Suspension bridge deformation and internal forces under the concentrated live load: Analytical algorithm

Suspension bridges’ excellent spanning capacity is compromised by their insufficient stiffness, making their live load response quite challenging. This study introduces an analytical method for solving the response of the suspension bridge under the temperature-vehicle combined loading. The deformation of the main cable is estimated based on the elastic catenary theory. The variation of internal forces expresses the pylon’s and the beam’s deformation. Displacements of key nodes are estimated and set as constraints. Given the high non-linearity and complexity of suspension bridges, the residual sum of squares of all constraints is the objective function in an optimization algorithm. The analytical solutions to the system of equations are found by employing the generalized reduced gradient method (GRG), yielding deformations and internal forces of the suspension bridge. The proposed method demonstrates high computational efficiency and accuracy, achieving a computation time of less than 1 min for a 1700 m suspension bridge and a maximum vertical displacement error of only 0.59%. Further analysis reveals that the coupling effect between temperature and vehicle loads has a limited impact on vertical displacement calculations but causes a non-negligible influence on beam-end rotations. These findings highlight the necessity of considering temperature-vehicle interaction in suspension bridge assessment to ensure more precise and reliable predictions.

The «reverse» numerical-analytical method for definition the residual bearing capacity of steel frame elements after buckling is proposed. The method allows to take in consideration the post-critical behavior of plates making up the frame element and large plastic strain overflowing into the self-hardening stage.The solution is carried out by the reverse sequence: it is offered to define values of deformational and non-deformational internal forces by numerical unitless procedure according to a given post-limit deformed state of the most loaded cross-section of an element under compression and bending in one or two planes. Wherein deformational forces are assumed as actually acting forces, taking in consideration geometrical nonlinearity, and non-deformational forces are assumed as fictitious forces, compensating nonlinear material behavior and local buckling. The latter ones are considered to be the result of sequential symmetrical acting of two additional axial fictitious forces with one or two eccentricities on the elastic element. The first fictitious force compensates the initial stage of increase of plastic strains before element buckling, and the second one compensates local buckling and further increase of plastic strains in some part of element span after element buckling. The effect of the geometrical nonlinearity on internal forces is defined by «straight» unitless analytical solution of the problem, considering deformed state, using the elastic model of element compressed by actually acting and fictitious forces with their eccentricities. Evaluated internal forces are used in the reverse solution to define eccentricities of actually acting force on the ends of element. The proposed method has a sufficient accuracy for practical application and allows to reduce by orders the magnitude of computational time compared to numerical methods. The graphs showing how the post-buckling bearing capacity reduction coefficients depends on the value of the normalized strain of the most stressed fiber for some of the cross-sections most widely used in construction practice are presented.

Large diameter shield tunnel becomes increasingly popular for under water and undersea channels built in cities. The probability of going through multi-layered ground formation within the tunnel depth is increasing as the diameter of shield tunnel increases. So it is necessary to consider the influence of ground variation on deformation and internal forces of shield tunnel within the range of tunnel depth. In this paper, two dimensional elastic modulus random field model which is lognormal distributed is employed to characterize the ground variation. Five parameters including tunnel diameter, tunnel buried depth, mean value and COV of ground elastic modulus, and vertical SOF of elastic modulus random field are changed in orthogonal test to study how these parameters influence tunnel internal forces and deformation. Monte Carlo simulation is performed and distributions of tunnel deformation and internal forces are all normally distributed. Mean value of tunnel deformation and internal forces are almost negative linear with mean value of ground elastic modulus, but not sensitive to COV of ground elastic modulus. Tunnel crown bending moment has the largest variability while invert axial force has the smallest variability among all structural response indicators.

Research on Calculation Method of Suspension Bridge Internal Force under Random Traffic Load

Anti-slipping safety factor between the main cable and saddle, deflection-to-span ratio of main girder and force in the mid-tower, which are not important factors in two-tower suspension bridge design, yet becoming dominant ones in three-tower. Moreover, these factors are all controlled by live load. Thus geometrical nonlinearity under live load for three-tower suspension bridge becomes even more significant. This paper takes Taizhou Yangtze River Bridge as the study object, and uses linear deflection theory, incremental UL formulation and total CR formulation to study the geometrical nonlinearity of various key responses of the structure under live load. It is concluded that accuracy and efficiency of total CR formulation is the highest among the three as well as the maximum error of incremental UL formulation is no more than 0.3%; however, the error of widely used linear deflection theory is 6.6%, 4.5% and -2.64% respectively, which is conservative and can not meet the requirements of sophisticated analysis.

Genetic Algorithms for the Dependability Assurance in the Design of a Long‐Span Suspension Bridge

<p>A central buckle is generally set in the middle of long-span suspension bridge to improve the structure mechanical performance. With a large number and sophisticated composition of steel plates, the mechanical behaviour of central buckle region is obscure. In this paper, a shell-beam hybrid finite element model of a 428m main span self-anchored suspension bridge was established, and the mechanical characteristics of central buckle region were analysed. The result shows that the normal stress of steel plates in central buckle region is mainly dependent on by dead loads, the effect caused by live loads only accounts for approximately 15% of that caused by dead loads; axial force of central buckle is mainly transmitted to the diaphragms and webs of the girder.</p>

Through predict activities trend of ground fissures, given to the ground surface subsidence curve on the topper side in the next 50 years. Established a tall concrete frame construction model, using SAP2000 finite element programs, take a distance of the building depart from the fissure as analytical variables, in considering the dead load, live load, horizontal seismic action and combine with foundation differential settlement working conditions, analyze the elastic displacement and internal forces of the structure. The results showed that，in the topper side area near to the fissure, affected by the avoidance distance, the displacements and internal forces of the frame structure change remarkably. The growth and redistribution of internal forces performance are the most serious in the building base floor of framework， the internal forces change in ends of both beam and column will cause a change in the direction of bending moment， but also an inflection point of the column will change with the internal forces growth and regression.

The central buckle is essential for maintaining longitudinal stability in suspension bridges. However, conventional steel buckles are often excessively stiff, leading to stress concentration and insufficient durability. Moreover, they tend to perform poorly under fatigue loading conditions. This study proposes a novel flexible central buckle system based on a Carbon Fiber-Reinforced Polymer (CFRP) to address these limitations. This study proposes a novel flexible central buckle system based on Carbon Fiber-Reinforced Polymer (CFRP) to address these limitations. Taking the long-span Shiziyang Suspension Bridge as a case study, a finite element model is developed to investigate the effects of CFRP central buckles with eight different stiffness levels on the static and dynamic responses of the bridge. The results indicate that a CFRP central buckle with a low elastic modulus achieves comparable displacement control performance to that of traditional steel buckles, while inducing significantly lower internal forces, demonstrating strong potential as a substitute. Based on this finding, a coordinated control strategy combining the CFRP central buckle with end-span restraining devices is proposed. This integrated system reduces midspan displacement and central buckle internal force by 61.1% and 49.8%, respectively. Considering both performance and cost-efficiency, a low-modulus CFRP material such as T300 is recommended. The proposed approach offers a new and effective solution for longitudinal control in ultra-long-span suspension bridges.

Fire resistance analysis and protection measures for cable components of suspension bridges

In suspension bridge, the main cable is the major bearing member, instead of the 1770MPa cable wire normally adopted in current design, the application of cable wire strengths up to 1960MPa can lighten the dead weight, reduce the size of tower and anchorage, and shorten the construction period, obtain economical design. In this paper, a under-construction suspension bridge with span of 1688m is taken as a case-study, Comparative analyses are performed mainly focusing on basic parameters, carrying efficiency of main cable, static behavior and dynamic properties as different high strength cable are adopted in this suspension bridge. The results show that compared with 1770MPa main cable, using 1960MPa main cable in suspension bridge is benefit for improving the carrying efficiency of main cable, the steel consumption is also saved by 13%, but the vertical stiffness of the structure is reduced partly; the changes of main cable slightly affect the natural vibration frequency of girder, but have greater influences on vibration of main cable.

Preliminary static analysis of suspension bridges

Stone cantilever staircases are present in case of both new constructions and reconstructions. The aim of the present paper is to understand the mechanical behaviour of these staircases with the help of discrete element simulations, and to compare the calculated behaviour to the estimations given by the existing manual calculation methods. First a literature review is presented on the statical calculation of cantilevered staircases: manual calculation methods suggested in the 1990s for straight and spiral staircases are introduced, focusing on Heyman’s theory and its improved counterparts. Then the discrete element method is used as a tool to perform virtual experiments, in order to evaluate the mechanical behaviour of the straight and spiral staircases for selfweight, live loads and support movement. The results obtained (internal forces, stresses, deflections) are then compared with the manual calculation results. The most important conclusions are: (1) the term “cantilever stair” is misleading: significant torsion moments occur in the treads, while the bending moments are much smaller than in a free cantilever; (2) the type of the connection between wall and treads (i.e. the end of the tread is simply supported by the wall against translation and torsion, or it is also partly clamped) has a fundamental influence on the internal forces and stress distributions; (3) for simply supported treads the existing manual methods are conservative for straight stairs, but for spiral stairs they dangerously underestimate the torsional moments.

The principle objective of this project is to analysis and design a multi-storeyed building [G + 10 (3-dimensional frame)] using SAP2000. The design involves load calculations manually and analyzing the whole structure by SAP2000. The design methods used in SAP2000 analysis are conforming to Indian Standard Code of Practice and features a state-of-the-art user inter face, visualization tools, powerful analysis and design engines with advanced finite element and dynamic analysis capabilities. From model generation, analysis and design to visualization and result verification. The project is designed in accordance with Indian codes, considering various loads such as Reinforced concrete (IS 456-2000), dead load (IS875-1987 part1), live load (IS875-1987 part2), wind load (IS875-1987 part3), seismic load (IS1893-2016 part1) and load combinations are considered as per the (IS875-1987 part-5) code books. The analysis considers seismic zone III and ensures safety by considering dead load, live load, seismic and wind forces, and balancing economy and safety. Structural design is crucial for Civil Engineers, and proper analysis can prevent structure failure and loss of life. Engineers analyze structures considering constraints like serviceability and deformability, following IS codes. Our project focuses on analyzing and designing superstructures like slabs, beams, and columns, considering dead load, live load, seismic and wind forces Response Spectrum Analysis and Shear Wall. The analysis parameters such as shear force, bending moment, and displacement. KEYWORDS: Response Spectrum Analysis, Shear Wall, SAP2000, Seismic and Wind loads.

<p>It is rapidly developing the construction of long-span suspension bridges in China. It is an important issue for the structural design of suspension bridges. It is a problem that needs further study for high-speed and heavy-haul railway suspension bridges. There is the characteristics of heavy train live loads, high speed and high demand for running security and passenger comfort, the technical standards and so on. The paper is analysis the stiffness evaluation indexes of railway suspension bridges adopted by the codes of various countries in the world, and compares them with the regulations in China’s general bridge codes. The key technologies of the thousand-meter-scale road-rail suspension bridges for high speed for passenger trains, 120 km/h for freight trains) and heavy load are studied. Based on the research on the road-rail suspension bridge with main span of 1 196 m, the influences of different supporting systems, arrangement of auxiliary piers, ratio of height to span, ratio of width to span and ratio of vertical to span on the vertical and lateral stiffness of the bridge are analysis, and the stiffness evaluation indexes and suggested values for thousand-meter-scale road-rail suspension bridges are proposed. The proposed long-span suspension bridge scheme is technically feasible, economically reasonable, and has good horizontal and vertical stiffness, smoothness and running comfort.</p>