutting and sewing. Considering the fabric properties, the 3-dimensional CAD software and sewing machines, which are generally used in the clothing industry, are also suitable for the processing of the reinforced fabrics. This study aims also to the changes of property arising from the sewing process. Bending stiffness and changes of thickness after sewing are studied. These properties will provide input data for CAD pattern design.

An Inelastic Material Model for Lateral Torsional Buckling and Biaxial Bending of Steel W-Shapes

A new material model for beam elements was developed for use as normalized tangent modulus expressions when performing 3-dimensional second-order inelastic analyses of steel I-section beams.The stiffness matrix of a 14 degree-of-freedom beam element was updated to include the effects of yielding on St.Venant’s torsion and bimoment stiffness at the initial and terminal nodes.A validation study compared the new model’s results with those from published detailed finite element analyses and was found to be in very close agreement.A biaxial end-moment study with two different depth-to-flange-width ratios provided expected and consistent results over a range of moment conditions.

Discrete Numerical Study on Type II Fracture of Partially Detached Concrete Panels in Cold Region

When the upper chord beam of the beam-string structure(BSS)is made of concrete-filled steel tube(CFST),its overall stiffness will change greatly with the construction of concrete placement,which will have an impact on the design of the tensioning plans and selection of control measures for the BSS.In order to accurately obtain the bending stiffness of CFST beam and clarify its impact on the mechanical properties of composite BSS during con-struction,the influence of some factors such as height-width ratio,wall thickness of steel tube,elasticity modulus of concrete,and friction coefficient on the bending stiffness are analyzed parametrically by the numerical simula-tion technology based on an actual project.The calculation formula of the equivalent bending stiffness of CFST is also established through mathematical statistical simulation.Then,the equivalent bending stiffness is introduced into the construction and use stages of the composite BSS,respectively,and the mechanical properties such as prestress-tensioning control value,structural deformation,and internal force of key members are comparatively analyzed when adopting two different construction plans.Moreover,the optimal construction plan of concrete placementfirst and then prestress-tensioning is proposed.