1296 Advances in Computational Modeling and Simulation

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1 Applied Mechanics and Materials Online: ISSN: , Vols , pp doi: / Trans Tech Publications, Switzerland Dynamic Response Analysis of Suspenders of Arch Bridges Sudden Failure on Failure-safety Theory Hua Li 1,a, Rui Li 1,b, Yue Chen 2,c and Dexiang Zhu 3,d 1 College of Architectural Engineering, Kunming University of Science and Technology, Kunming, Yunnan, China 2 Yunnan Province Road Administration Management Corps, Kunming, Yunnan, China 3 Yunnan Province Yunling Expressway Engineering Consulting Co., LTD, Kunming, Yunnan, China a li_hua1988@126.com, b liruiking@163.com, c chenyue196677@sina.com, d lanyuzdx@126.com Keywords: half-through and through arch bridge, double suspender, suspender sudden failure, dynamic response, failure-safety Abstract. Suspenders are main force-transmission components of half-through and through arch bridge, It is crucial for safety of bridges to its reliability and durability. Safety of the arch bridge will change when a suspender sudden failure, and affect the safety of the structure. Selecting a through arch bridge in Yunnan Province as the research object, it based on the three-dimensional finite element, this paper studied the dynamic response of arch bridge suspenders sudden failure on the failure-safety theory. Introduction Due to the uneven distribution of stress, corrosion and other reasons, lead to the tension of individual suspenders of arch bridge is excessive, and then cause structural bearing capacity to reduce[1, 2, 3, 4, 5, 6].All of these reasons raise the possibility of suspender sudden failure[7, 8, 9, 10, 11, 12]. Fracture mechanics discussed the main points and implementation of failure-safety theory, Any structure in use process will be damage, and this damage is inevitable, But when the damage gradually deepen to a certain degree that the structure reach the critical strength of damage. The structure reaches its limit state of the bearing, before this state is reached, despite the damage exists, The structure is relatively safe, these are his main idea of failure-safety theory. Arch bridge suspender is based on failure-safety theory, known as system calls failure-safety suspender. The theory is that for the current regular double suspender system, by controlling the unit value, such as adjusting the sizes of angles, sections, or tensile stress, makes stress of different suspenders exerting on the same spot differ from each other. The useful life varies because of these stress differences, thus preventing two suspenders from failing at the same time. In addition, the displacement, moment and shear between the long suspender and short suspender is not the same. Selecting a through arch bridge in Yunnan Province as the research object, it based on the three-dimensional finite element, this paper studied the dynamic response of arch bridge suspenders sudden failure on the failure-safety theory. All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, (ID: , Pennsylvania State University, University Park, USA-13/05/16,11:00:54)

2 1296 Advances in Computational Modeling and Simulation Relevant theories about the impact of suspender sudden broken to the bridge structure The instantaneous impact of the bridge structure is caused by suspender sudden failure. Because the existing institutions has reached equilibrium under the combined action of the suspender tension, the structure of gravity and suffered loads, so after suspenders sudden failure, the weight Department of Bridge Road can be ignored, we recognize suspender tensile of sudden failure suspenders sudden failure as a Reverse sudden-loading on the bridge structure. In the sudden-loading effect, the maximum response of the structure will be achieved within a very short time. Damper plays little direct role in the maximum reflection that all control structure produced, Damping force had a chance to absorb more energy from the structure before the structure reached the maximum reflection[15] The dynamic amplification factor of sudden load effect is the ratio of the maximal stress and deformation, which is generated by sudden load on the structure, to the stress and deformation generated by the same amount of static load Project example Project Profile. The Bridge is a through arch bridge. Using parabola as its arch axis, Its Calculated span is m and rise - span ratio is f = 1/4, the deck design two-way four-lane, Motor vehicle lanes: 19.0 m wide, isolation band :2 2.5 m wide, non-motor vehicle lane: m wide,sidewalks: m wide, total bridge deck: 40.0 m wide. Design load is Truck-Load over 20,trailer 100 and crowd 3.5KN/m 2 The bridge has a total of seven pairs of suspender; the center spacing among suspenders is 5.0 m. The relative length of the side suspender is short, to improve its displacement caused by the change of the adaptation load, temperature and other factors and avoid material fatigue and strength reduce of suspenders, Design uses HVMBDSQ7-73-type ball-hinge boom. The rest of the suspenders using HVMLZM7-121 galvanized steel wire cold cast anchor finished beam suspenders. It set two suspenders in each lifting point, boom center-to-center spacing of 100cm, the center spacing among suspenders is 100cm. Side suspenders use 2 40Cr round rod Equivalent to 73φ7mm in galvanized steel wire upset head anchor in a lifting point, The area of each wire of each suspender: A s = 2809mm 2, The remaining suspenders in a lifting point use 2 121φ7mm galvanized steel wire finished cold cast anchor cable, The area of each wire of each suspender: A s =4657mm 2, standard strength:r y b =1670 Mpa. Three-dimensional finite element model. In this paper, we used FEA software to build the model of 3D finite element model of through arch bridge. Figure 1 is the finite element model of full - bridge. Fig.1 The finite three-dimensional element model of full - bridge

3 Applied Mechanics and Materials Vols The Analyses of the results of model calculation Internal force analysis of the suspender in fatigue vehicles loads. Bridge structure to withstand dynamic load is the load of the vehicle, in this paper, we simplified the vehicle load to simplify ideal charge in the process of finite element analysis. The deck design two-way four-lane. I treat axle load as uniform movement of concentration loaded on the deck, to find the area of the bridge structure needs more attention where badly stressed in the fatigue vehicles Loads, we took the calculated data of three suspenders(the end, 1/4 span, mid-span)for comparison: No. 1 (short suspenders), No. 3 (medium suspenders), No. 4 (long suspenders). The axis force response of suspenders in fatigue vehicles loads as shown below: Fig.2 The axis force response of No. 1 suspender and No. 3 suspender Fig.3 The axis force response of No. 4 suspender and No. 5suspender The axial force response of the No. 1 suspender, No. 3 suspender, No. 4 suspender and No. 5 suspender in vehicles loads, axial force of suspenders is FZ, Draw of fatigue stress curve of Nodes is based on FZ divided by the cross-sectional area of the suspender. Figure 2 and figure 3 shows that the internal forces response of the 1st suspender is more larger than 3, 4, 5 suspender under the Vehicle Load, the axial force of 3th suspender equal to the 5th suspender s, but the axial force is in the opposite direction. The force of short suspenders is most unfavorable, we will analyze the dynamic response of bridge under the conditions of short suspender sudden broken. Calculated conditions. The bridge has a total of seven pairs of suspender, there are two suspenders in each lifting point, they are F cable (the main bearing cable) and S cable (security cable). Let the cross-sectional area between F suspender and S suspender are equal(a F <A s,but A F plus As is equal to the sectional area of the original the double suspender),so the internal forces and Stress of the two suspenders F F <F s,σ F =σ s. By exceed tension of F cable, making the stress of F cable is greater than S cable s in the same lifting point:σ F >σ s, however, the internal forces of the two suspenders F F =F s. During use, F cable that the stress is greater will break before S cable. After F cable broken off, the S cable and the remaining suspenders will together bear. F cables broken in each lifting point 12 kinds of analysis loading cases are drafted. Analysis and explanation of the loading cases are as follows.

4 1298 Advances in Computational Modeling and Simulation 1. Dead loads+ live loads cases: The dead loads that affect the force of suspenders of arch bridges are mainly the self gravity of vertical and horizontal beams and secondary dead loads, the live loads that affect the force of suspenders are mainly vehicle load, impact load of vehicle and non-vehicle load. F cable and S cable bear these loads together. 2. Operation cases: Before the bridge was set up and pre-commissioning, Based on F cable and S cable with different area ratio, By exceed tension of F cable, the internal forces of the two suspenders are equal ( F F =F s ) 3. Broken suspender cases: The moment of F cables broken,the load effect that need to be considered are dead loads, live loads and axial forces that be caused by the impact of broken suspender. Dead loads mainly include the self gravity of vertical and horizontal beams and secondary dead loads, live loads mainly include vehicle load, impact load of vehicle and non-vehicle load, plus impact load that be caused by suspenders sudden failure. 4. After suspenders broken cases: After the F cables broken, the load effect mainly include the dead loads and axial force that be caused by live loads, the S cable in the same lifting point and the remaining suspenders will together bear the whole bridge structure. The analysis of the maximum internal force of the remaining suspenders at the moment of F cables broken. Under the fatigue vehicles Loads, The force of short suspenders is the most disadvantage, we analyzed the impacts of F cables sudden failure on the remaining structure of the bridge. a. The axial force of F cable at the moment of b.the axial force of F cable at the moment of the F cable of 1th suspender sudden failure t he F cable of 1th suspender sudden failure on broken suspender side on broken suspender side c. The axial force of F cable at the moment of the F cable of 1th suspender sudden failure on the other side Fig.4 The maximum internal force of remaining cables at the moment of the F cable of 1th suspender sudden failure As can be seen from Fig.4, the impacts of F cables sudden failure of the 1th suspender on broken suspender side is greater than that on the other side. The most dramatic in the impact response of broken cables is the S cable that have the same lifting point with the broken F cable, followed by

5 Applied Mechanics and Materials Vols those suspenders near the broken suspender. F cable and S cable had a great response in the lifting point. As can be seen from Fig.4 b, the maximum internal force of S cable is 2826KN. The internal force of the S cable of 1th suspender is the greatest at the moment of F cable broken. The effect of F cable sudden failure on the displacement of the suspender at the top and bottom. When the F cable of 1th suspender broken, Displacement at the top and bottom will change over time, Fig.5 is time history curves of displacement at the top and bottom. Fig.5 Time history curves of displacement at the top and bottom when the F cable of 1th suspender broken As can be seen from Fig.5, at the moment of F cable of 1th suspender broken, the displacement of cable bridge deck quickly from 15.13mm to 24.32mm, The maximum displacement values appear in the s after the F cable broken, later on, due to impact generated by the broken suspender, the deck vibrated in the vertical plane. Conclusion (1)Fig.2 and fig. 3 shows that the internal forces response of the 1st suspender is more larger than No.3, No.4 and No.5 suspender under the vehicle load, the axial force of 3th suspender equal to the 5th suspender s, but the axial force is in the opposite direction. The force of short suspenders is most unfavorable, (2)The impacts of F cables sudden failure of the 1th suspender on broken suspender side is greater than that on the other side. The internal force of the S cable of 1th suspender is the greatest at the moment of F cable broken. (3)When F cable of the short suspender (No.1 suspender) broken, the displacement of F cable at the top and bottom increased quickly under the impact of the broken cable.

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7 Advances in Computational Modeling and Simulation / Dynamic Response Analysis of Suspenders of Arch Bridges Sudden Failure on Failure-Safety Theory /