• Structural Engineering and Mechanics
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• 제47권2호
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• pp.287-305
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• 2013

Economic performances of consecutive multi-span suspension bridges are studied. The material amount and cost estimation formulas of the bridges have been derived in the part 1 of the study. A parametric study is carried out based on the formulas for investigating the different factors' effect on the bridge cost. The factors include the bridge sag, the bridge span, the bridge foundation and the environment condition, etc. Then, an economical layout of the bridges is proposed for different conditions. Lastly, a selection of suspension bridge types is discussed based on the economy of bridges.

• Structural Engineering and Mechanics
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• 제73권6호
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• pp.641-649
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• 2020

The determination of midtower longitudinal stiffness has become an essential component in the preliminary design of multi-tower suspension bridges. For a specific multi-tower suspension bridge, the midtower longitudinal stiffness must be controlled within a certain range to meet the requirements of sliding resistance coefficient and deflection-to-span ratio. This study presents a numerical method to divide different types of midtower and determine rational range of longitudinal stiffness for rigid midtower. In this method, influence curves of midtower longitudinal stiffness on sliding resistance coefficient and maximum vertical deflection-to-span ratio are first obtained from the finite element analysis. Then, different types of midtower are divided based on the regression analysis of influence curves. Finally, rational range for longitudinal stiffness of rigid midtower is derived. The Oujiang River North Estuary Bridge which is a three-tower four-span suspension bridge with two main spans of 800m under construction in China is selected as the subject of this study. This will be the first three-tower four-span suspension bridge with steel truss girders and concrete midtower in the world. The proposed method provides an effective and feasible tool for engineers to design midtower of multi-tower suspension bridges.

• 한국강구조학회 논문집
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• 제23권6호
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• pp.669-677
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• 2011

다경간 현수교란 3개 이상의 주탑을 가지는 현수교로 중앙부에 주 경간을 2개 이상 가지는 현수교이다. 다경간 현수교 설계시 중앙주탑과 측주탑의 적절한 강성비를 가지도록 설계하는 것이 경제성이나 구조적인 효율성 측면에서 중요하다. 본 연구는 다경간 현수교의 중앙주탑과 측주탑의 적절한 강성비를 찾기 위해 다경간 현수교의 거동을 용이하게 파악할 수 있는 간편한 방법을 제안하는 것을 목적으로 하고 있다. 그 방법으로 다경간 현수교의 주케이블을 등가의 케이블 스프링으로 이상화하고, 주케이블에 작용하는 장력을 주탑상단에 수평력과 수직력의 외력으로 치환시키는 방법으로 다경간 현수교를 등가 다경간 현수교 모델로 치환하였다. 등가 다경간 현수교 모델에 대한 평형방정식을 유도하고 비선형해석을 통해 방정식의 해를 구하였다. 중앙지간장 3,000m의 4경간 현수교의 FEM 해석을 통해 각 주탑에서 발생하는 변위와 모멘트 반력을 계산하고, 이 결과를 등가 4경간 현수교 모델의 해석결과와 비교하여 본 연구의 연구결과를 검증하였다. 검증 결과, 본 연구의 제안방법은 FEM 해석결과와 비슷한 경향을 나타내었다.

• 대한토목학회논문집
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• 제36권1호
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• pp.21-29
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• 2016

본 연구에서는 고정하중을 받는 다경간 현수교의 예비해석을 위한 케이블 부재의 초기평형상태 해석방법을 제안한다. 본 연구에서 제안한 초기 평형상태 해석 알고리즘은 타 연구들에서 사용된 기존 방법들보다 간편하고 실용적이며, 3경간 현수교 및 다경간 현수교에 적용 가능하다. 제안방법의 타당성을 검증하기 위해, 3경간 현수교 예제모델과 4경간 현수교인 국내의 새천년대교 및 중국의 Yingwuzhou Bridge 모델을 사용하여 초기평형상태 해석을 수행하였다. 검증 결과, 본 연구에서 제안한 초기평형상태 해석방법에 의한 결과가 3경간 예제모델의 선행 연구결과 및 새천년대교의 설계값과 잘 일치하는 경향을 나타내었으며, 제안 방법은 Yingwuzhou Bridge에 대한 초기형상을 잘 유지하는 초기값들을 도출하였다.

• Structural Engineering and Mechanics
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• 제47권2호
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• pp.265-286
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• 2013

A study on economic performances of consecutive multi-span suspension bridges is carried out. In this part of the study, material amount and structural cost estimation formulas of the bridges is derived based on the structural ultimate carrying capacity. The bridge cost includes the part of superstructure and the part of substructure. Three types of bridge foundations, bored piles, concrete caissons and floating foundations, are considered in substructure. These formulas are to be used for the parametric study of the bridge cost in order to define its more economical layout under different conditions in the part two of the study.

• Structural Engineering and Mechanics
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• 제42권3호
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• pp.291-311
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• 2012

The multi-span suspension bridge having double main cables in the vertical plane is investigated regarding endurance of live load distribution in the case of non-displaced pylon and pylon displacement. The coefficient formula of live load distribution described as the ratio of live load on the bottom cable to the top cable is obtained. Based on this formula, some function in respect of this bridge are derived and used to analyze its characteristics. This analysis targets the cable force, the cable sag and the horizontal displacement at the pylon top under live load etc. The results clarified that the performance of the live load distribution and the horizontal force of cables in the case of non-deformed pylon has a similar tendency to those in the case of deformed pylon, and the increase of pylon rigidity can increase live load distributed to the bottom cable and slightly raise the cable horizontal force under live load. However, effect on the vertical rigidity of bridge and the horizontal force increment of cables caused by live load is different in the case of non-deformed pylon and deformed pylon.

• Structural Engineering and Mechanics
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• 제87권3호
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• pp.255-272
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• 2023

Spatial cable systems can provide more transverse stiffness and torsional stiffness without sacrificing the vertical bearing capacity compared with conventional vertical cable systems, which is quite lucrative for long-span earth-anchored suspension bridges' development. Higher economy highlights the importance of refined form-finding analysis. Meanwhile, the internal connection between the lateral and vertical sags has not yet been specified. Given this, an analytic algorithm of form-finding for the earth-anchored suspension bridge with spatial cables is proposed in this paper. Through the geometric compatibility condition and mechanical equilibrium condition, the expressions for cable segment, the recurrence relationship between catenary parameters and control equations of spatial cable are established. Additionally, the nonlinear general reduced gradient method is introduced into fast and high-precision numerical analysis. Furthermore, the analytic expression of the lateral and vertical sags is deduced and discussed. This is very significant for the space design above the bridge deck and the optimization of the sag-to-span ratio in the preliminary design stage of the bridge. Finally, the proposed method is verified with the aid of two examples, one being an operational self-anchored suspension bridge (with spatial cables and a 260 m main span), and the other being an earth-anchored suspension bridge under design (with spatial cables and a 500 m main span). The necessity of an iterative calculation for hanger tensions on earth-anchored suspension bridges is confirmed. It is further concluded that the main cable and their connected hangers are in very close inclined planes.

• Structural Engineering and Mechanics
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• 제90권2호
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• pp.159-175
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• 2024

In order to solve the problem of calculating the reasonable completed bridge state of a self-anchored hybrid cable-stayed suspension bridge (SA-HCSB), this paper proposes an analytical method. This method simplifies the main beam into a continuous beam with multi-point rigid supports and solves the support reaction forces. According to the segmented catenary theory, it simultaneously solves the horizontal forces of the main span main cables and the stay cables and iteratively calculates the equilibrium force system on the main beam in the collaborative system bridge state while completing the shape finding of the main span main cable and stay cables. Then, the horizontal forces of the side span main cables and stay cables are obtained based on the balance of horizontal forces on the bridge towers, and the shape finding of the side spans are completed according to the segmented catenary theory. Next, the difference between the support reaction forces of the continuous beam with multiple rigid supports obtained from the initial and final iterations is used to calculate the load of ballast on the side span main beam. Finally, the axial forces and strains of each segment of the main beam and bridge tower are obtained based on the loads applied by the main cable and stay cables on the main beam and bridge tower, thereby obtaining analytical data for the bridge in the reasonable completed state. In this paper, the rationality and effectiveness of this analytical method are verified through a case study of a SA-HCSB with a main span of 720m in finite element analysis. At the same time, it is also verified that the equilibrium force of the main beam under the reasonably completed bridge state can be obtained through iterative calculation. The analytical algorithm in this paper has clear physical significance, strong applicability, and high accuracy of calculation results, enriching the shape-finding method of this bridge type.

• 전산구조공학
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• 제31권2호
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• pp.22-33
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• 2018

• Structural Engineering and Mechanics
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• 제80권6호
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• pp.749-765
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• 2021

Suspension bridges bear large eccentric live loads in rush hours when most vehicles travel in one direction on the left or right side of the bridge. With the increasing number and weight of vehicles and the girder widening, the eccentric live load effect on the bridge behavior, including bending and distortion of the main girder, gets more pronounced, even jeopardizing bridge safety. This study proposes an analytical algorithm based on multi-catenary theory for predicting the suspension bridge responses to eccentric live load via the nonlinear generalized reduced gradient method. A set of governing equations is derived to solve the following unknown values: the girder rigid-body displacement in the longitudinal direction; the horizontal projection lengths of main cable's segments; the parameters of catenary equations and horizontal forces of the side span cable segments and the leftmost segments of middle span cables; the suspender tensions and the bearing reactions. Then girder's responses, including rigid-body displacement in the longitudinal direction, deflections, and torsion angles; suspenders' responses, including the suspender tensions and the hanging point displacements; main cables' responses, including the horizontal forces of each segment; and the longitudinal displacement of the pylons' tower top under eccentric load can be calculated. The response of an exemplar suspension bridge with three spans of 168, 548, and 168 m is calculated by the proposed analytical method and the finite element method in two eccentric live load cases, and their results prove the former's feasibility. The nonuniform distribution of the live load in the lateral direction is shown to impose a greater threat to suspension bridge safety than that in the longitudinal direction, while some other specific features revealed by the proposed method are discussed in detail.