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.

Numerical Analysis of Flow-Induced Vibration and Noise Generation in a Variable Cross-Section Channel

Flow channels with a variable cross-section are important components of piping system and are widely used in variousfields of engineering.Using afinite element method and modal analysis theory,flow-induced noise,mode shapes,and structure-borne noise in such systems are investigated in this study.The results demonstrate that the maximum displacement and equivalent stress are located in the part with variable cross-sectional area.The aver-age excitation force on theflow channel wall increases with theflow velocity.The maximum excitation force occurs in the range of 0–20 Hz,and then it decreases gradually in the range of 20–1000 Hz.Additionally,as theflow velocity rises from 1 to 3 m/s,the overall sound pressure level associated with theflow-induced noise grows from 49.37 to 66.37 dB.Similarly,the overall sound pressure level associated with the structure-borne noise rises from 40.27 to 72.20 dB.When theflow velocity is increased,the increment of the structure-borne noise is higher than that of theflow-induced noise.

Analysis of the mass of behind-armor debris generated by RHA subjected to normal penetration of variable cross-section EFP

Analyzing the mass of behind-armor debris (BAD) generated by Rolled Homogeneous Armor (RHA) subjected to normal penetration of variable cross-section Explosively Formed Projectile (EFP) is the purpose of this paper. So theoretical analysis, numerical simulation and experimental data are combined to analyze the influence of variable cross-section characteristic on the time history of crater radius. Moreover the relationships between time history of crater radius (as well as mass of BAD) and the thickness of RHA (from 30mm to 70 mm) and the impact velocity of EFP (1650 m/s to 1860 m/s) are also investigated. The results indicate that: 1) being compared to the variable cross-section characteristic is ignored, the theoretical time history of crater radius is in better agreement with the simulation results when the variable cross-section characteristic is considered;2) being compared to the other three conditions of plug, the theoretical mass of BAD is in the best agreement with the simulation results when the shape of plug is frustum of a cone and the angle between generatrix and bottom is 45- and the axial length of mushroom is considered.

Modeling and analysis of piezoelectric beam with periodically variable cross-sections for vibration energy harvesting

A bimorph piezoelectric beam with periodically variable cross-sections is used for the vibration energy harvesting. The effects of two geometrical parameters on the first band gap of this periodic beam are investigated by the generalized differential quadrature rule （GDQR） method. The GDQR method is also used to calculate the forced vibration response of the beam and voltage of each piezoelectric layer when the beam is subject to a sinusoidal base excitation. Results obtained from the analytical method are compared with those obtained from the finite element simulation with ANSYS, and good agreement is found. The voltage output of this periodic beam over its first band gap is calculated and compared with the voltage output of the uniform piezoelectric beam. It is concluded that this periodic beam has three advantages over the uniform piezoelectric beam, i.e., generating more voltage outputs over a wide frequency range, absorbing vibration, and being less weight.

Dynamic Deformation Monitoring of Lotsane Bridge Using Global Positioning Systems (GPS) and Linear Variable Differential Transducers (LVDT)

The measurements and analysis of deformation of engineering structures such as dams, bridges and high-rise buildings are important tasks for civil engineers. It is evident that, all civil engineering structures are susceptible for deterioration over a period of time. Bridges in particular, deteriorate due to loading conditions, environmental changes, earth movement, material used during construction, age and corrosion of steel. Continuous monitoring of such structure is the most important aspect as it provides quantitative information, assesses the state of the structure, detects unsafe positions and proposes early safety measures to be taken before it can threaten the safety of vehicles, goods and human life. Despite government’s efforts to construct roads and highways, bridge deformation monitoring has not been given priority in most of African countries and ultimately causes some bridges to collapse unexpectedly. The purpose of this research is to integrate Global Positioning System (GPS) and Linear Variable Differential Transducers (LVDT) to monitor deformation of a bridge. The horizontal positions of reference and monitoring points were determined using Global Positioning System (GPS) while the vertical deflections, accelerations and strain were determined using Linear Variable Differential Transducers (LVDT). The maximum displacements obtained between zero and first epochs in x, y and z components were 0.798 m, at point LT08, 0.865 m at point BR13, and 0.56 m at point LT02 respectively. The maximum deflections for LVDT 1, 2 and 3 are 28.563 mm, 31.883 mm and 40.926 mm respectively. Finally, the correlation coefficient for the observations was 0.679 with standard deviations of 0.0168 and 0.0254 in x and y respectively. Our results identified some slight displacements in horizontal components at the bridge.

Study of the Bearing Capacity at the Variable Cross-Section of A Riser- Surface Casing Composite Pile

Reducing the cost of offshore platform construction is an urgent issue for marginal oilfield development.The offshore oil well structure includes a riser and a surface casing.The riser,surface casing and oil well cement can be considered special variable cross-section piles.Replacing or partially replacing the steel pipe pile foundation with a variable cross-section pile to provide the required bearing capacity for an offshore oil platform can reduce the cost of foundation construction and improve the economic efficiency of production.In this paper,the finite element analysis method is used to investigate the variable cross-section bearing mode of composite piles composed of a riser and a surface casing in saturated clay under a vertical load.The calculation formula of the bearing capacity at the variable section is derived based on the theory of spherical cavity expansion,the influencing factors of the bearing capacity coefficient N_(c) are revealed,and the calculation method of N_(c) is proposed.By comparing the calculation results with the results of the centrifuge test,the accuracy and applicability of the calculation method are verified.The results show that the riser composite pile has a rigid core in the soil under the variable cross-section,which increases the bearing capacity at the variable cross-section.

The development of real time data driving multi-axis linkage and synergic movement control system of 3D variable cross-section roll forming machine

The three dimensional variable cross-section roll forming is a kind of new metal forming technol- ogy which combines large forming force, multi-axis linkage movement and space synergic movement, and the sequential synergic movement of the ganged roller group is used to complete the metal sheet forming according to the shape of the complicated and variable forming part data. The control system should meet the demands of quick response to the test requirements of the product part. A new kind of real time data driving multi-axis linkage and synergic movement control strategy of 3D roll forming is put forward in the paper. In the new control strategy, the forming data are automatically generated according to the shape of the parts, and the multi-axis linkage movement together with cooperative motion among the six stands of the 3D roll forming machine is driven by the real-time information, and the control nodes are also driven by the forming data. The new control strategy is applied to a 48 axis 3D roll forming machine developed by our research center, and the control servo period is less than 10ms. A forming experiment of variable cross section part is carried out, and the forming preci- sion is better than ＋ 0.5mm by the control strategy. The result of the experiment proves that the control strategy has significant potentiality for the development of 3D roll forming production line with large scale, multi-axis ganged and svner^ic movement

CFD-Based Numerical Analysis of a Variable Cross-Section Cylinder

Using ANSYS-CFX, a general purpose fluid dynamics program, the vortex-induced vibration(VIV) of a variable cross-section cylinder is simulated under uniform current with high Reynolds numbers. Large eddy simulation(LES) is conducted for studying the fluid-structure interaction. The vortex shedding in the wake, the motion trajectories of a cylinder, the variation of drag and lift forces on the cylinder are analyzed. The results show that the vortices of variable cross-section cylinder are chaotic and are varying along the cylinder. In places where cross-sections are changing significantly, the vortices are more irregular. The motion trail of the cylinder is almost the same but irregular. The drag and lift coefficients of the cylinder are varying with the changes of diameters.

In-Plane Impact Dynamics Analysis of Re-Entrant Honeycomb with Variable Cross-Section

Due to the unique deformation characteristics of auxetic materials(Poisson’s ratioμ<0),they have better shock resistance and energy absorption properties than traditional materials.Inspired by the concept of variable crosssection design,a new auxetic re-entrant honeycomb structure is designed in this study.The detailed design method of re-entrant honeycomb with variable cross-section(VCRH)is provided,and five VCRH structures with the same relative density and different cross-section change rates are proposed.The in-plane impact resistance and energy absorption abilities of VCRH under constant velocity are investigated by ABAQUS/EXPLICIT.The results show that the introduction of variable cross-section design can effectively improve the impact resistance and energy absorption abilities of auxetic re-entrant honeycombs.The VCRH structure has better Young’s modulus,plateau stress,and specific energy absorption(SEA)than traditional re-entrant honeycomb(RH).The influence of microstructure parameters(such as cross-section change rateα)on the dynamic impact performance of VCRH is also studied.Results show that,with the increase in impact velocity andα,the plateau stress and SEA of VCRH increase.A positive correlation is also found between the energy absorption efficiency,impact load uniformity andαunder both medium and high impact speeds.These results can provide a reference for designing improved auxetic re-entrant honeycomb structures.

Dynamic symmetry breaking and structure-preserving analysis on thelongitudinal wave in an elastic rod with a variable cross-section

The longitudinal wave propagating in an elastic rod with a variable cross-section owns wide engineering background,in which the longitudinal wave dissipation determines some important performances of the slender structure.To reproduce the longitudinal wave dissipation effects on an elastic rod with a variable cross-section,a structure-preserving approach is developed based on the dynamic symmetry breaking theory.For the dynamic model controlling the longitudinal wave propagating in the elastic rod with the variable cross-section,the approximate multi-symplectic form is deduced based on the multi-symplectic method,and the expression of the local energy dissipation for the longitudinal wave propagating in the rod is presented,referring to the dynamic symmetry breaking theory.A structure-preserving method focusing on the residual of the multi-symplectic structure and the local energy dissipation of the dynamic model is constructed by using the midpoint difference discrete method.The longitudinal wave propagating in an elastic rod fixed at one end is simulated,and the local/total energy dissipations of the longitudinal wave are investigated by the constructed structure-preserving scheme in two typical cases in detail.

THE APPROXIMATE ANALYTICAL SOLUTION FOR THE BUCKLING LOADS OF A THIN-WALLED BOX COLUMN WITH VARIABLE CROSS-SECTION

For a thin-walled box column with variable cross-section, the three governing equations for torsional-flexural buckling are ordinary differential equations of the second or fourth order with variable coefficients, so it is very difficult to solve them by means of an analytic method. In this paper, polynomials are used to approximate the geometric properties of cross-section and certain coefficients of the differential equations. Based on the energy principle and the Galerkin's method, the approximate formulas for calculating the flexural and torsional buckling loads of this kind of columns are developed respectively, and numerical examples are used to verify the correctness of the solutions obtained. The results calculated in this paper provide the basis for demonstrating the stability of thin-walled box columns with variable cross-section. This paper is of practical value.

An extended multiple-support response spectrum method incorporating fluid-structure interaction for seismic analysis of deep-water bridges

The effects of ground motion spatial variability(GMSV)or fluid-structure interaction(FSI)on the seismic responses of deep-water bridges have been extensively examined.However,there are few studies on the seismic performance of bridges considering GMSV and FSI effects simultaneously.In this study,the original multiple-support response spectrum(MSRS)method is extended to consider FSI effect for seismic analysis of deep-water bridges.The solution of hydrodynamic pressure on a pier is obtained using the radiation wave theory,and the FSI-MSRS formulation is derived according to the random vibration theory.The influence of FSI effect on the related coefficients is analyzed.A five-span steel-concrete continuous beam bridge is adopted to conduct the numerical simulations.Different load conditions are designed to investigate the variation of the bridge responses when considering the GMSV and FSI effects.The results indicate that the incoherence effect and wave passage effect decrease the bridge responses with a maximum percentage of 86%,while the FSI effect increases the responses with a maximum percentage of 26%.The GMSV and FSI effects should be included in the seismic design of deep-water bridges.

METHOD FOR BRIDGE BEARING CAPACITY ASSESSMENT BASED ON ANALYTIC HIERARCHY PROCESS

By analyzing the existing methods for the bridge bearing capacity assessment, an analytic hierarchy pro cess estimation model with a variable weight and fuzzy description is proposed based on the nondestructive infor mation. Considering the actual strength, the bearing capacity is first calculated from its design state, and then modified based on the detection information. The modification includes the section reduction and the structure deterioration. The section reduction involves the concrete section and the steel cross-section reduction. The structure deterioration is decided by six factors, i.e. , the concrete surface damage, the actual concrete strength, the steel corrosion electric potential, the chloride ion content, the carbonization depth, and the protective layer depth. The initial weight of each factor is calculated by the expert judgment matrix using an analytic hierarchy process. The consistency approximation and the error transfer theory are used. Then, the variable weight is in- troduced to expand the influences of factors in the worse state. Finally, an actual bridge is taken as an example to verify the proposed method. Results show that the estimated capacity agrees well with that of the load test, thus the method is objective and credible

Failure analysis and control technology of intersections of large‑scale variable cross‑section roadways in deep soft rock

In deep underground mining,achieving stable support for roadways along with long service life is critical and the complex geological environment at such depths frequently presents a major challenge.Owing to the coupling action of multiple factors such as deep high stress,adjacent faults,cross-layer design,weak lithology,broken surrounding rock,variable cross-sections,wide sections up to 9.9 m,and clusters of nearby chambers,there was severe deformation and breakdown in the No.10 intersection of the roadway of large-scale variable cross-section at the−760 m level in a coal mine.As there are insufcient examples in engineering methods pertaining to the geological environment described above,the numerical calculation model was oversimplifed and support theory underdeveloped;therefore,it is imperative to develop an efective support system for the stability and sustenance of deep roadways.In this study,a quantitative analysis of the geological environment of the roadway through feld observations,borehole-scoping,and ground stress testing is carried out to establish the FLAC 3D variable cross-section crossing roadway model.This model is combined with the strain softening constitutive(surrounding rock)and Mohr–Coulomb constitutive(other deep rock formations)models to construct a compression arch mechanical model for deep soft rock,based on the quadratic parabolic Mohr criterion.An integrated control technology of bolting and grouting that is mainly composed of a high-strength hollow grouting cable bolt equipped with modifed cement grouting materials and a high-elongation cable bolt is developed by analyzing the strengthening properties of the surrounding rock before and after bolting,based on the Heok-Brown criterion.As a result of on-site practice,the following conclusions are drawn:(1)The plastic zone of the roof of the cross roadway is approximately 6 m deep in this environment,the tectonic stress is nearly 30 MPa,and the surrounding rock is severely fractured.(2)The deformation of the roadway progressively increases from small to large cross-sections,almost doubling at the largest cross-section.The plastic zone is concentrated at the top plate and shoulder and decreases progressively from the two sides to the bottom corner.The range of stress concentration at the sides of the intersection roadway close to the passageway is wider and higher.(3)The 7 m-thick reinforced compression arch constructed under the strengthening support scheme has a bearing capacity enhanced by 1.8 to 2.3 times and increase in thickness of the bearing structure by 1.76 times as compared to the original scheme.(4)The increase in the mechanical parameters c andφof the surrounding rock after anchoring causes a signifcant increase inσt;the pulling force of the cable bolt beneath the new grouting material is more than twice that of ordinary cement grout,and according to the test,the supporting stress feld shows that the 7.24 m surrounding rock is compacted and strengthened in addition to providing a strong foundation for the bolt(cable).On-site monitoring shows that the 60-days convergence is less than 30 mm,indicating that the stability control of the roadway is successful.

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.

Semi-active Control with Variable Damper for Pier-Beam Transversal Vibration

In this paper, the method of semi-active control with variable damper is presented to deal with the relatively poor transversal seismic condition of bridge. Based on the LQR control algorithm the control effectiveness for transverse vibration of pier-beam structure of bridge are discussed. Taking the structure as a multiple-degree of freedom system, the calculating model of structure-variable damper system is set up and the differential equation is derived, combined with practical example the control system is simulated and studied by various semi-active control algorithms and passive strategy with MATLAB. The results show that the semi-active control with variable damper can decrease the transverse vibration effectively and the control effect is obvious.

Identification of Connection Flexibility Effects Based on Load Testing of a Steel-Concrete Bridge

In the case of composite girders, an effective cooperation of both parts of the section is influenced by deformability of connectors. Limited flexural stiffness of welded studs, used commonly in bridge structures, does not provide full interaction of a steel beam and a concrete slab. This changes strain distribution in cross-sections of a composite girder and results in redistribution of internal forces in steel and concrete element. In the paper partial interaction index defined on the basis of a neutral axis position, which can be used for verification of steel-concrete interaction in real bridge structures rather than in specimens is proposed. The range of the index value changes, obtained during load testing of a typical steel-concrete composite beam bridge, is presented. The investigation was carried out on a motorway viaduct, consisting of two parallel structures. During the testing values of strains in girders under static and quasi-static loads were measured. The readings from the gauges were used to determine the index, characterizing composite action of the girders. Results of bridge testing under movable load, changing position along the bridge span is presented and obtained in-situ influence functions of strains and index values are commented in the paper.

大跨度斜拉桥模态参数长期追踪及其变异性分析

为了丰富大跨度斜拉桥模态参数的实测数据库,依托苏通大桥结构健康监测系统采集的数据,采用所建立的模态自动识别和追踪方法,获取了2010年期间该桥的模态参数值,并据此分析了在温度和风速作用下桥梁模态参数的变异性。研究结果表明,大桥主梁模态频率的变化受温度和风速共同影响,随着温度的升高而降低,随着风速的升高而增加。大桥主梁模态阻尼比的变异性显著大于模态频率,低风速下主梁一阶侧弯阻尼比在0.5%~15%之间波动,风速大于9 m/s时逐渐降低并稳定在2%左右。大桥主梁前四阶竖弯阻尼比受气动阻尼的影响较大,在风速较小时随着风速的增加略有增加。研究结果可为大桥的服役性能评估与运营管理提供参考。

盾构施工诱发临近桥梁安全风险评价

针对地铁盾构施工诱发临近桥梁安全风险评估结果不完善、存在失真等问题,提出一种基于变权可拓云模型的盾构施工诱发临近桥梁安全风险评价方法。首先,结合以往研究基础和实际工程经验,建立盾构施工诱发临近桥梁安全事故机理模型,进而确定孕险环境、致险因子和承险体3个1级指标,其中包括有岩土层物理性能参数、隧道工程条件、盾构施工条件、盾构施工参数、施工管理风险、桥梁现状及桥梁自身条件7个2级指标和内摩擦角、弹性模量等27个3级指标为依据建立盾构施工诱发临近桥梁安全风险评价指标体系。其次,通过改进CRITIC客观赋权法获取评价指标权重,并采用变权可拓云模型构建盾构施工诱发临近桥梁安全风险评价模型,其中引入变权理论得到使评价结果更加科学合理的变化权重。最后,对某市轨道交通1号线一期工程Ⅱ标段沿线桥梁进行实例分析。研究结果表明,4座盾构施工临近桥梁安全风险等级分别为Ⅲ、Ⅱ、Ⅱ、Ⅰ级。其中,该施工场地各项土体指标、隧道覆跨比、隧道埋深、隧道直径及桥桩与隧道的相对位置等指标风险较大,即该段隧道盾构施工时对于桥梁自身情况及其施工场地环境需要重点监测,并严格做好周围土体加固等各项技术措施。研究结果可为盾构施工诱发临近桥梁安全风险防控提供科学有效的参考依据。

震陷场地变截面单桩动力特性与损伤评价

为探明震陷场地变截面单桩动力响应特性与损伤状况,以翔安大桥为工程背景,基于大型振动台试验,开展了0.10g~0.45g地震动强度下变截面单桩动力响应特性的研究,评价分析了变截面单桩损伤程度。结果表明:受桩周软弱土层震陷特性的影响,变截面单桩桩顶水平位移动力响应、桩身加速度动力响应及桩身弯矩动力响应均随地震动强度增大呈增大趋势,桩基基频逐渐减小;变截面单桩弯矩最大值出现在震陷土层分界处,地震动强度为0.30g时,超过了其抗弯承载力;地震动强度为0.20g时,变截面单桩桩顶水平位移、桩身加速度、桩身弯矩显著增大,桩基基频突降。基于系统损伤理论,震陷场地变截面单桩损伤状况分为稳定阶段、加剧损伤阶段、塑性破坏阶段共3个阶段。试验结束后,变截面位置处产生弯曲塑性破坏。