Theory of Flexural Shear, Bending and Torsion for a Thin-Walled Beam of Open Section

Aspects of the general Vlasov theory are examined separately as applied to a thin-walled channel section cantilever beam under free-end end loading. In particular, the flexural bending and shear that arise under transverse shear and axial torsional loading are each considered theoretically. These analyses involve the location of the shear centre at which transverse shear forces when applied do not produce torsion. This centre, when taken to be coincident with the centre of twist implies an equivalent reciprocal behaviour. That is, an axial torsion applied concentric with the shear centre will twist but not bend the beam. The respective bending and shear stress conversions are derived for each action applied to three aluminium alloy extruded channel sections mounted as cantilevers with a horizontal principal axis of symmetry. Bending and shear are considered more generally for other thin-walled sections when the transverse loading axes at the shear centre are not parallel to the section = s centroidal axes of principal second moments of area. The fixing at one end of the cantilever modifies the St Venant free angular twist and the free warping displacement. It is shown from the Wagner-Kappus torsion theory how the end constrained warping generates an axial stress distribution that varies with the length and across the cross-section for an axial torsion applied to the shear centre. It should be mentioned here for wider applications and validation of the Vlasov theory that attendant papers are to consider in detail bending and torsional loadings applied to other axes through each of the centroid and the web centre. Therein, both bending and twisting arise from transverse shear and axial torsion applied to each position being displaced from the shear centre. Here, the influence of the axis position upon the net axial and shear stress distributions is to be established. That is, the net axial stress from axial torsional loading is identified with the sum of axial stress due to bending and axial stress arising from constrained warping displacements at the fixing. The net shear stress distribution overlays the distributions from axial torsion and that from flexural shear under transverse loading. Both arise when transverse forces are displaced from the shear centre.

Modeling and Free Vibration Behavior of Rotating Composite Thin-walled Closed-section Beams with SMA Fibers

Smart structure with active materials embedded in a rotating composite thin-walled beam is a class of typical structure which is using in study of vibration control of helicopter blades and wind turbine blades. The dynamic behavior investigation of these structures has significance in theory and practice. However, so far dynamic study on the above-mentioned structures is limited only the rotating composite beams with piezoelectric actuation. The free vibration of the rotating composite thin-walled beams with shape memory alloy（SMA） fiber actuation is studied. SMA fiber actuators are embedded into the walls of the composite beam. The equations of motion are derived based on Hamilton＇s principle and the asymptotically correct constitutive relation of single-cell cross-section accounting for SMA fiber actuation. The partial differential equations of motion are reduced to the ordinary differential equations of motion by using the Galerkin＇s method. The formulation for free vibration analysis includes anisotropy, pitch and precone angle, centrifugal force and SMA actuation effect. Numerical results of natural frequency are obtained for two configuration composite beams. It is shown that natural frequencies of the composite thin-walled beam decrease as SMA fiber volume and initial strain increase and the decrease in natural frequency becomes more significant as SMA fiber volume increases. The actuation performance of SMA fibers is found to be closely related to the rotational speeds and ply-angle. In addition, the effect of the pitch angle appears to be more significant for the lower-bending mode ones. Finally, in all cases, the precone angle appears to have marginal effect on free vibration frequencies. The developed model can be capable of describing natural vibration behaviors of rotating composite thin-walled beam with active SMA fiber actuation. The present work extends the previous analysis done for modeling passive rotating composite thin-walled beam.

GEOMETRICALLY NONLINEAR FINITE ELEMENT MODEL OF SPATIAL THIN-WALLED BEAMS WITH GENERAL OPEN CROSS SECTION

Based on the theory of Timoshenko and thin-walled beams, a new finite element model of spatial thin-walled beams with general open cross sections is presented in the paper, in which several factors are included such as lateral shear deformation, warp generated by nonuni- form torsion and second-order shear stress, coupling of flexure and torsion, and large displacement with small strain. With an additional internal node in the element, the element stiffness matrix is deduced by incremental virtual work in updated Lagrangian （UL） formulation. Numerical examples demonstrate that the presented model well describes the geometrically nonlinear property of spatial thin-walled beams.

Experimental study on seismic behavior of semi-rigid connection between steel beam and concrete wall

Beam-column or beam-wall connections are an important problem in high-rise buildings. In this study, based on the analysis of an example structure, an analytical model for design of the semi-rigid connections between steel beams and RC walls in high-rise hybrid buildings is proposed. Also, the mechanical characteristics of these connections subjected to low-reversed cyclic loading are investigated through comparison of experimental results from three semi-rigid connections and two rigid connections. Moreover, some latent problems for design of these connections as well as the corresponding solutions are discussed. The results from the experiments and analyses indicate that semi-rigid connections exhibit satisfactory capacity and seismic performance, and the proposed design can be used in practice.

Optimal Design for Thin-Walled Box Beam Based on Material Strength Reliability

According to the reliability of material strength,the optimal design for the cross sectional size of thin walled box beam was studied.Firstly the cross sectional size as design random variable was determined,then its stochastic nature was researched,with which the objective function is to seek the maximum reliability of the beam under given constraint conditions.This way is not the same as the conventional optimal design for the minimum weight of the material.With establishing the optimal objective,the reliability of the material under conditions of static and fatigue was considered.The corresponding calculated expressions are given.Normally the cross section sizes are fitted to the normal distribution,for the simplification of the design variable,the variation of the section size is assumed as a dependent variable proportional to the mean of the size.The way is different not only with the conventional optimal design but also with the common reliability design.The maximum reliability of material is obtained,meanwhile the area of the cross section is reduced,i.e.,the weight of the material is decreased.

Rapid Repair of Earthquake Damaged RC Interior Beam-wide Column Joints and Beam-wall Joints Using FRP Composites

This paper studies the seismic performance of FRP-strengthened RC interior non-seismically detailed beam-wide columns and beam-wall joints after limited seismic damage.Four eccentric and concentric beam-wide column joints and two beam-wall joints,initially damaged in a previous study,were repaired and tested under constant axial loads(0.1fc′Ag and 0.35fc′Ag) and lateral cyclic loading.The rapid repair technique developed,aimed to restore the original strength and to provide minimum drift capacity.The repair schemes were characterized by the use of:(a) epoxy injections and polymer modified cementitious mortar to seal the cracks and replace spalled concrete;and(b) glass(GFRP) and carbon(CFRP) sheets to enhance the joint performance.The FRP sheets were effectively prevented against possible debonding through the use of fiber anchors.Comparison between responses of specimens before and after repair clearly indicated reasonable restoration in strength,drift capacity,stiffness and cumulative energy dissipation capacity.All specimens failed with delamination of FRP sheets at beam-column joint interfaces.The rapid repair technique developed in this study is recommended for mass upgrading or repair of earthquake damaged beam-column joints.

Analysis and seismic tests of composite shear walls with CFST columns and steel plate deep beams

A composite shear wall concept based on concrete filled steel tube （CFST） columns and steel plate （SP） deep beams is proposed and examined in this study. The new wall is composed of three different energy dissipation elements： CFST columns; SP deep beams; and reinforced concrete （RC） strips. The RC strips are intended to allow the core structural elements - the CFST columns and SP deep beams - to work as a single structure to consume energy. Six specimens of different configurations were tested under cyclic loading. The resulting data are analyzed herein. In addition, numerical simulations of the stress and damage processes for each specimen were carried out, and simulations were completed for a range of location and span-height ratio variations for the SP beams. The simulations show good agreement with the test results. The core structure exhibits a ductile yielding mechanism characteristic of strong column-weak beam structures, hysteretic curves are plump and the composite shear wall exhibits several seismic defense lines. The deformation of the shear wall specimens with encased CFST column and SP deep beam design appears to be closer to that of entire shear walls. Establishing optimal design parameters for the configuration of SP deep beams is pivotal to the best seismic behavior of the wall. The new composite shear wall is therefore suitable for use in the seismic design of building structures.

Microstructures and Properties of 550 MPa Grade High Strength Thin-walled H-beam Steel

The microstructures and mechanical properties of 550 MPa grade lightweight high strength thin-walled H-beam steel were experimentally studied. The experimental results show that the microstructure of the air-cooled H-beam steel sample is consisted of ferrite, pearlite and a small amount of granular bainites as well as fine and dispersive V（C,N） precipitates. The microstructure of the water-cooled steel sample is consisted of ferrite and bainite as well as a small amount of fine pearlites. The microstructure of the water-cooled sample is finer than that of the air-cooled sample with the average intercept size of the surface grains reaching to 3.5 gna. The finish rolling temperature of the thin-walled high strength H-beam steel is in the range of 750 ~C-850 ~C. The lower the finish rolling temperature and the faster the cooling rate, the finer the ferrite grains, the volume fraction of bainite is increased through water cooling process. Grain refinement strengthening and precipitation strengthening are used as major strengthening means to develop 550 MPa grade lightweight high strength thin- walled H-beam steel. Vanadium partially soluted in the matrix and contributes to the solution strengthening. The 550 MPa grade high-strength thin-walled H-beam steel could be developed by direct air cooling after hot rolling to fully meet the requirements of the target properties.

A new finite element of spatial thin-walled beams

Based on the theories of Timoshenko＇s beams and Vlasov＇s thin-walled members, a new spatial thin-walled beam element with an interior node is developed. By independently interpolating bending angles and warp, factors such as transverse shear deformation, torsional shear deformation and their Coupling, coupling of flexure and torsion, and second shear stress are considered. According to the generalized variational theory of Hellinger-Reissner, the element stiffness matrix is derived. Examples show that the developed model is accurate and can be applied in the finite element analysis of thinwalled structures.

Static behavior of semi-rigid thin-walled steel-concrete composite beam-to-column joints with bolted partial-depth flush end plate:experimental study

A new type of semi-rigid thin-walled steel-concrete composite beam-to-column joint has been proposed in this paper.Five semi-rigid composite beam-to-column joint specimens subjected to hogging moments under monotonic loading were tested to study the static behavior of this new type of joint.The main variable parameters for the five joint specimens were the longitudinal reinforcement ratio and the joint type.The experimental results designated that the magnitude of extension of the longitudinal reinforcement is the most important factor that influenced the moment-rotation characteristic of the new type of joint.The concrete slabs could resist 3.8%-19.1% of the total shear load applied to the cross-sections near the beam-to-column connection.The edge stiffened elements,such as the flange of the lipped I-section thin-walled steel beam,were capable of having considerable inelastic deformation capacity although they had comparatively large width-to-thickness ratios.The shear failure of the concrete cantilever edge strip must be taken into account in practical design because it has significant influence on the anchorage of the longitudinal reinforcement in the new type of external joints.

THE ANALYSIS OF THIN WALLED COMPOSITE LAMINATED HELICOPTER ROTOR WITH HIERARCHICAL WARPING FUNCTIONS AND FINITE ELEMENT METHOD

In the present paper, a series of hierarchical warping functions is developed to analyze the static and dynamic problems of thin walled composite laminated helicopter rotors composed of several layers with single closed cell. This method is the development and extension of the traditional constrained warping theory of thin walled metallic beams, which had been proved very successful since 1940s. The warping distribution along the perimeter of each layer is expanded into a series of successively corrective warping functions with the traditional warping function caused by free torsion or free beading as the first term, and is assumed to be piecewise linear along the thickness direction of layers. The governing equations are derived based upon the variational principle of minimum potential energy for static analysis and Rayleigh Quotient for free vibration analysis. Then the hierarchical finite element method. is introduced to form a,. numerical algorithm. Both static and natural vibration problems of sample box beams axe analyzed with the present method to show the main mechanical behavior of the thin walled composite laminated helicopter rotor.

Finite difference modeling of sinking stage curved beam based on revised Vlasov equations

For the static analysis of the sinking stage curved beam, a finite difference model was presented based on the proposed revised Vlasov equations. First, revised Vlasov equations for thin-walled curved beams with closed sections were deduced considering the shear strain on the mid-surface of the cross-section. Then, the finite difference formulation of revised Vlasov equations was implemented with the parabolic interpolation based on Taylor series. At last, the finite difference model was built by substituting geometry and boundary conditions of the sinking stage curved beam into the finite difference formulation. The validity of present work is confirmed by the published literature and ANSYS simulation results. It can be concluded that revised Vlasov equations are more accurate than the original one in the analysis of thin-walled beams with closed sections, and that present finite difference model is applicable in the evaluation of the sinking stage curved beam.

A new beam element for analyzing geometrical and physical nonlinearity

Based on Timoshenko＇s beam theory and Vlasov＇s thin-walled member theory, a new model of spatial thin-walled beam element is developed for analyzing geometrical and physical nonlinearity, which incorporates an interior node and independent interpolations of bending angles and warp and takes diversified factors into consideration, such as traverse shear deformation, torsional shear deformation and their coupling, coupling of flexure and torsion, and the second shear stress. The geometrical nonlinear strain is formulated in updated Lagarange （UL） and the corresponding stiffness matrix is derived. The perfectly plastic model is used to account for physical nonlinearity, and the yield rule of von Mises and incremental relationship of Prandtle-Reuss are adopted. Elastoplastic stiffness matrix is obtained by numerical integration based on the finite segment method, and a finite element program is compiled. Numerical examples manifest that the proposed model is accurate and feasible in the analysis of thin-walled structures.

Shear deformable finite beam elements for composite box beams

The shear deformable thin-walled composite beams with closed cross-sections have been developed for coupled flexural, torsional, and buckling analyses. A theoretical model applicable to the thin-walled laminated composite box beams is presented by taking into account all the structural couplings coming from the material anisotropy and the shear deformation effects. The current composite beam includes the transverse shear and the restrained warping induced shear deformation by using the first-order shear deformation beam theory. Seven governing equations are derived for the coupled axial-flexural-torsional-shearing buckling based on the principle of minimum total potential energy. Based on the present analytical model, three different types of finite composite beam elements, namely, linear, quadratic and cubic elements are developed to analyze the flexural, torsional, and buckling problems. In order to demonstrate the accuracy and superiority of the beam theory and the finite beam elements developed by this study,numerical solutions are presented and compared with the results obtained by other researchers and the detailed threedimensional analysis results using the shell elements of ABAQUS. Especially, the influences of the modulus ratio and the simplified assumptions in stress-strain relations on the deflection, twisting angle, and critical buckling loads of composite box beams are investigated.

Fracture Assessment for Electron Beam Welded Damage Tolerant Ti-6Al-4V Alloy by the FITNET Procedure

Fracture assessment of the cracked structures is essential to avoiding fracture failure.A number of fracture assessment procedures have been proposed for various steel structures.However,the studies about the application of available procedures for titanium alloy structures are scarcely reported.Fracture assessment for the electron beam(EB) welded thick-walled damage tolerant Ti-6Al-4V(TC4-DT) alloy is performed by the fitness-for-service(FFS) FITNET procedure.Uniaxial tensile tests and fracture assessment tests of the base metal and weld metal are carried out to obtain the input information of assessment.The standard options and advanced options of FITNET FFS procedure are used to the fracture assessment of the present material.Moreover,the predicted maximum loads of compact tensile specimen using FITNET FFS procedure are verified with the experimental data of fracture assessment tests.As a result,it is shown that the mechanical properties of weld metal are inhomogeneous along the weld depth.The mismatch ratio M is less than 10% at the weld top and middle,whereas more than 10% at the weld bottom.Failure assessment lines of standard options are close to that of advanced option,which means that the standard options are suitable for fracture assessment of the present welds.The accurate estimation of the maximum loads has been obtained by fracture assessment of standard options with error less than 6%.Furthermore,there are no potential advantages of applying higher options or mismatch options.Thus,the present welded joints can be treated as homogeneous material during the fracture assessment,and standard option 1 can be used to achieve accurate enough results.This research provides the engineering treatment methods for the fracture assessment of titanium alloy and its EB welds.

钢管混凝土键连接框架梁和剪力墙的受剪性能

目的 研究钢管混凝土键连接框架梁和剪力墙的受剪性能,为工程应用提供设计依据。方法 应用有限元分析软件ABAQUS对比钢管混凝土键连接与现浇连接梁墙的结构受剪性能,分析前者受剪机理及不同因素对受剪性能的影响。结果 钢管混凝土键连接梁墙的结构承载力和延性系数较现浇结构分别提高约10%和34%;钢材强度从Q235到Q390,初始刚度增加8.44%;截面高度从100 mm到120 mm,延性系数提高17.73%;截面厚度每增加2 mm,承载力提高约15%;截面长度和混凝土强度等级对承载力、初始刚度和延性系数的影响均小于15%,纵向距离对其受剪性能几乎无影响。结论 采用钢管混凝土键连接梁墙的结构总体受剪性能优于现浇结构;钢材强度和截面厚度分别是影响初始刚度和承载力的主要因素。

FLEXURAL WAVE DISPERSION IN MULTI-WALLED CARBON NANOTUBES CONVEYING FLUIDS

Motivated by the great potential of carbon nanotubes for developing nanofluidic devices, this paper presents a nonlocal elastic, Timoshenko multi-beam model with the second order of strain gradient taken into consideration and derives the corresponding dispersion relation of flexural wave in multi-walled carbon nanotubes conveying fuids. The study shows that the moving flow reduces the phase velocity of flexural wave of the lowest branch in carbon nanotubes. The phase velocity of flexural wave of the lowest branch decreases with an increase of flow velocity. However, the effects of flow velocity on the other branches of the wave dispersion are not obvious. The effect of microstructure characterized by nonlocal elasticity on the dispersion of flexural wave becomes more and more remarkable with an increase in wave number.

Selection of isolated and individual single-walled carbon nanotube from a film and its usage in nanodevices

Individual and isolated single-walled carbon nanotubes （SWNTs） are important for fabricating relevant nanodevices and studying the properties of the SWNT devices. In this work, we demonstrate that individual and isolated SWNT can be selected and obtained from a film containing a huge number of SWNTs. By using both the polymethylmethacrylate （PMMA） as a negative resist and the electron beam lithography, the selected SWNT can be fixed on a substrate, while the other SWNTs in the film can lift off. The selected SWNT can be used to fabricate nanodevice and a gas sensor of oxygen is demonstrated in this work.

模块化防屈曲钢板墙抗震性能

考虑经济性和便利性,提出了模块化防屈曲钢板墙及其常用模数,然后基于已有的防屈曲钢板墙的简化计算模型,推导了在不同墙数量情况下,模块化防屈曲钢板墙充分发挥抗震性能时,周边梁的承载力和刚度需求,并提出了周边梁的设计方法.进而,对模块化防屈曲钢板墙和整体墙进行了对比验证试验及其有限元模拟分析.研究结果表明:模块化防屈曲钢板墙能够达到与整体钢板墙相同的抗震性能,且周边梁未发生明显转动和破坏,说明所提出的周边梁设计方法是合理的;在层间位移角为1/50时,防屈曲钢板墙上下周边梁均未进入塑性,且承载力和初始刚度等的有限元值与试验值误差小于6%,从而进一步验证了其抗震性能.

Experimental and analytical study on seismic behavior of steel-concrete multienergy dissipation composite shear walls

In this paper, a steel-concrete multi-energy dissipation composite shear wall, comprised of steel-reinforced concrete （SRC） columns, steel plate （SP） deep beams, a concrete wall and energy dissipation strips, is proposed. In order to study the multi-energy dissipation behavior and restorability after an earthquake, two stages of low cyclic loading tests were carded out on ten test specimens. In the first stage, test on five specimens with different number of SP deep beams was carried out, and the test lasted until the displacement drift reached 2%. In the second stage, thin SPs were welded to both sides of the five specimens tested in the first stage, and the same test was carried out on the repaired specimens （designated as new specimens）. The load-bearing capacity, stiffness, ductility, hysteretic behavior and failure characteristics were analyzed for both stages and the results are discussed herein. Extrapolating from these results, strength calculation models and formulas are proposed herein and simulations using ABAQUS carried out, they show good agreement with the test results. The study demonstrates that SRC columns, SP deep beams, concrete wall and energy dissipation strips cooperate well and play an important role in energy dissipation. In addition, this study shows that the shear wall has good recoverability after an earthquake, and that the welding of thin SP＇s to repair a deformed wall is a practicable technique.