Frictional Dissipation in Axially Loaded Simple Straight Strands

In this paper, an analytical investigation is made of the frictional damping properties of axially loaded metallic cables made from one layer of wires helically wrapped around a central wire. Our efforts are focused on the quantity of energy dissipated through friction due to the motions between wires when a cable is loaded. Although the local interwire pivoting drives the response of the cables studied, a first linear model is built where pivoting is allowed, but friction is not taken into account. Then, a law of friction is established and linearized to extend the linear model into a tractable piecewise linear hysteretic one. Through a variety of examples, it appears that the energy dissipated in friction over a load cycle is very small compared to other sources of dissipation, because axially loaded simple straight strands do not experience fretting-induced failures, except close to terminations. It is also shown that modifying the design of such cables is not expected to significantly improve their damping properties.     

Design of Mechanical Viscous Dampers for Stay Cables

External dampers have been utilized in a number of cable-stayed bridges to suppress transverse cable vibrations. However, simple and accurate damper design recommendations that concurrently consider all important cable parameters are lacking. Previous efforts have been based on the idealization of cables as taut strings. In this paper, the governing differential equation for vibration of cables containing a viscous damper was first converted to a complex eigenvalue problem containing nondimensional cable parameters. Then, a parametric study was conducted involving repeated solutions of the eigenvalue problem for a wide range of nondimensional parameters. Based on the results of the parametric study, the effects of dampers on first mode vibration frequencies and first mode cable damping ratios were presented in nondimensional format. It is shown that for the range of parameters involved in most stay cables, the influence of cable sag is insignificant, whereas the cable bending stiffness can have a significant influence on the resulting cable damping ratios. Simplified nondimensional relationships are proposed for calculating damper-induced changes in the first mode cable damping ratios. Results of laboratory tests on a scaled model cable are compared with the estimated values using the formulation presented. Finally, example problems are presented for comparison with other relationships, and for the design of mechanical viscous dampers for suppression of cable vibrations including rain-wind induced vibrations.     

Three-Dimensional Elastic Catenary Cable Element Considering Sliding Effect

The nonlinear behavior of cable-supported bridges is governed by the geometric nonlinearity of cables, which is attributable to sag and sliding effects at the saddle. In a cable-stayed bridge with a midspan saddle, and in all suspension bridges, cable sliding can occur at the saddle under extreme forces, such as those caused by an earthquake or typhoon. However, the conventional method of analysis of cable-supported bridges does not consider the effect of cable sliding at the saddle; instead it regards those cables as fixed. This assumption might lead to a misunderstanding of the global structure system. The goal of this study is to develop a three-dimensional (3D) elastic cable finite element that considers the sliding effect and uses a geometric nonlinear cable finite element based on elastic catenary theory. In this study, two types of sliding were considered: the roller sliding condition without friction and the frictional sliding condition. These were formulated to derive the nodal force vectors and tangential stiffness matrices. To validate the proposed 3D cable sliding element, experiments were conducted for both sliding conditions, and results were compared with calculations of the amount of sliding and displacement at the loading point. In addition, a cable-supported structural system was analyzed to investigate the characteristics of a realistic structure with cable sliding. Overall calculations using the 3D cable sliding model were in very good agreement with the measured values.     

Control of Scour at Vertical Circular Piles under Waves and Current

An experimental study on the control of scour at vertical circular piles under monochromatic waves and a steady current is presented. The experiments on wave and steady currents were carried out under live-bed and clear-water regimes, respectively. In waves, splitter plate attached to the pile along the vertical plane of symmetry and threaded pile (helical wires or cables wrapped spirally on the pile to form threads) were found to be effective to reduce the scour depth. For the Keulegan–Carpenter numbers 6–100, the vortex shedding is the main mechanism of scour under waves. The splitter plate and threaded pile disrupt the vortex shedding. The average reduction of the scour depth by the splitter plate was 61.6%. For threaded piles, different combinations of cable and pile sizes were tested, and the best combination was found for a cable–pile diameter ratio equaling 0.75, in which average scour depth reduction was 51.1%. The average reductions of scour depths for other cable–pile diameter ratios of 0.33 and 0.5 were 43.2 and 48.1%, respectively. On the other hand, in a steady current, the threaded pile proved to be effective to control scour depth to a great extent. Cables wrapped spirally forming threads on the pile help to weaken the downflow and horseshoe vortex, which are the principal agents of scour under a steady current. The experimental results showed that the scour depth consistently decreases with an increase in cable diameter and the number of threads, and with a decrease in thread angle. The maximum reduction of scour depth observed was 46.3% by using a triple threaded pile having a thread angle of 15° and a cable–pile diameter ratio of 0.1. The proposed methods of controlling scour are easy to install and are economical.     

中厚板辊式矫直过程弯辊作用分析

 为了进一步提高中厚板产品矫直质量,采用弹塑性差分的曲率积分方法,分析了弯辊对矫直效果的影响,研究了弯辊量与压下量的关系,为建立中厚板辊式矫直过程的弯辊设定模型奠定了基础。计算结果表明,为了使板材矫直后的残余曲率和残余应力最小化,施加弯辊时要考虑入口压下量的影响。单从降低残余曲率的角度考虑,小压下量和大压下量下都可以施加负弯辊,但正弯辊只适用于小压下量。从控制宽度方向残余应力的角度考虑,正弯辊施加于小入口压下量时弯辊作用明显,为了消除正弯辊对厚度方向残余应力的不利作用,采用正弯辊时入口压下量不宜过大。施加弯辊会增加矫直力,因此设定弯辊量时要考虑矫直机能力的限制。研究发现了弯辊对塑性变形率的影响规律：负弯辊出现了使塑性变形率随着入口压下量的增加而减少的阶段,正弯辊可消除塑性变形率为零的阶段。     

Estimation of Tension in Cables with Intermediate Elastic Supports Using Finite-Element Method

Cables with intermediate elastic supports are widely used in bridge engineering, but there is a lack of effective methods for estimating the tensions in these cables. In this paper, an analytical form of the equilibrium equation for a tension bar has been used to provide a shape function to develop a suitable finite-element model for a cable. A program for estimating the tension in cables with intermediate elastic supports has been developed in which the bending stiffness of the cable, the stiffness of the end restraints, and the stiffness of the intermediate supports are taken into account by using this element and MATLAB. The program has been verified by comparison of the results from laboratory experiments. The method has been applied to compute the tension in the tie bars of a concrete-filled steel tube arch bridge. This demonstrates that the cable tension estimated by the present method is suitably accurate.     

Isolation System for Vibration Control of Stay Cables

Rain-wind induced cable vibration can cause serious problems in cable-stayed bridges. Externally attached dampers have been used to provide an effective means to suppress the vibration of relatively short stay cables. For very long stay cables, however, such damper systems are rendered ineffective, as the dampers need be attached near the end of the cables for aesthetic reasons. This paper investigates a new stay-cable isolation system to mitigate the cable vibration. The proposed isolation system, which consists of a laminated rubber bearing and an internal damper, may be installed inside of the cable anchorage. A simple analytical model of the cable-damper system is developed first based on the taut string representation of the cable. The response of a cable with the proposed isolation system is obtained and then compared to those of the cable with and without an external passive damper. The proposed stay-cable isolation system is shown to perform better than the optimal passive viscous damper, thereby demonstrating its applicability in large cable-stayed bridges.     

棒材二辊矫直过程曲率的全流程定量解析

为了摸清棒材斜辊矫直过程中各曲率的变化规律,应用小曲率平面弯曲弹复理论以及棒材弯曲弹复的曲率方程式,实现棒材一次反弯弹复的计算模型,基于棒材每旋转半周反弯一次的规律以及上一次弹复后的残余曲率认为是下一次弯曲的原始曲率,建立棒材全流程二辊矫直过程弯曲弹复模型,获得整个矫直过程中原始曲率、弯曲曲率、弹复曲率以及残余曲率的演变过程,得到棒材最终的残余曲率.应用该理论模型对现场生产过程进行了计算,与现场结果一致,验证了理论模型的正确性.应用所建立的理论模型对不同直径、不同材料屈服强度、不同原始挠度的棒材矫直过程分别进行分析,获得了不同来料参数情况下矫直过程的变形规律.该模型可以为二辊矫直机辊型优化设计与工艺参数计算提供理论依据.      

Analytical Model of Curved I-Girder Web Panels Subjected to Bending

Curvature greatly complicates the behavior of curved plate girders used in bridges. The out-of-plane “bulging” displacement of the curved web results in an increase in stress, which must be considered in the design of plate girders with significant curvature. The currently used Guide Specifications for Horizontally Curved Bridges provides web slenderness reduction equations that account for curvature effects, but these equations were based on a regression of limited data from experimental and unit-strip analyses conducted in the early 1970s. This paper presents a theoretically pure analytical model that can be used to predict the transverse displacement and induced plate bending stresses of curved I-shaped plate girder web panels subjected to bending. Several boundary conditions are demonstrated and compared, and the finite-element method is used to verify the closed-form solutions. The effects of curvature on the elastic buckling behavior of curved web panels is also presented. Furthermore, a comprehensive literature review is presented, including numerous Japanese publications not readily available to American researchers.     

Cable Modal Parameter Identification. II: Modal Tests

The cable dynamic stiffness describes the load–deformation behavior that reflects the cable intrinsic dynamic characteristics. It is defined as a ratio of response to excitation and represents a very similar frequency response property to the frequency response function (FRF). Therefore, by fitting both analytical cable dynamic stiffness and measured frequency response function, the modal parameters of cables can be identified. Based on the simplified cable dynamic stiffness proposed in the first part of the two-part paper, this paper presents a cable dynamic stiffness based procedure to identify the cable modal parameters (natural frequencies and damping ratios) by modal tests. To carry out the curve fitting, a nonlinear least-squares approach is used. A numerical simulation example is first introduced to illustrate the feasibility of the proposed method. Further, a series of cable modal tests are conducted in the laboratory with different cable tensions and the frequency response functions are measured accordingly. A number of issues related to the cable modal tests have been discussed, such as accelerometer arrangement and excitation placement, frequency resolution, windowing, and averaging. It is demonstrated that the cable modal parameters can be effectively identified by using the proposed method through the cable modal tests.     

Behavior of Curved I-Girder Webs Subjected to Combined Bending and Shear

Two previous papers by the writers described the buckling and finite-displacement behavior of curved I-girder web panels subjected to pure bending, presented a theoretically pure analytical model, and presented equations that describe the reduction in strength due to curvature. This paper describes the buckling and finite-displacement behavior of curved web panels under combined bending and shear. Unlike straight girder web panels, the addition of shear in curved panels is shown to increase the transverse “bulging” displacement of the web prior to buckling. The accompanying decrease in moment carrying capacity is analyzed in a manner similar to that used for the combined bending and shear nominal strength interaction for straight girder design. Preliminary recommendations are made toward forming design criteria for curved webs.     

Monitoring of Steel Railway Floor Beams Prestressed by Steel Plates

Steel cables and tendons are commonly used in reinforcing steel beams as well as in concrete beams. However, the structural detail of cable anchors in steel beams tends to be complicated, and the effect on reducing live load stresses is not significant because of the relatively small stiffness of cables and tendons. On the contrary, by using high strength steel plates instead of cables and tendons, structural detail of the anchor area becomes simpler, and live load stresses as well as dead load stresses can be reduced in steel beams because of the relatively large stiffness of steel plates. In this study, the steel plate prestressing method is applied to beam specimens and intermediate floor beams of a steel railway through girder bridge. The behavior of the reinforcing steel plates and reinforced steel beams is monitored during prestressing and live loading, in order to assess the effects of prestressing and reinforcement. The study confirmed that these effects are beneficial to the performance of steel railway floor beams.     

Number of Cable Effects on Buckling Analysis of Cable-Stayed Bridges

Cables instead of interval piers support cable-stayed bridges, and the bridge deck is subjected to strong axial forces due to the horizontal components of cable reactions. The structural behavior of a bridge deck becomes nonlinear because of the axial forces, large deflection, and nonlinear behavior of the cables and the large deformation of the pylons as well as their interactions. The locations and amplitude of axial forces acting on the bridge deck may depend on the number of cables. Agrawal indicated that the maximum cable tension decreases rapidly with the increase in the number of cables. This paper investigates the stability analysis of cable-stayed bridges and considers cable-stayed bridges with geometry similar to those proposed in Agrawal's paper. A digital computer and numerical analysis are used to examine 2D finite element models of these bridges. The eigen buckling analysis has been applied to find the minimum critical loads of the cable-stayed bridges. The numerical results indicate that the total cumulative axial forces acting on the bridge girder increase as the number of cables increases, yet because the bridge deck is subjected to strong axial forces, the critical load of the bridges decreases. Increasing the number of cables may not increase the critical load on buckling analysis of this type of bridge. The fundamental critical loads increase if the ratio of Ip∕Ib increases until the ratio reaches the optimum ratio. If the ratio of Ip∕Ib is greater than the optimum ratio, depending on the geometry of an individual bridge, the fundamental critical load decreases for all the types of bridges considered in this paper. In order to make the results useful, they have been normalized and represented in graphical form.     

Structural Characteristics and Applicability of Four-Span Suspension Bridge

A four-span suspension bridge which has two main 2,000 m spans is investigated with respect to the deformation characteristics. Generally, deformation behavior of the four-span suspension bridge is mainly influenced by rigidity of the center tower. This study is focused on properties such as bending and torsional rigidity of the girder, sag ratio, and dead load. The result of this investigation clarified that the lower rigidity under live load than the three-span bridge is caused by the smaller cable spring coefficient of the main span, which is 1/6 of the side span. Nevertheless, the tendency is stable and can be assisted by stiffened rigidity of the center tower. Live load deflection of the girder can be reduced to less than 1/200 of the main span length, which is useful and economical, by stiffening the bending coefficient of the center tower. Moreover, relatively lower rigidity of the center tower is sufficient for the 2,000 m span suspension bridge than for the 1,000 m span case, keeping the same deflection ratio. Three-dimensional sag geometry of the main cable is effective in limiting the torsional deformation, which is an especially important issue for the four-span suspension bridge caused by twist of the center tower.     

Field Static Load Test on Kao-Ping-Hsi Cable-Stayed Bridge

Field load testing is an effective method for understanding the behavior and fundamental characteristics of a cable-stayed bridge. This paper presents the results of field static load tests on the Kao-Ping-Hsi cable-stayed bridge, the longest cable-stayed bridge in Taiwan, before it was open to traffic. A total of 40 loading cases, including the unit and distributed bending and torsion loading effects, were conducted to investigate the bridge behavior. The atmospheric temperature effect on the variations of the main girder deflections was also monitored. The results of static load testing include the main girder deflections, the flexural strains of the prestressed concrete girder, and the variations of the cable forces. A three-dimensional finite-element model was developed. The results show that the bridge under the planned load test conditions has linear superposition characteristics and the analytical model shows a very good agreement with the bridge responses. Further discussion of deflection and cable forces of the design specifications for a cable-stayed bridge is also presented.     

Response Analysis of Field-Scale Fully Grouted Standard Cable Bolts Using a Coupled ANN–FDM Approach

This paper presents a coupled approach using an artificial neural network (ANN) and the finite difference method (FDM) that has been developed to predict the distribution of axial load along fully grouted standard cable bolts in the field using laboratory pullout test data. A back-propagation training algorithm was used in ANN to determine axial loads in the cables tested in the laboratory. The ANN component of the computational model was trained using two different types of data sets. At first, the ANN was trained to predict the axial loads in a series of short cables grouted with Portland cement at a specific water-to-cement ratio and subjected to different radial confining stiffness values. Next, the ANN model was trained for an expanded case to include the influence of lateral confining stress on the distribution of axial load in the cable reinforcement. Finally, the ANN model was implemented into a widely used, FDM-based geotechnical software (FLAC). The accuracy of the ANN–FDM model is demonstrated in this paper against measured data from laboratory and field tests. The analysis approach introduced in this study is a valuable computational tool that can be used to determine the axial load distribution in long standard cable bolts, which are commonly installed to stabilize rock masses in various geotechnical, transportation, and mining applications.     

Roebling Suspension Bridge. II: Ambient Testing and Live-Load Response

This is the second part of a two-part paper on the evaluation of the historic Roebling suspension bridge using dynamic-analysis techniques. Dynamic properties are determined using ambient field testing under natural excitation. The finite-element (FE) model described in the first part of this two-part paper is modified to more accurately represent current bridge properties. Modifications of the model are based on correlating the FE model frequencies with ambient test frequencies by adjusting the FE model stiffness parameters. The updated 3D FE model is subsequently subjected to an extreme live-load condition to evaluate static safety margins. In addition, cable areas are reduced by 10 to 40% to simulate further deterioration and corrosion. The safety margin of the main cables is demonstrated to be good even when assuming a very conservative 40% cable area reduction, and truss member forces remain within the maximum load-carrying capacity even when the cable areas are reduced by 40%.     

Experimental Verification of Smart Cable Damping

Stay cables, such as are used in cable-stayed bridges, are prone to vibration due to their low inherent damping characteristics. Transversely attached passive viscous dampers have been implemented in many bridges to dampen such vibration. However, only minimal damping can be added if the attachment point is close to the bridge deck. For longer bridge cables, the relative attachment point becomes increasingly smaller, and passive damping may become insufficient. A recent analytical study by the authors demonstrated that “smart” semiactive damping can provide increased supplemental damping. This paper experimentally verifies a smart damping control strategy employing H2/linear quadratic Gaussian (LQG) clipped optimal control using only force and displacement measurements at the damper for an inclined flat-sag cable. A shear mode magnetorheological fluid damper is attached to a 12.65?m inclined flat-sag steel cable to reduce cable vibration. Cable response is seen to be substantially reduced by the smart damper.     

Continuous bending and straightening technology of Q345c slab based on high-temperature creep deformation

A new continuous bending and straightening casting curve with the aim of full using of high-temperature creep deformation was proposed.The curvature of bending and straightening segment varies as sine law with arc length.The basic arc segment is shortened significantly so that the length of bending and straightening area can be extended and the time of creep behavior can be increased.The distance from solidifying front in the slab was calculated at 1 200°C by finite element method.The maximum strain rate of new casting curve at different locations inside the slab is 6.39×10~(-5) s~(-1) during the bending segment and it tends to be 3.70×10-5 s~(-1) in the straightening segment.The minimum creep strain rate is 7.45×10~(-5) s~(-1)when the stress is 14 MPa at 1 200°C.The strain rate of new casting machine can be less than the minimum creep strain rate.Thus,there is only creep deformation and no plastic deformation in the bending and straightening process of steel continuous casting.Deformation of slabs depending on creep behavior only comes true.It is helpful for the design of the new casting machine and improvement of old casting machine depending on high temperature creep property.     

Performance of a Nongasketed Flange Joint under Combined Internal Pressure and Bending Loading

Performance of a bolted flange joint is characterized mainly due to its “strength” and “sealing capability.” A number of analytical and experimental studies have been conducted to study these characteristics only under internal pressure loading. A very limited amount of work is found in the literature under combined internal pressure and bending loading. Due to the ignorance of this external loading, i.e., bending loading, the optimized performance of the bolted flange joint cannot be achieved. The present design codes do not address the effects of bending loading on the structural integrity and sealing ability. To investigate joint strength and sealing capability under combined loading, an extensive comparative experimental and numerical study of a nongasketed flange joint is carried out and overall joint performance and behavior is discussed. Actual joint load capacity is determined under both the design and proof test pressure with maximum additional external bending loading that can be applied for safe joint performance. In addition, as experimentally it is impossible to test different flange joint sizes under combined loading application, hence finite element model developed and verified with the experimental results, presented in this paper can be used as base to study the behavior for different nongasketed flange joint sizes for different classes under combined pressure and bending loading.