ULTIMATE LOAD-CARRYING CAPACITY OF SELF-ANCHORED CONCRETE SUSPENSION BRIDGE

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1 ULTIMATE LOAD-CARRYING CAPACITY OF SELF-ANCHORED CONCRETE SUSPENSION BRIDGE Meng Jiang*, University of Technology Dalian, P. R. China Wenliang Qiu, University of Technology Dalian, P. R. China Lihua Han, University of Technology Dalian, P. R. China 34 th Conference on OUR WORLD IN CONCRETE & STRUCTURES: August 29, Singapore Article Online Id: The online version of this article can be found at: This article is brought to you with the support of Singapore Concrete Institute All Rights reserved for CI Premier PTE LTD You are not Allowed to re distribute or re sale the article in any format without written approval of CI Premier PTE LTD Visit Our Website for more information

2 34 th Conference on OUR WORLD IN CONCRETE & STRUCTURES: August 29, Singapore ULTIMATE LOAD-CARRYING CAPACITY OF SELF-ANCHORED CONCRETE SUSPENSION BRIDGE Meng Jiang*, University of Technology Dalian, P. R. China Wenliang Qiu, University of Technology Dalian, P. R. China Lihua Han, University of Technology Dalian, P. R. China Abstract Because of the difference of anchorage of main cable, the ultimate loadcarrying capacity of self-anchored suspension bridge is very different from earth anchored suspension bridge. For reinforced concrete having many material nonlinearity characteristics different from steel, it is more important to study the ultimate load-carrying capacity of self-anchored concrete suspension bridge. Based on nonlinear full-range analysis considering both geometrical and material nonlinearity, ultimate load-carrying capacity of a self-anchored concrete suspension bridge of 16 m in span is calculated, and the effects of several influencing factors on ultimate load-carrying capacity of the structure are studied. The influencing factors include loading method, shrinkage and creep of concrete, reinforcement ratio of stiffening girder and tower, safety coefficient of hanger rod, elastic modulus of main cable and restraint of bearing. The results show that the effects of loading method, safety coefficient of hanger rod and restraint of bearing are great. The effects of shrinkage and creep of concrete, reinforcement ratio of stiffening girder and tower and elastic modulus of main cable are little, but their effects on displacement are much great. The study indicates that the elastic ultimate loadcarrying capacity is much greater than elastic-plastic one, the difference between loading in whole bridge and loading in mid-span is little, and the weight of the anchorage at the two ends of the stiffening girder is very benefit to increase the ultimate load-carrying capacity. Keywords: concrete suspension bridge, ultimate load-carrying capacity, nonlinearity analysis, geometrical nonlinearity, material nonlinearity 1. Introduction Because of the aesthetic look, high adaptability and satisfying low cost, the concrete selfanchored suspension bridges are developing quickly in china in the past few years, and the span becomes longer and longer [1][2]. Because of the different anchorage of main cable, self-anchored suspension bridge is very different from earth anchored suspension bridge. Besides the pylon, the stiffening girder is also subjected to compression that is same as the cable-stayed bridge. So the stability of self-anchored concrete suspension bridge needs to be studied. For reinforced concrete has many material nonlinearity characteristics different from steel, it is more important to study the

3 ultimate load-carrying capacity of self-anchored concrete suspension bridge. Based on nonlinear fullrange analysis considering both geometrical and material nonlinearity, ultimate load-carrying capacity of a self-anchored concrete suspension bridge of 16 m in span is calculated, and the effects of several influencing factors on ultimate load-carrying capacity of the structure are studied. The results of the study are very useful for design of self-anchored concrete suspension bridge. 2. Analytical method of ultimate load-carrying capacity For the structure of self-anchored suspension bridge is very complicated and flexible, it has many geometric and material nonlinearities, so the analysis of ultimate load-carrying capacity is very complicated. In order to obtain the accurate calculated result, the nonlinear influencing factors must be fully considered, and the software that can analyze full-range nonlinear process must be used. Self-anchored suspension bridge mainly has the following three geometric nonlinearities: (1) sag effect of main cable, (2) initial internal forces in main cable, stiffening girder and pylon, (3) large structural deformation. The increment equilibrium equation considering the geometric and material nonlinearities can be expressed as following: {[ ] [ K ]}{ u} = { F} K ep + σ Where, [ K ep ] is elasto-plastic stiffness matrix of the structure, [ K σ ] is geometric stiffness matrix. The equation can be calculated by Newton-Raphson iteration method. For reinforced concrete pylon and stiffening girder, the layered beam element and deduced stiffness method are used to produce the elasto-plastic stiffness matrix considering material nonlinearities [3][4][5]. The material constitutive relationship model and loading method are introduced as the following. 2.1 Constitutive relationship model The stress-strain relationship of concrete is shown in figure 1, in which the form of segment OC is expressed by second order parabola as following, 2 ε ε σ = σ 2 ( ε ε ) ε ε When ε t = ε t, the concrete has no tensile softening behavior, and it will be broken when the stain reaches the limit strain. σ is the maximum stress and σ =.85f ck. f is the column compressive ck strength of concrete. Here ε =. 2 and the limit strainε u =. 35. The stress-strain relationship of reinforcement can use bilinear hardening model with same yield strength in tension and compression. The stress-strain relationship of high strength steel wire, such as tendon, hanger and main cable, uses the model shown in figure 2. εs is yield strain corresponding to the yield strength σs =.84σ pu, and σ pu is the tensile strength of steel wire. u t t Fig. 1 Constitutive relationship of concrete s.15 Fig. 2 Constitutive relationship of steel wire The pylon and stiffening girder of Wanxin Bridge shown in figure 3 are reinforced concrete [6]. The section of stiffening girder is a box girder with 5 cells, and the section of pylon is rectangle. The characteristic value of compressive strength of concrete is 35.MPa, tensile strength is 3.MPa. The yield strength of steel bar is 345.MPa, the tensile strength of hanger is 167.MPa, and the tensile strength of main cable is 196.MPa.

4 Fig. 3 Wanxin Bridge in China (Unit: m) 2.2 Loading method The self weight of the stiffening girder P d =783.4kN/m, the live load including motor vehicle and crowd P l =81.6kN/m, and the sum of the load P d +P l =865.kN/m. In this paper, the following loading method is adopted for calculating ultimate load-carrying capacity of Wanxin Bridge. Under the self weight equilibrium condition, uniform load P=(L-1)P d acts on all spans and main span of girder respectively, the sum of self weight of girder and load P is L P d, L is called load factor. With the load factor L increasing from 1., when the concrete compression strain of any section of the stiffening girder and pylon gets to the limit strainε u, the steel tensile strain of any section of the main cable or hangers gets to.93 σ pu, the structure can t carry more load because of rigidity decreasing, the structure reaches its ultimate load-carrying capacity and comes to failure, at this time, L reaches the maximum value L max. The maximum load L max P d that can be carried by the structure is called the ultimate load-carrying capacity, and safety coefficient of the ultimate load-carrying capacity is defined as following: L Pd n = max P + P Where, n denotes the times of ultimate load-carrying capacity and design load. 3. Ultimate load-carrying capacity of loading on all spans 3.1 Elasto-plastic analysis d At the beginning of loading, the moments of stiffening girder and pylon are very little, all of the concrete is compressed, the reinforced concrete works in full section, and the rigidity of the bridge is large. After the load (L-1)P d acts on all spans of the bridge and with the load factor L increasing, the upper surface of girder near the pylon begins to crack when L=1.22, and the bottom surface of girder near middle of the main span begins to crack when L=1.36. When L=1.4, the bottom surface of girder in about 9.m near middle of the main span cracks, and the top surface of girder in about 4.m near the pylon cracks. Because of the cracking, the relationship of load and Fig. 4 V-L curve for loading on all spans displacement becomes nonlinear when L is form 1.2 to 1.4. The relationship of load factor L and vertical displacement v of middle point of main span shown in figure 4 shows that the rigidity of the structure is decreased. After L=1.4, the rigidity of the structure is not markedly effected by the rigidity of the girder. So, the rigidity of the structure remains stable, and the relationship of load and displacement remains linear when L is from 1.4 to 3.. Additionally, the bottom of pylon begin to crack when L=1.65, but the rigidity of the structure is affected little, so the rigidity of pylon has little influences on the rigidity of the structure. l

5 When the load factor L reaches 2.83, the stress of No. 28 hanger reaches its yield stress. No. 27 hanger yields When L=2.96. The other hangers of main span yield one by one with L increasing, and the hangers from No. 22 to No. 28 have yielded When L=3.16. The relationship of load and displacement becomes nonlinear, and the rigidity of the structure decreases quickly with the number of yielding hanger increasing. When L=3.31, the stress of No. 28 hanger reaches its tensile strength and is broken, the other hangers next to No. 28 hanger are broken one by one and the structure reaches its ultimate load-carrying capacity. At this time, the maximum vertical displacement of main span girder is 4.488m, the maximum vertical displacement of side span girder is.54m, the maximum horizontal displacement of pylon is.821, and the maximum tension of main cable is 17843kN that is larger than the yield tension 16859kN. So the elasto-plastic safety coefficient of the = 865. ultimate load-carrying capacity is n = Elastic analysis Without considering material nonlinearity, the elastic ultimate load-carrying capacity only considering geometric nonlinearity is calculated in this paper, and the vertical displacement v of main span curve versus load factor L is shown in figure 5. The relationship of load and displacement remains linear when L is increasing from 1. to 15., but he relationship curve becomes nonlinear when L is larger than 15., and the nonlinearity increases with the load increasing. At last the relationship curve of load and displacement reaches its peak, the structure can not carry more load because of buckling. At this time, the maximum vertical displacement of main span girder is m, the maximum vertical displacement of side span girder is 1.349m, the maximum horizontal displacement of pylon is 9.888m, they are 5.94, 24.98, 12.4 times of the displacements considering material nonlinearity. So elastic safety coefficient of the elastic ultimate loadcarrying capacity is n = = , Fig. 5 V-L curve for elastic analysis that is 5.8 times of the elasto-plastic safety coefficient. The results show that the internal forces of girder and pylon, tension of hanger and tension of main cable are very different between the elastic and elasto-plastic analysis. When the structure goes into elasto-plastic phase, the internal forces are redistributed markedly. The elasto-plastic moment of girder is smaller than the elastic moment, the ratio is.4~.6. The elasto-plastic shear forces of girder near the pylon is much smaller than elastic ones, the ratio is about.2. The elasto-plastic axial compression force of girder is larger than elastic one, the ratio is The tension of main cable and hanger are larger than elastic ones, the ratios are in 1.2~ Influencing factors on ultimate load-carrying capacity 4.1 Ultimate load-carrying capacity of loading on main span Load (L-1)P d acts on main span at the initial state of self weight equilibrium, and the structure comes to failure when L increases to At this time, the maximum vertical displacement of main span girder is 5.27m, the maximum vertical displacement of side span girder is 1.887m, the maximum horizontal displacement of pylon is 1.358m. The vertical displacement of main span curve versus load factor is shown in figure 6. So the safety coefficient of ultimate load-carrying capacity when loading on main span is n = = 2. 7, that is 9% of the safety coefficient loading on 865. all spans. From above analysis, it is found that the side pier is tensioned before the structure reaches its ultimate load-carrying capacity. If the side pier can not bear tension and can not restrict the upward movement of anchor, the concrete of pylon and girder reach the limit strength when L=1.76. So the

6 safety coefficient of the elastic ultimate load-carrying capacity without restraint of side pier is 1.59, which is 58.9% of the safety coefficient with restraint of side pier. The comparison is shown in figure 7. Fig. 6 L-v curve for loading in main span Fig.7 Effect of restraint of the anchorage 4.2 Effects of shrinkage and creep of concrete The past studies show that the shrinkage and creep of concrete are main factors influencing selfanchored concrete suspension bridge. So the following will study the effects of shrinkage and creep of concrete on the ultimate load-carrying capacity. The load (L-1)P d is applied on the bridge after 3 years when the creep and shrinkage has occurred. When L increases to be 3.25, the structure comes to failure, so the safety coefficients of ultimate load-carrying capacity is 2.96, that is 98.8% of the safety coefficient without considering the shrinkage and creep. The comparison is shown in figure 8. Fig. 8 Effect of shrinkage and creep of concrete 4.3 Effects of reinforcement ratio of stiffening girder and tower The reinforcement ratio decides the bearing capacity of reinforced concrete structure, and the capacity increases with increment of reinforcement ratio. So we want to know how much reinforcement ratios of girder and pylon affect on the ultimate load-carrying capacity. For Wanxin Bridge, the reinforcement ratios of girder and pylon are 1.54% and.73% respectively. The studies show that, when the reinforcement ratios of girder are.77%, 1.54% and 3.8%, the safety coefficients of the ultimate load-carrying capacity are 2.95, 3. and 3.4 respectively, and the maximum vertical displacements of main span are 5.574m, 4.488m and 4.1m respectively. When the reinforcement ratios of pylon are.37%,.73% and 1.46%, the elasto-plastic safety coefficients of the ultimate load-carrying capacity are 2.97, 3. and 3.3 respectively, and the maximum vertical displacements of main span are 4.621m, 4.488m and 4.389m respectively. The results are shown in figure 9 and figure 1.

7 So the effects of reinforcement ratio of stiffening girder and tower and elastic modulus of main cable are little, but their effects on displacement are much greater. Fig. 9 Effect of reinforcement ratio of main girder Fig. 1 Effect of reinforcement ratio of tower 4.4 Effects of hanger safety coefficient The section areas of hangers are changed to study effects of the safety factor of hanger on the ultimate load-carrying capacity. Hence, a changeable factor a is multiplied to the section area of hanger in real bridge. Figure 11 shows the vertical displacement of main span curves versus load factor when a is.8, 1. and 1.2 respectively. The three curves corresponding with different value of a nearly overlap at beginning and only separate from each other before broken, and the hangers yield at the separate points. So it can be deduced that yielding of hanger decides the ultimate load-carrying capacity of the bridge. For the three values of a, the load factors L are 2.76, 3.31 and 3.71, and the safety coefficients of the ultimate load-carrying capacity are 2.5, 3. and 3.4. Fig. 11 Effect of safety coefficient of hanger Fig. 12 Effect of elastic modulus of main cable International 4.5 Effects of cable elastic modulus The cable of Wanxin Bridge consists of 85 steel wire ropes, the elastic modulus is MPa, but the common used cable is made of parallel-wire strands with elastic modulus of MPa, they are much different. The vertical of main span displacement versus load factor curves for the two cables are shown in figure 12. When the structures reach their ultimate load-carrying capacity, the load factors are 3.41 for steel wire rope and 3.31 for parallel wires, the maximum vertical displacements of main span are 4.112m and 4.488m respectively, and the safety coefficients of the elastic ultimate load-carrying capacity are 3.9 and 3. respectively. So the elastic modulus of main

8 cable affects little on the ultimate load-carrying capacity, but affects markedly on the rigidity of structure. 5. Conclusion Based on the study of ultimate load-carrying capacity of Wanxin Bridge, the following conclusion can be given: (1) The results based on elasto-plastic analysis and that based on elastic analysis are greatly different for displacement and internal forces, showing that the structure comes to the elasto-plastic stage with a significant redistribution of internal force. The safety coefficients of ultimate load-carrying capacity are respectively and 3., the ratio is 5.8. (2) The safety coefficients of ultimate bearing capacity are respectively 3. and 2.7 for loading in all spans and main span, so different loading methods must be considered. (3) The safety factor of hanger is main influencing factor, so attention should be paid to selection of the safety factor in design of hanger. The effects of shrinkage and creep of concrete, reinforcement ratio of stiffening girder and tower and elastic modulus of main cable are little, but their effects on displacement are much great. The weight of the anchorage at the two ends of the stiffening girder is very benefit to increase the ultimate load-carrying capacity. References [1] Ochsendorf J A. Self-anchored suspension bridge [J]. Journal of Bridge Engineering, 1999, (3): [2] Qiu W L. Nonlinear analysis and experimental study of self-anchored suspension bridge [D], Dalian University of Technology, 24. [3] Li G H. Vibration and stability of bridge [M], China, China Railway Press, [4] Chandra R. Elastic-plastic analysis of steel space structures [J], Journal of Structural Engineering, ASCE, 199, 116(4): [5] Pan J J, Zhang G Z and Cheng Q G. Geometrical and material nonlinear analysis for determining ultimate load-carrying capacity of long-span bridges, China Civil Engineering Journal [J], 2, 33(1):5-8. [6] Zhang Z, Teng Q J and Qiu W L. Design and stress analysis of a new type self anchored suspension bridge s anchorage [J], Journal of Dalian University of Technology, 24, 44(6):

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