Force Analysis of Self-Anchored Suspension Bridges After Cable Clamp Slippage

S S symmetry

Article Force Analysis of Self-Anchored Suspension Bridges after Cable Clamp Slippage

Hongfeng Li *, Yancheng Liu, Chunwei Li , Hao Hu and Quansheng Sun

School of Civil Engineering, Northeast Forestry University, Harbin 150040, China; [email protected] (Y.L.); [email protected] (C.L.); [email protected] (H.H.); [email protected] (Q.S.) * Correspondence: [email protected]

Abstract: The slippage of cable clamps during the long-term operation of suspension bridges is a common and detrimental phenomenon. From an experimental point of view, the cable clamp slippage of a suspension bridge was investigated to reveal the effect of this sliding on the force acting on the full bridge. The forces acting on the bridge before and after the slippage were analyzed using a ﬁnite element model. The calculation results showed that the cable clamp slippage directly affects the cable forces of the hangers. The hanger cable force decreased by 19.2% when the slippage reached 10.2 cm, while the maximum increase in the cable force of adjacent hangers was 147.7 kN, an increase of 7.25%. The variation of forces in the hanger cable disrupted the force balance of the main girder, thereby producing a torque effect at the corresponding position in the girder, i.e., increased torque. Meanwhile, the slippage affected the axial tension in the main cable and the main girder. The impact of the tower internal force was less than 1%. Hence, the study concluded that the effect of cable clamp slippage is better understood, ensuring the safety of the suspension bridge.

Citation: Li, H.; Liu, Y.; Li, C.; Hu, Keywords: self-anchored suspension bridge; cable clamp; slippage; force analysis H.; Sun, Q. Force Analysis of Self-Anchored Suspension Bridges after Cable Clamp Slippage. Symmetry 2021, 13, 1514. https:// 1. Introduction doi.org/10.3390/sym13081514 In suspension bridges, cable clamps are key nodes connecting the main cables and hangers. With the progress and development of suspension bridges, cable clamps have Academic Editors: Yang Yang, Ying Lei, Xiaolin Meng and Jun Li gradually evolved from eyebars and pin-type hinge structures to riding straddle and pin- type structures. The choice is closely related to the type of hanger used: riding straddle

Received: 22 July 2021 cable clamps are commonly used for wire rope hangers, whereas pin-type cable clamps are Accepted: 16 August 2021 used for parallel wire hangers. In the U.S. and Japan, preference is given to riding straddle Published: 18 August 2021 cable clamps, whereas pin-type cable clamps are more common in China and Europe [1]. Figure1 shows the different types of cable clips. Publisher’s Note: MDPI stays neutral During the construction and operation, the cable clamp will no longer be firmly with regard to jurisdictional claims in anchored because of the loosening of the fastening bolts, the main cable has a thinner published maps and institutional afﬁl- section under long-term loading, and the linear expansion coefficient is inconsistent iations. under the influence of temperature. These factors are important inducements that cause slippage of the suspension bridge cable clamps. Therefore, the cable clamp slippage is a common phenomenon that is detrimental to suspension bridges. In the inspection manual for suspension bridges developed by the Honshu–Shikoku Bridge

Copyright: © 2021 by the authors. Construction Corporation, Japan, cable clamp slippage is listed as a key inspection Licensee MDPI, Basel, Switzerland. item [2]. In the United States, the cable inspection and strength assessment guidelines This article is an open access article provide detailed inspection requirements for hangers and cable clamps [3]. There are distributed under the terms and strict regulations on cable clamp slippage in the Chinese Highway Bridge Technical conditions of the Creative Commons Condition Assessment Standard [4]. Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Symmetry 2021, 13, 1514. https://doi.org/10.3390/sym13081514 https://www.mdpi.com/journal/symmetry Symmetry 2021, 13, x FOR PEER REVIEW 2 of 16

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(a) (b)

Figure 1. Different types of cable clips: (a) abridged general view of a riding straddle cable clip; (b) abridged general view of a pin-type cable clamp. (a) (b) Figure Cable1. DifferentDifferent clamps types types of withcable cable clips: clips:poor ( (aa)) abridgedanti-sliding abridged general general performaview view of of a a riding ridingnce straddle straddle tend cable cable to slideclip; clip; ( (bb )along) abridged abridged the general general main view view cable, of a pin-type cable clamp. asof ashown pin-type cablein Figure clamp. 2, which directly causes a loss of stress in the entire structure and major safety hazards in the structuralCableCable clamps clamps system. with with poor poor Insuanti-sliding anti-slidingfficient performa performance anti-skidnce tend tend performance to to slide slide along along the theof main mainthe cable, cable,cable clamp will cause theasas shown showncable in inclamp Figure Figure 22, ,to which slide directly down causes the aa lossmain of stress cable, in the which entire structurewill lead and majorto the safetysafety hazards hazards in in the structural system. Insu Insufﬁcientfficient anti-skid anti-skid performance performance of of the cable redistribution of theclampclamp internal will will cause cause force the the of cable cable the clamp clampprincipal to to slide slide force-bearing down down the the main componentscable, which which will will such lead toas thethe main cable, hanger,redistribution redistributionand main beam. of of the the internal internal The internal force force of of the theforce pr principalincipal deviates force-bearing force-bearing from the components components design suchvalue such as as andthe the safety reserve ofmainmain the cable, cable,structure hanger, hanger, is and andcut. main main In beam.practice, beam. The The internal engineering internal force force deviates deviatesproblems from from the due design the designto value the value poor and theand safety the safety reserve reserve of the of structure the structure is cut. is In cut. practice, In practice, engineering engineering problems problems due to due the to poor the anti-sliding performanceanti-slidingpoor anti-sliding of performancecable performance clamps of cable ofmay cable clamps force clamps may a may projectforce force a project ato project be to toterminated be be terminated terminated oror or even even rebuilt. Hence, scholarsrebuilt.rebuilt. have Hence, Hence, extensively scholars scholars have have studied extensively extensively the studied studied problem the the problem problem of cable of of cable cable clamp clamp slippage. slippage.

Figure 2. Actual images of a cable clip after slipping.

In 2000, Ji et al. analyzed the additional force due to the hanger pull acting on the screws in the hanger, with an objective to improve the cable clamp design of the Kurima Figure 2. Actual imagesBridge, of Figurea Japan. cable 2. The Actualclip Liaison after images slipping.Bridge of a cable Corporation clip after slipping. proposed the application of pin-type cable clamps for the first time [5]. Since 2009, scholars have started paying attention to cable clampIn slippage 2000, Ji in et suspension al. analyzed br theidges. additional Ren et al. force analyzed due to the the anti-skid hanger friction pull acting coefficient on the In 2000, Ji et al.ofscrews aanalyzed cable in theclamp hanger, the and additional the with main an objective cable force void to improveratiodue byto conducting thethe cable hanger clamp an anti-sliding pull design acting of thetest Kurima on thethe screws in the hanger,mainBridge, with cable Japan. an and objective Thecable Liaison clamp to Bridge [6]. improve Huang Corporation et al.the studied cable proposed the clamp variations the application design in the of lateral pin-typethe displace-Kurima cable Bridge, Japan. The Liaisonmentclamps of the for Bridge themain first cable Corporation time and [5 ].the Since lateral 2009,proposed deflecti scholarson anglethe have application of started the cable paying clamp of attentionpin-type under the to effect cable ofclamp hanger slippage tension in in suspension the main cable bridges. [7]. RenIn 2013, et al. Li analyzed et al. determined the anti-skid the frictionupper limit coefficient of the clamps for the firsttransverseof time a cable [5]. clamp elastic Since and modulus the2009, main based scho cable onlars void the ratiohave macroscopic by started conducting force paying an of anti-sliding an ideally attention testarranged on to the maincable main clamp slippage in suspensioncablecable [8]. and In cable 2014, br clampidges. Ruan [et6 ]. Renal. Huang studied et al. et and al.analyzed studiedanalyzed the the variations spatial anti-skid effect in the andfriction lateral stress displacement distributioncoefficient of a cable clamp andcharacteristicsof thethe main main cable of cable a andcable thevoid clamp[9]. lateral ratio deflection Ma by et conductingal. conducted angle of the jack an cable pushanti-sliding clamp tests underon the test the main effect on cable the of ofhanger a suspension tension bridge in the mainto analyze cable the [7]. friction In 2013, coefficient Li et al. determined of the cable theclamp upper against limit sliding of the main cable and cableand clamp the internal [6]. Huangand external et al.void studied ratios of thethe cable variations clamp [10]. in Zhugethe lateral et al. studied displace- the ment of the main cable and the lateral deflection angle of the cable clamp under the effect of hanger tension in the main cable [7]. In 2013, Li et al. determined the upper limit of the

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transverse elastic modulus based on the macroscopic force of an ideally arranged main cable [8]. In 2014, Ruan et al. studied and analyzed the spatial effect and stress distribution characteristics of a cable clamp [9]. Ma et al. conducted jack push tests on the main cable of a suspension bridge to analyze the friction coefficient of the cable clamp against sliding and the internal and external void ratios of the cable clamp [10]. Zhuge et al. studied the friction factor of a carbon fiber reinforced plastic (CFRP) cable–cable clamp interface [11]. Li et al. proposed the Tsai–Hill failure criterion for composite materials [12]. In 2015, Zhou et al. calculated the anti-sliding friction coefficient and the internal and external void ratios of a steel wire main cable clamp coated with a zinc–aluminum alloy [13]. In 2016, Sun et al. derived a simplified calculation formula to determine the increase in the elevation of the main cable mid-span control point and the average increment in the hanger cable force [14]. In 2018, Shen et al. analyzed the change laws of the ultimate anti-sliding friction resistance of a cable clamp under the action of the cable force, and the contact force between the main cable and the cable clamp surface [15,16]. In 2019, Ruan et al. proposed a theoretical model considering transversely isotropic materials based on the generalized Hooke’s law. Through anti-slipping performance tests, they determined the actual ultimate sliding resistance and comprehensive friction coefficient of a cable clamp [17]. In 2020, Miao et al. proposed a new slippage-based failure criterion based on an analytical model [18] and briefly revised the original slippage resistance formula using the Coulomb friction law. In summary, most studies have been based on the interface performance of the main cable and the cable clamp, focusing on the analysis of the effects of the clamping force of the cable clamp and the friction coefficient on the anti-slipping performance. Studies on the total force acting on suspension bridges are lacking. The integrity of the overall structure of a full bridge following cable clamp slippage has rarely been studied. In practice, although cable clamp slippage is minor, it is a key factor causing a change in the forces acting on the entire bridge. Therefore, this study mainly analyzed the overall force acting on suspension bridges following cable clamp slippage. In this paper, the influence of pin-type cable clamp slippage on a self-anchored suspension bridge is reported. Considering the geometric nonlinear influence of the bridge, a finite element simulation was conducted. First, we selected a large-span self-anchored bridge as an example to describe the geometry of self-anchored suspension bridges and the magnitude of the cable clamp slippage in detail. Subsequently, a method for simulating the cable clamp slippage was proposed and verified through examples. Additionally, the total force acting on the suspension bridge before and after cable clamp slippage was analyzed, and recommendations for operation and maintenance was provided.

2. Background A self-anchored suspension bridge with double towers and double cable planes (see Figure3) was selected as the research object. The main span, side span, auxiliary span, cable sag ratio, and sag-span ratio of this bridge are 248 m, 108 m, 46 m, 49.6 m, and 1/5, respectively. The main tower is a double-tower portal structure system with a height of 80.5 m; the main cable is a parallel steel wire; the hanger is a parallel steel wire strand; and the stiffening girder is a steel–concrete composite girder system. The construction of this self-anchored suspension bridge was initiated in 2011. A recent structural inspection revealed that the cable clamp close to the main tower has caused severe cable clamp slippage, as shown in Figure4. Hence, this bridge was thoroughly checked for cable clamp slippage. Symmetry 2021, 13, x FOR PEER REVIEW 4 of 16

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Figure 3. Overview of a self-anchored suspension bridge (m): (a) standard cross section at the hanger; (b) standard cross section without sling; (c) standard cross section of the main tower; (d) photo of a self-anchored suspension bridge.

The construction of this self-anchored suspension bridge was initiated in 2011. A re-

cent structural inspection revealed that the cable clamp close to the main tower has caused FigureFigure 3. 3. OverviewOverview of of a a self-anchored self-anchored suspension suspension bridge bridge (m): (m): ( (aa)) standard standard cross cross section section at at the the hanger; hanger; ( (bb)) standard standard cross cross sectionsection without without sling; sling; ( (cc)) standard standardsevere cross cross cable section section clamp of of the the main slippage, tower; tower; ( das) photo shown of a self-anchored in Figure 4. suspension Hence, bridge.this bridge was thoroughly checked for cable clamp slippage. The construction of this self-anchored suspension bridge was initiated in 2011. A recent structural inspection revealed that the cable clamp close to the main tower has caused severe cable clamp slippage, as shown in Figure 4. Hence, this bridge was thoroughly checked for cable clamp slippage.

FigureFigure 4. Image4. Image and and schematic schematic of a cable of a clamp cable after clamp slipping. after slipping. Figure 4. Image and schematic of a cable clamp after slipping. As showed in Figure 4, the sliding direction of the cable clamp is along the radial directionAs showed of the in Figuremain cable.4, the slidingAfter inspection, direction of thethe radialcable clamp sliding is alongdistance the radialof all cable clamps directionwas measured of the main in cable. detail, After and inspection, the number the radial of each sliding sliding distance cable of all clamp cable clamps and the amount of was measured in detail, and the number of each sliding cable clamp and the amount of

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Symmetry 2021, 13, x FOR PEER REVIEW 5 of 16 As showed in Figure4, the sliding direction of the cable clamp is along the radial direction of the main cable. After inspection, the radial sliding distance of all cable clamps was measured in detail, and the number of each sliding cable clamp and the amount ofslippage slippage was was recorded. recorded. In the In establishment the establishment of the of finite the ﬁniteelement element model, model, adjusting adjusting the po- thesition position of the ofcable the clamp cable clampsimulates simulates the actual the actualbridge bridgestress condition. stress condition. In order In to order empha- to emphasizesize the influence the inﬂuence of the ofchange the change in the in position the position of the of cable the cable clamp clamp on the on whole the whole bridge, bridge, the thecable cable clamp clamp with with the thelargest largest slip slip amount amount is mainly is mainly simulated simulated during during the the simulation. simulation. DuringDuring thethe inspectioninspection ofof thethe suspensionsuspension bridge,bridge, itit waswas foundfound thatthat thethe cablecable clampclamp thatthat belongedbelonged toto thethe thirdthird hangerhanger inin thethe mid-spanmid-span direction direction of of the the W1 W1 main main tower tower was was the the mostmost serious.serious. A detailed inspection inspection of of the the re remainingmaining cable cable clamps clamps revealed revealed that that a atotal total of of20 20cable cable clamps clamps in inthe the whole whole bridge bridge had had slipped. slipped. Among Among them, them, there there were were 11 sliding 11 sliding po- positionssitions of of the the west west cable cable clamp, clamp, and and 9 9 sliding sliding positions positions of the east cablecable clamp.clamp. FigureFigure5 5 showsshows thethe downwarddownward positionspositions ofof thethe cable cable clamps. clamps.

FigureFigure 5. 5.Positions Positions ofof thethe cablecable clampsclamps afterafter slipping. slipping.

TheThe measurements showed showed that that five ﬁve cable cable clamps clamps slipped slipped beyond beyond 5 cm, 5 cm,and andthe max- the maximumimum slippage slippage was was found found to be to 10.2 be 10.2cm. cm.Table Table 1 summarizes1 summarizes the theslippage slippage of the of thecable cable clip. clip. Table 1. Slippage of the cable clip.

TableSample 1. Slippage of the 1 cable2 clip. 3 4 5 6 7 8 9 10 SlippageSample (cm) 10.2 1 5.1 2 2.3 3 5.4 4 3.3 5 5.7 6 3.2 7 2.2 8 1.7 9 101.3 Sample 11 12 13 14 15 16 17 18 19 20 Slippage (cm) 2.4 10.2 2.6 5.1 2.1 2.3 1.8 5.4 1.2 3.3 3.3 5.7 2.4 3.2 2.26.7 1.73.1 1.32.5 Sample 11 12 13 14 15 16 17 18 19 20 Slippage (cm) 2.4 2.6 2.1 1.8 1.2 3.3 2.4 6.7 3.1 2.5 Because of the slipping of several cable clamps, the variation in the structural force acting on the full bridge is complicated. To eliminate the numerous interferences and ob- tain Becausethe most of representative the slipping ofsituation, several cablethe sli clamps,pping of the a single variation cable in clamp the structural on one side force is actingemployed on the for fullthe bridgesimulation. is complicated. We established To eliminate a model thefor the numerous slipping interferences of this clamp. and In obtainaddition the to most considering representative the weight situation, of the the main slipping cable, of stiffening a single cablebeams, clamp main on tower, one side and ishangers, employed it is for necessary the simulation. to consider We auxiliary established components, a model for such the as slipping the bridge of this deck clamp. paving, In additionsidewalks, to and considering guardrails, the and weight convert of the them main into cable, constant stiffening loads beams,for the simulation main tower, analy- and hangers,sis. The dead it is necessary load distribution to consider of the auxiliary bridge components, deck paving such asphalt, as the sidewalks, bridge deck and paving, guard- sidewalks,rails and other and guardrails,ancillary components and convert is them 132 intokN/m. constant loads for the simulation analysis. The dead load distribution of the bridge deck paving asphalt, sidewalks, and guardrails and3. Simulation other ancillary of Ca componentsble Clamp Slippage is 132 kN/m. 3.1. Finite Element Modelingsubsection MIDAS Civil was used to establish a finite element model for the theoretical calcula- tions. The bridge is first assembled from a free cables state to a finished bridge state and then changed from a finished bridge state to a slip state. In a structural analysis, the equilibrium equation of the force should be established based on the geometric position of the structure after deformation, and the relationship between the force and the deformation is nonlinear. Therefore, the model cannot be established directly from the slip state. When building the model, the finished bridge state model must be established first, and then the slip state should be established based on the finished bridge state. The models currently employed can mainly be divided into nondamaged bridge completion stage models and

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3. Simulation of Cable Clamp Slippage 3.1. Finite Element Modelingsubsection MIDAS Civil was used to establish a finite element model for the theoretical calcu- lations. The bridge is first assembled from a free cables state to a finished bridge state Symmetry 2021, 13, x FOR PEER REVIEWand then changed from a finished bridge state to a slip state. In a structural analysis, the6 of 16 equilibrium equation of the force should be established based on the geometric position of the structure after deformation, and the relationship between the force and the deformation is nonlinear. Therefore, the model cannot be established directly from the slip state. When single-hangerbuilding the model,slip whole the finished bridge bridgemodels state for modelcalculation must beand established comparison. first, andThe thenmain the girder andslip the state main should tower be of established the whole based bridge on mode the finishedl are simulated bridge state. by The beam models elements, currently and the mainemployed cables canand mainlyhangers be are divided mainly into stimulated nondamaged by bridge cable completionelements. Table stage models2 lists the and main modelingsingle-hanger material slip parameters. whole bridge models for calculation and comparison. The main girder and the main tower of the whole bridge model are simulated by beam elements, and the main cablesTable 2. and Specifications hangers are of mainly the main stimulated components. by cable elements. Table2 lists the main modeling material parameters. Modulus of Elasticity Design Compressive Design Tensile Structural Part Material Table 2. Specifications of(MPa) the main components.Strength (MPa) Strength (MPa) Galvanized high-strength Main cable Modulus of2 Elasticity× 105 Design Compressive — Design Tensile 1670 Structural Part Material steel wire (MPa) Strength (MPa) Strength (MPa) Galvanized high-strength Hanger Galvanized 2 × 1015 — 1770 Main cable 2 × 105 — 1670 high-strengthsteel steel wire wire Concrete main girder Galvanized Hanger 2 × 1015 — 1770 Tower column and lower girderhigh-strength C50 concrete steel wire 3.45 × 104 22.4 1.83 Concrete main girder of bridge tower C50 concrete 3.45 × 104 22.4 1.83 TowerBridge column deck and C55 concrete 3.55 × 104 24.4 1.89 lower girder of bridge Composite girdertower steel girder Q370qE 2 × 105 22.4 335 Bridge deck C55 concrete 3.55 × 104 24.4 1.89 Composite girder steel Q370qETo ensure that the force 2 × 105condition of the bridge 22.4 is simulated correctly 335 and is con- girder sistent with reality, when the model is established, the boundary conditions are as follows: consolidate the bottom nodes of the main tower; rigidly connect the top of the main cable to the mainTo ensure tower that and the then force release condition the of full the fixation bridge is in simulated the rest of correctly the direction and is consistent of the bridge displacement;with reality, whenrigidly the connect model isthe established, bottom of the the boundary main cable conditions to the aremain as follows:girder and con- con- strainsolidate all direction; the bottom elastic nodes ofsupport the main simulation tower; rigidly is adopted connect theat topeach of support the main of cable the to main the main tower and then release the full fixation in the rest of the direction of the bridge beam. The entire bridge is divided into 4706 elements and 5409 nodes. Among them, the displacement; rigidly connect the bottom of the main cable to the main girder and constrain mainall direction;cable has elastic106 elements, support simulationand only 98 is adoptedelements at of each the support hanger of are the used main as beam. tensile The members.entire Figure bridge 6 shows is divided the intomodel 4706 diagram. elements and 5409 nodes. Among them, the main cable has 106 elements, and only 98 elements of the hanger are used as tensile members. Figure6 shows the model diagram.

Figure 6. Integral ﬁnite element model of a bridge.

Figure 6. Integral finite element model of a bridge.

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3.2. Simulation Steps for Cable Clamp Slippage For cable clamp slippage, in this study, the method of double-cable element replacement with common nodes is adopted. A new construction stage after the last construction stage of the original bridge type is established and defined as the cable clamp slip stage. We compared the two stages and observed the variations in the structural parameters after cable clamp slippage. In the slipping stage, the original main cable element is passivated, and the adjusted main bridge state cable element is activated to ensure that the model follows the original design. In the sliding stage of the cable clamp, the original main cable element, without slipping of the cable clamp, is passivated, and the main cable element after the cable clamp slips is activated correspondingly. The model takes the original mechanical state when the bridge is erected under the original design without the stress cable length as the initial state, the adjusted cable element is used to re-calculate iteratively, and finally the model converges to the slip state to complete the cable clamp slip. In the simulation of the moved finite element model, the cable element of the aforementioned main cable is adjusted by modifying the unstressed length parameters of the main cable element. The original main cable element is controlled by the unstressed cable length given by the design, and the bridge is in the final state of the bridge with the original design cable length under the working force. The replaced cable element changes its unstressed length relative to the original cable element. The modifications are as follows: Using the measured or known slippage of the cable clamp in the final slipping state, the stress-free length change in the main cable section before and after the slipping of the cable clamp node is calculated, and the stress-free length of the main cable element, before and after the slipping of the cable clamp node, is manually adjusted. The total unstressed length of the main cable element before and after the adjustment should be kept constant.

3.3. Verification of Measured Cable Force Against Model Cable Force The hanger is the force transmission member that transfers the stiffening girder’s own weight and external load to the main cable. It is the link between the stiffening girder and the main cable that bears the axial tension. The magnitude of the constant load axial force in the hanger determines the behavior of the main cable in the suspension bridge. The overall linearity in the completed state of the bridge also determines the magnitude and distribution of the dead load bending moment of the stiffening girder; therefore, the hanger is key to studying the finished state of the bridge after completion of the suspension bridge. The cable force is the most intuitive measurement standard that reflects the overall force of the hanger [19]. The force distribution, between the main cable and the main girder of the actual spatial self-anchored suspension bridge, is mainly determined by the sling force, and the load on the main girder is transmitted by the hanger. Therefore, the load on the main beam is directly related to the weight of the main beam and the cable force of the sling. To ensure that the finite element simulation is consistent with the actual force trend in the actual completed state, the hanger cable force was used to verify the model. The verification method was used to measure the hanger frequency using the frequency method when the bridge was completed in 2011, and the result was then compared with the cable force obtained from the finite element method. The suspension bridge structure is a symmetrical structure, so only the cable forces of the model and actual bridge on one side of the structure are compared. As shown in Figure7, the cable force distribution in the model is consistent with the actual cable force distribution trend of the bridge in 2011. The maximum cable force in the finite element model is 2590 kN, and the maximum cable force measured in the bridge in 2011 was 2629.8 kN. The difference is 39.8 kN, and the positions are all close to the hanger of the main tower. Symmetry 2021, 13, 1514 8 of 16 SymmetrySymmetry 2021 2021, ,13 13, ,x x FOR FOR PEER PEER REVIEW REVIEW 88 of of 16 16

FigureFigureFigure 7. 7.7. Veriﬁcation VerificationVerification of ofof measured measuredmeasured and andand simulated simulatedsimulated cable cablecable forces. forces.forces.

AsAsAs shown shownshown in inin Figure FigureFigure8 8,,8, the thethe difference differencedifference between betweenbetween the thethe cable cablecable force forceforce provided providedprovided by byby the thethe ﬁnite finitefinite elementelementelement model modelmodel and andand the thethe measured measuredmeasured cable cablecable force forceforce of ofof the thethe bridge bridgebridge in inin 2011 20112011 is isis within withinwithin the thethe range rangerange of ofof 60.360.360.3 to toto 86.5 86.586.5 kN, kN,kN, with withwith the thethe difference differencedifference being beingbeing <5%. <5%.<5%. The TheThe maximum maximummaximum rate raterate ofof of change changechange on onon both bothboth sides sidessides of the hanger is 4.26%. This is because the length of the hanger on both sides is relatively ofof thethe hangerhanger isis 4.26%.4.26%. ThisThis isis becausebecause thethe lenglengthth ofof thethe hangerhanger onon bothboth sidessides isis relativelyrelatively short. In the actual test, the error of the cable force value calculated by the frequency short.short. InIn thethe actualactual test,test, thethe errorerror ofof thethe cablecable forceforce valuevalue calculatedcalculated byby thethe frequencyfrequency method will be relatively high; nevertheless, the test result and overall trend in the model methodmethod willwill bebe relativelyrelatively high;high; nevertheless,nevertheless, thethe testtest resultresult andand overalloverall trendtrend inin thethe modelmodel are in line with those observed in 2011 when the bridge was completed. Therefore, from areare inin lineline withwith thosethose observedobserved inin 20112011 whenwhen thethe bridgebridge waswas completed.completed. Therefore,Therefore, fromfrom the above comparison, it can be seen that the proposed model yields the same force state as thethe aboveabove comparison,comparison, itit cancan bebe seenseen thatthat ththee proposedproposed modelmodel yieldsyields thethe samesame forceforce statestate that of the bridge in 2011. The model can be used to simulate the single point slip of the asas thatthat ofof thethe bridgebridge inin 2011.2011. TheThe modelmodel cancan bebe usedused toto simulatesimulate thethe singlesingle pointpoint slipslip ofof thethe suspension bridge for a detailed analysis and calculation owing to the reliable accuracy. suspensionsuspension bridgebridge forfor aa detaileddetailed analysisanalysis andand calculationcalculation owingowing toto thethe reliablereliable accuracy.accuracy.

FigureFigureFigure 8. 8.8. Variations VariationsVariations in inin the thethe measured measuredmeasured and andand simulated simulasimulatedtedvalues valuesvaluesof ofofthe thethe hanger hangerhanger tensions. tensions.tensions.

ToToTo further furtherfurther verify verifyverify the thethe accuracy accuracyaccuracy of ofof the thethe clamp clclampamp slipping slippingslipping model modelmodel simulation, sisimulation,mulation, the thethe hanger hangerhanger cablecablecable force forceforce after afterafter clamp clampclamp slippage slippageslippage in inin the thethe model modelmodel is isis compared comparedcompared with withwith the thethe measured measuredmeasured cable cablecable force forceforce

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of the suspension bridge. As shown in Figure 9, the trend in the simulated hanger tension ofof thethe suspension bridge. As As shown shown in in Figure Figure 9,9 ,the the trend trend in in the the simulated simulated hanger hanger tension ten- after single-clamp slippage and the measured cable force is the same. The greater differ- sionafter aftersingle-clamp single-clamp slippage slippage and the and measured the measured cable cableforce forceis the issame. the same.The greater The greater difference in the individual cable force can be attributed to the reallocation of the hanger tension differenceence in the in individual the individual cable force cable can force be can attrib beuted attributed to the reallocation to the reallocation of the hanger of the hangertension after repeated cable clamp slippage during actual measurement. Nevertheless, the simu- tensionafter repeated after repeated cable clamp cable slippage clamp slippage during during actual actualmeasurement. measurement. Nevertheless, Nevertheless, the simu- the lated hanger tension after the most severe clamp slippage coincides with the trend in the simulatedlated hanger hanger tension tension after afterthe most the mostsevere severe clamp clamp slippage slippage coincides coincides with the with trend the trendin the measured data. Hence, the simulation of the single-clamp slippage by the finite element inmeasured the measured data. Hence, data. Hence,the simulation the simulation of the single-clamp of the single-clamp slippage slippage by the finite by the element ﬁnite model is accurate. elementmodel is model accurate. is accurate.

Figure 9. Cable forces after simulated slip of a single cable clip and measured hanger tension in FigureFigure2021. 9.9.Cable Cable forces forces after after simulated simulated slip slip of aof single a single cable cable clip andclip measuredand measured hanger hanger tension tension in 2021. in 2021. AsAs shownshown inin FigureFigure 10 10,, thethe overalloverall cablecable forceforce afterafter thethe measuredmeasured slipslip inin 2021 2021 is is As shown in Figure 10, the overall cable force after the measured slip in 2021 is greatergreater thanthan thethe ﬁnite finite element element model model simulation simulation result. result. The The overall overall difference difference between between greater than the finite element model simulation result. The overall difference between thethe measuredmeasured cablecable force and and the the simulated simulated cable cable force force is is<10%, <10%, where where the the maximum maximum dif- the measured cable force and the simulated cable force is <10%, where the maximum dif- differenceference in inthe the measured measured and and simulated simulated cable cable forces forces after after clamp clamp slippage slippage is 137.1 is 137.1 kN, kN,and andference the in simulated the measured cable forceand simulated is 7.26% lowercable forces than the after measured clamp slippage cable force. is 137.1 The kN, above and the simulated cable force is 7.26% lower than the measured cable force. The above com- comparisonthe simulated shows cable that force the is proposed7.26% lower ﬁnite than element the measured model yields cable theforce. same The result above as com- the parison shows that the proposed finite element model yields the same result as the force forceparison state shows measured that the in proposed 2021, indicating finite elemen that thet model accuracy yields of the the same proposed result suspensionas the force state measured in 2021, indicating that the accuracy of the proposed suspension bridge bridgestate measured model is reliablein 2021, and indicating can be usedthat the for furtheraccuracy analysis of the andproposed calculation. suspension bridge model is reliable and can be used for further analysis and calculation. model is reliable and can be used for further analysis and calculation.

FigureFigure 10. 10.Variations Variations in in the the simulated simulated and and measured measured hanger hanger tensions tensions after after the the simulated simulated slip slip of of a a Figuresingle cable10. Variations clamp in 2021.in the simulated and measured hanger tensions after the simulated slip of a singlesingle cablecable clampclamp inin 2021.2021.

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4.4. ResultsResults ofof FiniteFinite ElementElement CalculationCalculation InIn thethe analysisanalysis toto clearlyclearly illustrateillustrate thethe impactimpact ofof cablecable clampclamp slippageslippage onon thethe overalloverall structurestructure ofof thethe self-anchoredself-anchored suspensionsuspension bridge,bridge, thisthis studystudy conductedconducted aa single-pointsingle-point slipslip analysisanalysis to simulate and and analyze analyze the the impact impact on on the the structure. structure. The The most most serious serious clamp clamp slip- slippingping location location on onthis this bridge bridge is isselected selected for for the the slippage slippage simulation simulation of the singlesingle cablecable clamp.clamp.

4.1.4.1. HangerHanger CableCable ForceForce beforebefore andand afterafter CableCable ClampClamp SlippageSlippage InIn thethe studystudy ofof cablecable clampclamp slippage,slippage, itit isis foundfound thatthat thethe mostmost directdirect resultresult ofof slippageslippage isis thethe changechange inin thethe magnitudemagnitude ofof thethe cablecable force.force. AsAs shownshown inin FigureFigure 11 11,, thethe cablecable forceforce before and after the slip of a single cable clamp is simulated using the ﬁnite element model, before and after the slip of a single cable clamp is simulated using the finite element and it is found that the slippage decreases the cable force of this hanger, while the cable model, and it is found that the slippage decreases the cable force of this hanger, while the force of the two adjacent hangers relatively increases. cable force of the two adjacent hangers relatively increases.

FigureFigure 11.11. DiagramDiagram ofof hangerhanger tensiontension beforebefore andand afterafter thethe slipslip ofof aa simulatedsimulated singlesingle cable cable clip. clip.

InIn combinationcombination withwith thethe cablecable forceforce ofof thethe entireentire bridgebridge hanger,hanger, thethe single-cablesingle-cable clampclamp slippageslippage affectsaffects aboutabout twotwo hangerhanger positionspositions atat thethe frontfront andand rear,rear, and and the the cable cable force force of of the the hangerhanger atat thethe farthestfarthest distancedistance isis <1%.<1%. FromFrom thethe overalloverall position,position, becausebecause ofof thethe stiffnessstiffness ofof thethe mainmain tower,tower, thethe slippageslippage inin thethe middlemiddle spanspan affectsaffects thethe cablecable forceforce ofof thethe sideside spanspan hangerhanger byby lessless thanthan 1%.1%. FigureFigure 1212 focusesfocuses onon thethe impactimpact ofof single-cablesingle-cable clampclamp slippageslippage onon thethe cablecable forceforce ofof adjacentadjacent hangershangers on the same side. As As observed observed,, the the cable cable force force at at the the slipping slipping position position is isreduced reduced by by 392.6 392.6 kN, kN, the the hanger hanger cable cable force force drops drops by 19.2% compared withwith thatthat beforebefore thethe slip,slip, andand thethe cablecable forceforce ofof thethe fourfour hangershangers beforebefore andand afterafter thethe slipslip isis increasedincreased byby 62.8,62.8, 123.3,123.3, 147.7,147.7, andand 26.226.2 kN.kN. ComparedCompared withwith pre-slip,pre-slip, thethe cablecable forceforce growthgrowth ratesrates areare 2.45%,2.45%, 6.19%,6.19%, 7.25%,7.25%, andand 1.29%.1.29%. TheThe impactimpact ofof thethe remainingremaining hangerhanger cablecable forceforce isis <1%.<1%. TheThe single-clampsingle-clamp slippage slippage affects affects other other hanger hanger cable cable forces. forces. The impactThe impact is only is inonly the rangein the ofrange the twoof the hangers two hangers before andbefore after. and after.

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FigureFigureFigure 12.12. 12. VariationVariation Variation inin in thethe the hangerhanger hanger tensiontension tension beforebefo beforere andand and afterafter after cablecable cable clipclip clipslippage. slippage. slippage.

4.2.4.2.4.2. Force Force ActingActing Acting onon on thethe the MainMain Main GirderGirder Girder beforebefore before andand and afterafter after CableCable Cable ClampClamp Clamp SlippageSlippage Slippage TheTheThe suspension suspensionsuspension bridgebridgebridge isisis a aa ﬂexible flexibleflexible structure, structstructure,ure, wherein whereinwherein the thethe stiffening stiffeningstiffening girder girdergirder mainly mainlymainly providesprovidesprovides the thethe torsional torsionaltorsional stiffness stiffnessstiffness and andand load loadload acting actingacting surface surfacesurface and transmits andand transmitstransmits the load thethe to load theload hanger. toto thethe Thehanger.hanger. hanger The The connects hanger hanger connects theconnects main the cablethe main main and cable thecable stiffening an andd the the stiffening girderstiffening and girder girder distributes and and distributes thedistributes load from the the theloadload stiffening from from the the girder stiffening stiffening to the girder girder main to cable.to the the main main Therefore, ca cable.ble. theTherefore, Therefore, change inthe the the change change hanger in in tensionthe the hanger hanger directly ten- ten- affectssionsion directly directly the force affects affects state the ofthe the force force main state state girder, of of the the and main main the effectgirder, girder, of and and single-clamp the the effect effect slippageof of single-clamp single-clamp on the main slipslip- girderpagepage on on is discussedthethe main main girder girder here. is is discussed discussed here. here. AsAsAs shownshown shown inin in FigureFigure Figure 1313, 13,, thethe the maximum maximum variationvariat variationion inin in thethe the bendingbending bending momentmoment moment atat at thethe the singlesingle- clampclampclamp slippingslipping slipping positionposition position isis is 118118 118 kN,kN, kN, andand and thethe the variationvariation variation raterate rate isis is 1.28%.1.28%. 1.28%. ThisThis This ﬁgurefigure figure alsoalso also showsshows shows thatthatthat the thethe magnitude magnitudemagnitude of ofof the thethe effect effecteffect decreases decreasesdecreases with wiwithth the thethe increase increaseincrease in inin the thethe slipping slippingslipping cable cablecable clamp clampclamp positionpositionposition distance,distance, distance, and and and the the the effect effect effect of of of mid-span mid-span mid-span slippage slippage slippage on on on the the the side-span side-span side-span main main main girder girder girder bending bend- bend- moment is <1%. inging moment moment is is <1%. <1%.

Figure 13. Variation in the bending moment of the main girder. FigureFigure 13.13. VariationVariation inin thethe bendingbending momentmoment ofof thethe mainmain girder.girder.

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After cable clamp slippage, because of the change in the cable force of the horizontal symmetricAfter cable hanger, clamp the slippage, force of the because main ofgirder the change is no longer in the on cable theforce same of horizontal the horizontal plane. symmetricAs a result, hanger, the change the force in the of cable the mainforce girdercausesis a local no longer torsion on effect the same on the horizontal stiffened plane.girder. AsTo a clearly result, theanalyze change the in influence the cable range force causesof the torque a local torsionchange effectin the on main the stiffenedgirder, the girder. main Togirder clearly at the analyze cable the clamp influence slipping range position of the is torquetaken as change the 0 point, in the and main the girder, distance the is main used girderto represent at the cable the influence clamp slipping range. positionThe change is taken in the as internal the 0 point, force and of the distancemain girder is used after toslipping represent was the carefully influence studied, range. and The it change was found in the that internal the influence force of the of the main slippage girder afterin the slippingmiddle wasspan carefully was only studied, within andthe middle it was found span, thatand thethe influenceinfluence of on the the slippage side span in thewas middlelow. span was only within the middle span, and the influence on the side span was low. FromFrom Figure Figure 14 14,, the the biggest biggest change change in in the the torque torque of of the the main main girder girder after after the the single single cablecable clamp clamp slips slips is is the the main main girder girder between between the the W1 W1 tower tower and and W2 W2 tower, tower, while while the the main main girder torque change of the side span is smaller. From a local analysis, the slippage of the girder torque change of the side span is smaller. From a local analysis, the slippage of the cable clamp only has an impact on the torque near the hanger, and the range of the four cable clamp only has an impact on the torque near the hanger, and the range of the four hangers is approximately its range of influence. Through distance analysis, the influence hangers is approximately its range of influence. Through distance analysis, the influence range of the single cable clamp on the main girder torque after slipping is 24 m in total. range of the single cable clamp on the main girder torque after slipping is 24 m in total. Among them, the slip of the single cable clamp has a greater impact on the torque of the Among them, the slip of the single cable clamp has a greater impact on the torque of the main beam close to the W1 main tower, with an impact range of 16 m, and an impact range main beam close to the W1 main tower, with an impact range of 16 m, and an impact range of 8 m in the mid-span direction. of 8 m in the mid-span direction.

FigureFigure 14. 14.Torque Torque of of the the main main girder. girder.

AsAs shown shown in in Figure Figure 15 15,, cable cable clamp clamp slippage slippage has has a a signiﬁcant significant impact impact on on the the local local torquetorque of of the the main main girder. girder. The The torque torque after after slippage slippage is is 3.5 3.5 times times that that before before slippage, slippage, and and thethe maximum maximum torque torque change change after after slippage slippage is is 1785 1785 kN. kN. In In terms terms of of the the long-term long-term torque torque effect,effect, this this is is unfavorable unfavorable to to the the main main girder girder in in terms terms of of the the force. force.

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Figure 15. Variations in the main girder torque before and after cable clamp slippage. FigureFigure 15. 15.Variations Variations in in the the main main girder girder torque torque before before and and after after cable cable clamp clamp slippage. slippage.

4.3.4.3.4.3. Forces ForcesForces Acting Acting on onon the thethe MainMain Main CableCable Cable before before and and and after after after Cable Cable Cable Clamp Clamp Clamp Slippage Slippage Slippage TheTheThe main main cable cable is isis the thethe mainmain main load-bearing load-bearing me member membermber of of ofthe the the structural structural structural system system system and and and is a is is a a geometricallygeometricallygeometrically varying varying body,body, body, mainlymainly mainly subjected subjected to to to tension. tension. tension. The The The main main main cable cable cable has has has a high a a high high initial initial initial tensiletensiletensile force forceforce under under constant constantconstant loading,loading, loading, providing providing “geometric “geometric “geometric stiffness” stiffness” stiffness” for for forthe the thesubsequent subsequent subsequent structure,structure,structure, not not onlyonly throughthrough its itsits own own elastic elastic de de deformation,formation,formation, but but but also also also through through through the thegeometry the geometry geometry to to affect the system equilibrium. Hence, cable clamp slippage will have a corresponding ef- toaffect affect the the system system equilibrium. equilibrium. Hence, Hence, cable cable clamp clamp slippage slippage will will have have a corresponding a corresponding effect on the tensile force. effectfect on on the the tensile tensile force. force. As shown in Figure 16, the maximum effect of single-clamp slippage on the main AsAs shown shown in in Figure Figure 16 16,, the the maximum maximum effect effect of of single-clamp single-clamp slippage slippage on on the the main main cable force is at the slippage location, while the maximum main girder force is 527.6 kN, cable force is at the slippage location, while the maximum main girder force is 527.6 kN, a cablea change force of is 1.21% at the before slippage and afterlocation, slippage while. The the maximum maximum change main isgirder 1.21%. force The isremain- 527.6 kN, change of 1.21% before and after slippage. The maximum change is 1.21%. The remaining aing change positions of 1.21% of the before main cableand after force slippage change is. The <1%, maximum and the middle-span change is 1.21%. clamp Theslippage remain- positions of the main cable force change is <1%, and the middle-span clamp slippage has a inghas positionsa certain effectof the on main it. The cable main force tower change stiffness is <1%, is higher and the on middle-span the mid-span clamp side of slippage the certain effect on it. The main tower stiffness is higher on the mid-span side of the main hasmain a certaincable, and effect the onforce it. changeThe main on the tower side stiffness span side is of higher the main on cablethe mid-span tension is side <1%. of the cable,main andcable, the and force the change force change on the sideon the span side side span of side the mainof the cable main tension cable tension is <1%. is <1%.

Figure 16. Rate of change of main cable tension before and after cable clip slippage.

FigureFigure 16. 16.Rate Rate of of change change of of main main cable cable tension tension before before and and after after cable cable clip clip slippage. slippage.

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4.4.4.4. ForcesForces inin thethe MainMain TowerTower before before and and after after Cable Cable Clamp Clamp Slippage Slippage InIn aa suspensionsuspension bridge,bridge, thethe mainmain tower tower is is a a compression-bending compression-bending member. member. InIn thethe verticalvertical direction, direction, the the main main tower tower bears bears the the vertical vertical force force of of the the main main cable cable mainly mainly through through thethe constantconstant load.load. InIn thethe longitudinallongitudinal direction,direction, thethe horizontalhorizontal forceforce ofof thethe mainmain cablecable is is balancedbalanced onon bothboth sidessides ofof thethe towertower byby thethe effecteffect ofof the the constant constant load,load, andand nono bending bending momentmoment is is generatedgenerated on on the the tower.tower. After After cable cable clamp clamp slippage, slippage, the the unbalanced unbalanced state state of of the the loadload causes causes an an unbalanced unbalanced tension tension on on both both sides sides of the of mainthe main tower, tower, resulting resulting in a horizontal in a hori- displacementzontal displacement of the tower of the top. tower The top. single-clamp The single-clamp slippage atslippage the mid at span the mid causes span the causes main towerthe main to produce tower to a produce longitudinal a longitudinal top displacement top displacement of 0.242 mm. of 0.242 mm. AfterAfter thethe horizontalhorizontal displacementdisplacement ofof thethe toptop ofof thethe tower,tower, the the horizontal horizontal force force of of the the mainmain cablecable onon bothboth sidessides ofof thethe mainmain tower tower isis rebalanced, rebalanced, the the main main tower tower is is subjected subjected to to anan unbalancedunbalanced main cable tension, tension, and and the the be bendingnding moment moment is ischanged. changed. As Asshown shown in Fig- in Figureure 17, 17 the, the trend trend in the in the main main tower tower bending bending mome momentnt after after slippage slippage is consistent is consistent with with that thatbefore before slippage. slippage. Due Dueto the to single-clamp the single-clamp slippage, slippage, the maximum the maximum change change value value of the of main the maintower tower is 0.0558 is 0.0558 kN·m. kN ·m.

FigureFigure 17.17.Bending Bending momentmoment diagramdiagram ofof mainmain towertower before before and and after after cable cable clip clip slippage. slippage.

4.5.4.5. SuggestionsSuggestions forfor HandlingHandling CableCable ClampClamp SlippageSlippage AA forceforce analysis of self-anchored self-anchored suspension suspension bridges bridges after after single-clamp single-clamp slippage slippage re- revealedvealed that that cable cable clamp clamp slippage, slippage, which which typically typically brings about aa minorminor change,change, directlydirectly affectsaffects thethe forceforce ofof eacheach main main component. component. Practically,Practically,cable cableclamp clampslippage slippageis isnot nota a ﬁxed fixed state,state, butbut a a statestate thatthat continues continues to to deteriorate deteriorate with with the the operational operational phase phase of of the the bridge. bridge. As As moremore clamps clamps slip, slip, the the slipping slipping distance distance gradually gradually increases, increases, and and the the structural structural forces forces of the of bridgethe bridge tend tend to develop to develop unfavorably. unfavorably. If this If problemthis problem is ignored, is ignored, the safety the safety of the of bridge the bridge will bewill compromised. be compromised. Therefore, Therefore, if slipping if slipping of cable of cable clamps clamps in suspension in suspension bridges bridges is detected is de- duringtected during structural structural inspection, inspection, a detailed a detailed investigation investigation should should be conducted be conducted immediately, imme- anddiately, for cableand for clamps cable withclamps slippage with slippage <5 mm, <5 measures, mm, measures, such as such re-torqueing as re-torqueing of the bolts,of the shouldbolts, should be taken be to taken restore to therestore slip the resistance slip resi ofstance the clamps of the to clamps prevent to furtherprevent slippage. further slip- For cablepage. clampsFor cable with clamps a slippage with >5a slippage mm, immediate >5 mm, restorationimmediate restoration and adjustment and adjustment should be performed to ensure structural safety [20]. should be performed to ensure structural safety[20]. 5. Conclusions This study conducted an analysis of cable clamp slippage, a common phenomenon in actual bridges. To clarify the force acting on a self-anchored suspension bridge before and after cable clamp slippage, the slipping of a single clamp was used for the analysis.

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We focused on the forces acting on the hangers, main girder, main cable, and main tower before and after cable clamp slippage in the studied bridge. The main research results are as follows: (1) Simulations of the hanger cable force after single-clamp slippage revealed that the slippage directly affects the hanger cable force, and its inﬂuence range is at the two hanger positions before and after the change. After slippage, the corresponding hanger cable force was reduced by 19.2%, while the cable force of the adjacent hanger increased sharply (up to 7.25%). (2) The bending moment and torque of the main girder before and after single-clamp slippage revealed that the change in the bending moment of the main girder was up to 1.28%. Meanwhile, the local forces on the main girder induced by single-clamp slippage led to a torsion effect. As a result, the torque increased by 250%. (3) An analysis of the tension in the main cable before and after single-clamp slippage revealed a re-distribution of the main cable tension after the slippage. Speciﬁcally, the change in the main cable tension at the single-clamp slippage position was 1.21%, while the changes at the remaining positions were <1%. (4) After single cable clamp slippage, the top of the main tower exhibited a longitudinal displacement of 0.242 mm. Because of the greater rigidity of the main tower, the single-clamp slippage had a small effect on the bending moment of the main tower (up to 0.0558 kN). In the study of cable clamp slips, it was found that the most direct effect after the cable clamp slips is the change in the force of the hanger. From the perspective of the whole bridge, the slip of the cable clamp will directly lead to the imbalance of the force on the main girder, and this problem will cause the main girder to be subjected to torsion for a long time. Changes caused by the slippage of the cable clamp are often not conducive to the safe use of the bridge. Future research will continue to focus on this area, focusing on the slippage of the cable clamp and the limit of the slippage of the cable clamp. These studies are of great importance to the safety performance of the bridge.

Author Contributions: Conceptualization, H.L. and Y.L.; methodology, Y.L.; software, C.L.; ex- periment, Y.L. and H.H.; data curation, Y.L.; writing—original draft preparation, Y.L.; writing— review and editing, H.L. and Q.S. All authors have read and agreed to the published version of the manuscript. Funding: The research in this paper was supported by the Science and Technology Project of the Department of Transportation of Heilongjiang Province (2021HLJ01K42) and the Science and Technology Project of the Department of Transportation of Heilongjiang Province (2020HLJ018). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data that support the findings of this study are available upon reasonable request. Conflicts of Interest: The authors declare that they have no conflict of interest.

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