easpTreno, 56

Available online 17 December 2014

Keywords:

echinin

the re behavior of these structural elements, the ISO 834 standard curve was considered as re model

main

mechanical properties ending in the eventual collapse of the rope.The high carbon content and the wire drawing process producene pearlitic microstructures and high level of work hardening,thus combining a signicant increase in tensile strength with aworsening of material ductility (Wistreich [2], Fontanari et al. [3],

short time, henceoth recrystalliza-

view of thespread use of ropes in civil construction and mechanical ations, the current approaches to assess their re safety arelimited. No systematic studies yet sporadic contributionfound in the technical literature. Fontanari et al. [7] proposedrecently an approach to test the re behavior of full locked ropes,whereas Ridge and Hobbs [8] published an experimental investiga-tion on rope sockets behavior at elevated temperatures focusingboth on cast metal and polymeric socketing. Kim et al. [9] studiedthe re behavior of high strength concrete columns laterallyconned by wire ropes. Fontenot et al. [10] and by Horn et al.

Corresponding author.E-mail addresses: vigilio.fontanari@unitn.it (V. Fontanari), matteo.benedetti@

unitn.it (M. Benedetti), bernardo.monelli@ing.unipi.it (B.D. Monelli), fabio.degasperi@provincia.tn.it (F. Degasperi).

Engineering Structures 84 (2015) 340349

Contents lists availab

Engineering

lsewhich led to the ropes failure. In two cases, failure occurred in lessthan 15 min. This report gave a serious warning for any ropesapplication. The rope exposure to high temperatures is particularlycritical, since it produces a rapid deterioration of the wires

however, the rope generally collapses in a verysuggesting an almost negligible contribution of btion and creep phenomena.

Despite this somewhat alarming situation inhttp://dx.doi.org/10.1016/j.engstruct.2014.12.0040141-0296/ 2014 Elsevier Ltd. All rights reserved.wide-pplica-prettycan beand maintenance of civil infrastructures. The ever-increasing diffu-sion of ropes in tall buildings, bridges, cable car, as well as in indus-trial applications, gives the reason for investigating ropes rebehavior. After the serious accidents occurred at the beginning ofthe last decade (Kaprun funicular in Austria 2000, Zugspitze rope-way in Germany 2001), Oplatka [1] investigated the most impor-tant re events involving ropeways and recorded 35 cases, 10 of

benecial effect of work-hardening on the mechanical properties.A further increase of the temperature up to 600 C activates therecrystallization process, responsible for the nucleation andgrowth of a new crystalline structure. The resulting detrimentaleffects on the strength characteristics are well known in the liter-ature (Dieter [6]), moreover, for long exposure to high tempera-tures, viscous ow (creep) can be activated. During a re event,Full locked wire ropesWarrington Seale ropesFire safetyDamage mechanismsFire curve ISO 834Multi-physics nite element modelling

1. Introduction

Structural re safety is one of theowing to its severity. For this purpose, parametric nite element models, capable of simulating thethermo-mechanical response of both full locked and Warrington Seale ropes have been developed. Theobtained information in terms of load redistribution during the test as well as evolution of damageand failure mechanisms was used to set up the experimental investigation. The good agreement betweenexperimental and numerical results indicates the proposed approach as an effective methodology for theanalysis of the re behavior of wire ropes, once the material properties and loading conditions have beenestablished.

2014 Elsevier Ltd. All rights reserved.

concerns in the design

Ray et al. [4], Phelippeau et al. [5]). The wire exposition to temper-atures above 300 C activates the dislocation movements responsi-ble for the annealing, thus producing an irreversible loss of theRevised 27 October 2014Accepted 1 December 2014

The behavior of ropes subjected to severe thermal transients representative of re scenarios has beeninvestigated through numerical and experimental analyses. Since no standards are available for studyingFire behavior of steel wire ropes: Experimand numerical analysis

V. Fontanari a,, M. Benedetti a, B.D. Monelli b, F. DegaUniversity of Trento, Dipartimento di Ingegneria industriale, Via Sommarive, 9, 38123bUniversity of Pisa, Dipartimento di Ingegneria Civile e Meccanica, Largo Lucio Lazzarinc Laboratorio tecnologico impianti a fune (LaTIF), Via Provina 24, 38040 Trento, Italy

a r t i c l e i n f o

Article history:Received 30 July 2014

a b s t r a c t

This paper describes the moping a method for determ

journal homepage: www.ental investigation

eri c

to, Italy126 Pisa, Italy

anical behavior of wire ropes under re conditions with the aim of devel-g the re resistance of steel wire ropes for civil and ropeway applications.

le at ScienceDirect

Structures

vier .com/locate /engstruct

g St[11]. Presented some interesting results about the re behavior oftextile ropes. The high costs of the experiments and the difcultiesin setting up the experimental devices still represent a majorobstacle to the acquisition of an experimental database includingdifferent classes of ropes and to the development of a specicdesign code. For this reason, in facing the problem of the re char-acterization of ropes, it may be useful to look at what has beenalready published in the literature about civil infrastructures.Although some criticisms regarding its effectiveness have beenrecently raised by Almand [12], one way to investigate the reresistance of a structural element is to perform a standard reresistance test, in order to simulate the temperature prole expe-rienced by the structural part during a real re event. Differenttimetemperature histories are suggested by the standards: oneof the most used is the ISO 834 standard, which is aimed at repro-ducing the timetemperature evolution during a re accident in aclosed environment surrounding the structure (Hasofer [13], Drys-dale [14], Rasbash et al. [15]). The component, stressed by the inservice structural loads and undergoing the aforementionedtimetemperature history, is monitored until the nal collapse orthe loss of its functionality (i.e. excess of deformation, not compat-ible with its structural integrity). The standard temperature curvesrepresent an overestimate of the re heaviness: the thermal load atashover is considered, thus neglecting the initiation of the com-bustion and its expansion phase, during which the temperatureincreases more slowly.

Transferring the outcomes of these tests into the design of ropesis not an easy task since the thermal history of each single wire ishardly predictable during the re transient. In the scientic litera-ture, a great effort has been devoted to understand the mechanicalbehavior of wire ropes under different loading conditions. The verycomplex load distribution among wires has been explained bymeans of analytical models and more recently by nite elementsimulations. The books of Costello [16] and Feyrer [17] summarizethe theoretical foundations and also report a comprehensive data-base of experimental results. The analytical models are based onsome simplifying assumptions and can correctly evaluate theropes performance in the elastic regime (Velinsky [18], Velinsky[19]), Raoof and Kraincanic [20], Wang and McKewan [21], Elataet al. [22]). These approaches can reasonably describe some ofthe phenomena, such as contact, friction, large displacements(the full-slip regime vs. the no-slip regime), simultaneously affect-ing the ropes mechanical response and have been thereforeadopted in the design of ropes. Finite element analysis can contrib-ute to the comprehension of such complex phenomena. Signicantcontributions have been published by Nawrocki and Labrosse [23],Jiang et al. [24] Stanova et al. [25], Moradi et al. [26], Kmet et al.[27]. All of these papers are primarily focused on the rope responsein the elastic regime, very little can be found dealing with themechanical behavior of ropes in the elastoplastic regime and evenless during severe thermal transients.

In the present work, the structural response of wire ropes in thepresence of very severe thermal transients simulating a re sce-nario is addressed both experimentally and numerically. The prin-cipal aim is to dene a design tool for predicting the ropes reresistance. For this purpose, the method proposed by the authorsin [7] has been developed and extended to cover a broader classof ropes. Parametric FE models have been developed both for fulllocked and for stranded ropes, able to simulate the ropes thermo-mechanical response during the re transient following the ISO834 standard, representing a fully developed re in a compartment.The ISO 834 timetemperature curve was adopted considering thatsome very severe re accidents occurred in compartments, such as

V. Fontanari et al. / Engineerinfor example in the engine room of cableways. The results of thisanalysis are essential to dene the experimental setup for safelyperforming the tests on the ropes. The models were set up and cal-ibrated on the basis of experimental data measured on the rope andon single wires: i.e. tensile tests at room temperature, thermal his-tories of different wire layers during the ISO 834 thermal transient.Moreover, in order to correctly simulate the mechanisms of loadredistribution among wires during the thermal transient, an exten-sive campaign was carried out on single wires to build up a data-base of re curves at different temperatures. These curves werethen incorporated into the model for the simulation of thethermo-mechanical response of the rope. The information gainedfrom the numerical model, in terms of load redistribution, timeand mechanism of collapse made it possible to set up the experi-mental conguration. The results of experimental tests in termsof ropes time to failure were compared with the results of numer-ical modeling both for full locked and Warrington Seale ropes.

2. Geometry of the full locked and Warrington Seale strandropes

The analysis is focused on two rope congurations: full lockedand strand rope with polymeric core. In this last case the Warring-ton Seale strand conguration was considered in view of its wide-spread application. Different nominal diameters were investigated,but for the denition and the development of the nite elementmodel, two specic geometric congurations were considered, cor-responding to a full locked rope having a nominal diameter of60 mm composed of 124 wires and a stranded Warrington-Seale6 31 rope composed of 186 wires, respectively. These represen-tative geometries are briey described in the following.

2.1. The full locked rope

The sectional view shown in Fig. 1 depicts the constructivecharacteristics of the rope having a nominal diameter equal to60 mm, consisting of a central straight wire, three layers of roundwires and three external mantles of Z shaped wires, all with crosswinding conguration. The rope labeling indicates the number ofwires of each layer, starting from the core wire. The metal sectionof the rope is equal to 2486 mm2, which corresponds to a llingratio (ratio of metal to nominal cross section) of about 88%. Thisrope is usually adopted in buildings and bridges as tie rods.

2.2. The Warrington Seale rope

The Warrington-Seale strand conguration and the correspond-ing standard wires layers denition are illustrated in Fig. 2a. Thissolution consists of three concentric wire layers helically woundabout the core wire, comprising a total of 31 wires having differentcross sections, aligned in a parallel conguration. The rope cong-uration made up of 6 strands wound around a polymeric core isshown in Fig. 2b. The standard sequence labeling of the strand12 + 6/6 + 6 + 1 indicates the number of wires from the externallayer to the inner core, whereas the rope labeling includes informa-tion on the number of strands (6) and on the polymeric core (PPCpolypropylene core). The metal section area of the rope is equal to721 mm2, which corresponds to a lling ratio (ratio of metal tonominal cross section including core) of about 64%. This geometryis typically adopted for producing ropes used for cableways andsimilar applications.

3. Properties of the wires at room temperature

The wires were produced by cold drawing high carbon steel C80

ructures 84 (2015) 340349 341bars characterised by a pearlitic microstructure typical of nearlyeutectoid steels. The nominal chemical composition of the wiresis given in Table 1.

g St342 V. Fontanari et al. / EngineerinGiven the marked differences in terms of cross section geome-try and area between the wires, it is reasonable to expect that thesewill have different tensile properties. The experimental character-ization was carried out on twelve specimens for each type of wiresconstituting the two ropes using a servo-hydraulic universalmachine (Instron 8516 100 kN). The elongation was measuredwith an extensometer having a gauge length of 12.5 mm. The ten-sile curves are shown in [7] for full locked ropes and in [28] for WSropes. Table 2 summarizes the principal average tensile parame-ters and the measured scatter.

As expected, the extent of cold drawing and the Z-shapingdeformation affect the tensile properties of the wires. In fact, thewires with the highest diameter show an appreciable elongationat fracture, whereas wires having the smallest diameters display

Fig. 1. Geometry of th

(a)

(c)

Fig. 2. Schematic representation of the Warrington-Seale (WS 12 + 6/6 + 6 + 1) strand (a)(b), main geometric-constructive features (c).

Table 1Nominal chemical composition of C80 steel used for steel wires.

C Mn Si S Cu Sn

wt% 0.800.85 0.400.85 0.10.3

Table 2Tensile properties of the different wires.

Wire cross section Young Modulus (GPa) Yield strength (MPa) Tensile strength (MPa) Elongation at fracture (%)

(mm2) Mean Std. Dev. Mean Std. Dev. Mean Std. Dev. Mean Std. Dev.

Full locked rope [7]14.24 198 4 1482 9 1925 7.5 3.90 0.0713.14 199 6 1507 11.5 1942 9 3.82 0.0823.2 (Z) 202 5 1264 9.5 1765 6.5 3.30 0.045

Warrington Seale rope [28]3.33 196 7.5 1391 12.5 2025 7.5 2.30 0.22.90 203 5 1505 10.5 2045 22.5 1.42 0.125

.5

2 174 1179 1770 6.73 177 1170 1778 6.8

V. Fontanari et al. / Engineering Structures 84 (2015) 340349 343displacement between the gripping heads. Preliminary tests wereperformed both on full locked ropes and WS ropes in order to esti-mate the actual breaking load and the engineering strain at frac-ture. Based on this information, a supplementary test was carriedout maintaining the extensometer mounted beyond the elasticlimit, up to 85% and 75% of the estimated actual breaking load

WS rope 1 135 798 1150 4.62 141 769 1138 4.43 138 773 Not broken Not broken1.91 198 5.5 1646 103.20 202 5 1395 105.73 200 6 1351 17

Table 3Tensile properties of the ropes.

Test n YoungModulus(GPa)

Yieldstrength(MPa)

Tensilestrength(MPa)

Elongation atfracture (%)

Full lockedrope

1 172 1197 1792 6.9for Full locked ropes and WS ropes, respectively. The stress straincurve until extensometer removal are shown in [7] and [28] andare plotted for comparison with FE results in Figs 5 and 6. Table 3summarizes the principal tensile parameters.

5. The nite element model

The FE models were developed with Ansys Code rel. 10 and 13.Parametric models were built to analyze different rope sizes. Theaxial length of the FE model was chosen as a compromise betweenthe computational heaviness and the need to avoid any boundaryeffect related to the application of both loads and constraints tothe model. The bodies were discretized using 8-nodes structuralelements, whereas the contact was enforced by surface-to-surfacecontact elements. The element size was determined by a conver-gence analysis. In order to limit the computational effort, an itera-

(a)

Fig. 3. Full locked rope: FE mesh developed for the analytive procedure was set up to identify the contact surfaces and tominimize the number of contact pairs. The nal mesh and anexample of the surface of possible contact between two wires, asidentied by the iterative procedure, are shown in Figs. 3 and 4for the full locked rope and the WS rope, respectively. For the latterrope, the function of the central core is to radially support thestrands. A 3D model of the core was developed with the aim of sat-isfactorily representing the geometry. The polymeric core wasmodelled as a simplied bilinear isotropic hardening (BISO) mate-rial characterised by elastic modulus of 1.6 GPa, yield strength of50 MPa, and plastic modulus of 160 MPa. As discussed in [7], thecore carries only a marginal part of the applied load.

The material models were assumed as homogeneous, isotropicand following a J2 ow rule with the hypothesis of isotropic hard-ening. For each wire, the true stress-true strain curves previouslydescribed were introduced into the FE model.

The axial loading conditions were applied to one of the terminalcross sections, in order to reproduce the displacement eld corre-sponding to the axial elongation. In order to prevent the uncoilingtendency of the spirally wound wires, the displacements along thecircumferential direction were constrained. Accordingly, on oneterminal section, axial and circumferential displacements wereconstrained while radial displacements were left free, on the oppo-site section an increasing axial displacement was applied main-taining the same constraints on both circumferential and radialdisplacements.

6. Setup and validation of the FE models

The FE models were developed and calibrated by comparing thenumerical results with results of a specic experimental character-ization. The results of the tensile tests conducted at room temper-

2120 27.5 1.44 0.1252040 10 2.31 0.152020 10 3.32 0.155ature were used to set up the structural response of the model,whereas the temperature measurement carried out on the ropeand the environment when simulating the ISO 834 temperatureprole were used for the thermal analysis.

(b)

sis (a) and identication of the contact surfaces (b).

developed for the analysis.

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extensometer removal344 V. Fontanari et al. / Engineerin6.1. Ropes structural behavior at room temperature

Numerical and experimental results were compared to checkfor the model correctness in simulating the ropes structuralbehavior. They can be rigorously compared in the rst part of thestressstrain curve, until the extensometer removal. Experimentaland numerical curves are plotted in Figs. 5 and 6, while Table 4 liststhe values for the elastic modulus and the deviation from linearityobtained from the two approaches. The FE analyses correctlyreproduce the elastic behavior and reasonably capture the devia-tion from linearity and the rst part of the elasto-plastic regime.After extensometer removal, the nominal strain calculated on thebasis of the relative displacement between gripping heads cannotbe longer compared with FE results.

6.2. The ISO 834 curve: Set up of the thermal FE model

An electric oven mounted on the testing machine (technicaldetails can be found in [7]) was designed for reproducing theISO 834 curve on a rope segment of 1.5 m length. The short timeinterval allows for disregarding the effect of creep so that therope collapse can be principally ascribed to the temperature-induced worsening in the wires mechanical behavior. It is there-fore of paramount importance to correctly know the thermaltransient of each rope wire, since this can have a strong inu-ence on the load redistribution among wires. In order to cali-brate the FE models, a set of thermocouples (type K, DINEN60584 [32]) have been positioned in the ropes in differentradial positions, moreover four thermocouples have been placed

0

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Nom

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experimentalFEM

Fig. 5. Full locked rope 60: comparison between the experimental and FE curve.ructures 84 (2015) 340349in the oven chamber to measure the environmental temperature.An example of the measured temperature proles for the fulllocked rope is plotted in Fig. 7. The air thermocouple positionedin the center of the oven chamber indicates that in the oven theISO 834 temperature prole is attained after nearly 3 min andthen the heating control can satisfactorily follow the curve.The temperature ramp measured by the core thermocouplestarts with some delay (nearly 3 min) with respect to the othercurves. The temperature gap between skin and core becomesremarkable, this difference can have very important effects onthe wires behavior during the test. The FEM was calibrated forreproducing the timetemperatures curves measured in differentpositions of the cross section (Fig. 8). FE calibration was carriedout iteratively by setting some parameters: the global heattransfer coefcient between air and rope skin, the contact heatresistance between shaped wires layers and nally the contactheat transfer resistance for internal strands. By means of the

0

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Nom

in

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extensometer removal

Fig. 6. WS strand rope 38: comparison between the experimental and FE curve.

Table 4Comparison between mean experimental values and FE results for full locked and WSstrand ropes.

Rope Experimental Numerical

Full locked Elastic Modulus (GPa) 176 175Deviation from proportionality (MPa) 1350 1310

WS strand Elastic Modulus (GPa) 138 134Deviation from proportionality (MPa) 540 575

7. Mechanical properties of the wires material at differenttemperatures

The mechanical response of the wires depends on their positionin the rope and consequently on the temperature history. It istherefore necessary to collect a database of experimental stressstrain curves at different temperatures after different stabilizationtimes. Although the steel grade adopted for wire ropes is quitecommon, systematic information about its mechanical propertiesas a function of temperature is not available. Therefore a seriesof tests at different temperatures has been carried out on wiressegments extracted from the rope. Tests were carried out by usinga on a 100 kN servo hydraulic testing machine on which a heatingfurnace was mounted. The temperature and stabilization time havebeen chosen in order to comply with the typical timetemperaturehistories experienced by the wire during the re simulation. Thetests were performed at temperature ranging from 100 C to600 C. The systemwas stabilised at the testing temperature beforeto start the test. Two stabilization times were considered: the

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ISO 834Oven ChamberRope skinRope core

Fig. 7. Temperature ramps measured in the oven chamber as well on the ropes skinand core.

V. Fontanari et al. / Engineering Structures 84 (2015) 340349 345800

900experimental measurements and introducing the material ther-mal properties found in the literature [6,29,30], a good reproduc-tion of the thermal transient of each wires layer can be obtained(Fig. 8).

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Fig. 9. Wires of Full locked rope: re curves at different temshorter was typically 3 min, whereas the longer was nearly 8 min.Preliminary tests showed that Z-shaped wires nearly behave

like circular wires when tested at T > 200 C: differences below4% were observed for the principal tensile parameters: elasticmodulus, yield strength, ultimate tensile stress and elongation tofracture. The experimental campaign was therefore performedonly on the round wires. The re curves plotted in Fig. 9 at differ-ent testing temperatures and stabilization time have been obtainedfrom tests performed on round wires having diameter equal to/ = 4.09 mm.

The re curves plotted in Fig. 10 refer to the tests carried out onwires taken from the WS strands. Also in this case a preliminarycharacterization showed that the marked differences observed atroom temperature for wires with different diameters are stronglymitigated when tested at T > 200 C. For this reason, the curves cor-responding to wires having diameter equal to 2.06 mm have beenplotted and implemented in the FE model.

The differences between curves obtained at the two stabiliza-tion times change according to the testing temperature. The max-imal difference can be observed for tests carried out at about400 C. Negligible differences were observed at 100 C and200 C, as well as very small differences have been measured athigher temperatures. The kinetics of microstructural modicationsis responsible for these differences. At lower temperatures, thekinetics of the phenomena is slow and therefore longer times are

0.06 0.07 0.08 0.09 0.1 0.11

100 C200 C300 C - 3 min300 C - 8 min400 C - 3 min400 C - 8 min600 C - 3 min600 C - 8 min strain [/]

peratures and for two different stabilizing time intervals.

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346 V. Fontanari et al. / Engineering Structures 84 (2015) 340349necessary to cause signicant variations. On the contrary, at thehighest temperatures, the kinetics is accelerated and the micro-structural changes occur in a shorter time.

8. Fire resistance of the ropes: experimental and numericalresults

8.1. The thermo-structural FE model

The FE model described in the previous sections was adoptedfor the thermo-structural analysis of the rope during the re sim-ulation. For this purpose, temperature dependent tensile proper-ties were implemented. Since the material behavior depends onboth temperature and exposure time, two different analyses werecarried out, considering the results of the tensile tests obtainedafter the two stabilization times. Structural boundary and loadingconditions resemble those described for the tensile test at roomtemperature: the service nominal stress (nearly 30% of the ulti-mate tensile strength of the rope) was rstly applied at room tem-perature (T = 20 C). After preloading, the thermal transient wasstarted keeping constant the axial loads. Each wire layer is forcedto follow the temperature ramp measured during the experimental

00 0.01 0.02 0.03 0.04 0.05 0.06

True strain [/]

Fig. 10. Wires of WS rope: re curves at different temperatures and for differentstabilizing time intervals.simulation of the ISO 834 curve. The time temperature prolesapplied on the full locked rope and to the WS ropes are presentedin Figs. 11 and 12. As expected, the temperature proles are morediversied for the full locked rope.

The overall rope behavior can be represented in terms of nom-inal strain vs. time. Two lifetimes were estimated by introducing

Fig. 11. Full locked rope: timetemperature cinto the FE analysis the materials properties measured on wiresat different stabilization times. The shorter and the longer lifetimesare estimated considering the longer (8 min) and the shorter sta-bilization time (3 min), respectively. The strain vs. time curves cor-responding to the shorter and the longer life estimate obtained forthe full locked rope having diameter / = 60 mm are shown inFig. 13, while Fig. 14 illustrates the curves obtained for theWS ropewith diameter of 38 mm. The range bounded by the two lifetimesgives an idea about the uncertainty in the estimation of the ropelife due to the approximate knowledge of the mechanical responseof each wire. The curves are similar in the rst part showing almostlinear strain vs. time evolution, which can be mainly dictated bythe materials thermal expansion, whereas a marked differencecan be detected in the vicinity of the nal collapse, due to the onsetof general plastic ow as a consequence of material strain soften-ing and recrystallization. Anyway, especially for the WS rope, theanalysis provides a fairly narrow interval within which the failurewill occur.

The mechanisms of load redistribution calculated by the FEanalysis can be used to correctly control the experimental test inorder to preserve the integrity of the experimental devices. Theexternal wire layers, subjected to the highest temperatures,undergo an extensive plastic deformation at a nearly constant, oreven decreasing stress. The applied load is therefore progressively

Fig. 12. WS rope: timetemperature curves applied to the different wire layers.transferred to the internal wires. Since all wires experience thesame axial elongation, it is reasonable to assume that failure willoccur at the internal wires, as for the estimated time to rupturetheir temperature is between 350 and 450 C, corresponding tothe lowest rupture strain (Figs. 9 and 10). The rope collapse may

urves applied to the different wire layers.

g St0

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shorter life assessmentlonger life assessment

Fig. 13. full locked rope / = 60 mm: nominal strain increment vs. time curvesduring re simulation. Shorter and longer life assessment.

V. Fontanari et al. / Engineerinnot be catastrophic, in fact the external wires, which follow the recurves determined at nearly 600 C, can contain the broken wiresdissipating a consistent part of the released energy by plasticdeformation. The characteristic whip stroke experienced in theropes tensile tests at room temperature can be strongly smoothedor even suppressed, thus mitigating the risks for the experimentaldevices. This nding supports performing the experimental test onthe rope with reasonable safety.

The WS ropes have a polymer core that can play a not negligiblerole on the re response. In order to study the core behavior, somepreliminary tests were conducted, which showed that the coresoftens up to liquefaction and then burns, giving a signicant boostof energy. This phenomenon was not included in the FE analysis.

8.2. Comparison between numerical and experimental results

Fig. 15 shows the comparison between the numerical resultsand the experimental curves for the full locked ropes: the experi-mental curves are indistinguishable from the numerical curves inthe rst part, then an anticipated transition to a nonlinear behaviorand a less steep gradient in the nal part can be observed. A goodagreement between the experimental and the numerical resultswas found. In Fig. 16, the comparison carried out for WS rope isshown. It should be noted that the deterioration of the polymeric

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Fig. 14. WS rope / = 38 mm: nominal strain vs. time curves during re simulation.Shorter and longer life assessment.Fig. 15. Full locked ropes: strain vs. time curves predicted by FEM and obtained byexperimental tests.ructures 84 (2015) 340349 347core, that was not accounted for in the FE, causes the strain rateto increase in a time range of nearly 3040 s, and then to achievea steady-state value. Apparently, the rope maintained its strengthresources, being able to further sustain the applied load for a rela-tively long time interval. This transient phenomenon can be prob-ably ascribed to a repositioning of the strands due to the loss of thesupporting exerted by the core rather than to an acceleration of thedamage caused by the boost of energy produced by the polymercombustion. In this case as well, the FE analysis predicts with a rea-sonable precision the onset of rope collapse.

In both cases, the FE modeling correctly simulates the thermo-mechanical processes occurring in the rope during the thermal gra-dient. Moreover, it enables to perform an analysis of the stressstrain evolution in the cross section as a function of time andtemperature.

8.3. The ropes experimental response to re scenarios

The investigation was extended to ropes of different sizes,adopting the testing procedure described in [7]. In order to preventdamage of the heating system, the tests were interrupted at theachievement of a limiting strain estimated by the numerical anal-ysis. Tests on ropes of different diameters were carried out for eachof the two ropes congurations. The obtained timetemperature

Fig. 16. WS strand ropes: strain vs. time curves predicted by FEM and obtained byexperimental tests.

g St0.036

0.0426 mm

348 V. Fontanari et al. / Engineerincurves are presented in Fig. 17, whereas Fig. 18 shows the correla-tion between time to failure and ropes diameter.

Regarding the full-locked ropes, the experimental campaignwas conducted on two additional diameters. Specically, ropes

2009 [Art No. 5422343].

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Fig. 17. Strain vs. time curves measured on ropes with different diameter, (a) fulllocked ropes and (b) WS ropes.

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700

800

900

10 20 30 40 50 60

Tim

e to

failu

re [s

]

Nominal diameter [mm]

R2=0.9937

(a)

(b)

Fig. 18. Time to failure vs nominal diameter: (a) full locked ropes, linear tting(R2 = 0.9998), (b) WS ropes, T C1 tan h dd1

tting (R2 = 0.9937).[11] Horn GPab, Chaussidon Ja, Obstalecki Mac, Martin DAa, Kurath Pb, BackstromRGd, Kerber Sd. Evaluating re service escape ropes at elevated temperaturesand re conditions. Fire Technol 2013. 10.1007/s10694-013-0373-2.

[12] Almand KH. Structural re resistance experimental research priority needsof U.S. Industry. Final Report Prepared for the Engineering Laboratory NationalInstitute of Standards and Technology Grant #60NANB10D181 Fire ProtectionResearch Foundation, January 2012.

[13] Michael Hasofer A. Risk analysis in building re safety engineering. 1st ed.,Butterworth-Heinemann; 2007.

[14] Drysdale D. In: An introduction to re dynamics. J. Wiley; 1998.[15] Rasbash D, Ramachandran G, Kandola B, Watts J, Law M. Evaluation of re

safety. Wiley; 2004.[16] Costello GA. Theory of wire rope. Springer-Verlag; 1997.having nominal diameter equal to 80 mm and 26 mm were tested,thereby covering the range of most typically used diameters.

For the WS ropes, the tests were conducted on ropes of ve dif-ferent diameters: 14 mm, 24 mm, 35 mm, 38 mm and 52 mm. Thetriggering of the polymeric core deterioration can be observed inall the curves. It should be noted, however, that after an initialincrease in temperature, the oven resumes the ISO 834 curve andthe ropes prove to further sustain the applied load for a relativelylong time interval.

9. Conclusions

The results of an extensive research aimed at investigating theevolution of the mechanical behavior of wire ropes under re con-ditions and their re resistance were presented and discussed. Anumerical methodology for the study of the time temperature evo-lution of stress and strain in two different classes of ropes wasdeveloped. The nite element model proved to reproduce withremarkable accuracy the structural response of the two classes ofropes. The nite element model is fully parametric and the opera-tive scheme can be adopted to study ropes of different diameters.The FE analysis allows evaluating the redistribution of the loadamong the wires in the elasticplastic regime; this was used topredict the collapse of the rope and to conrm the possibility ofsafely carrying out the experimental tests. The experimentalresults yield a rst important collection of information about theresponse of two classes of wire ropes with different diameter inthe presence of thermal transients simulating a re scenario. Thispiece of information may be considered as a basis for the reassessment of ropes and can be included into the design phase inorder to improve the mechanical response of the rope.

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V. Fontanari et al. / Engineering Structures 84 (2015) 340349 349

Fire behavior of steel wire ropes: Experimental investigationand numerical analysis1 Introduction2 Geometry of the full locked and Warrington Seale strand ropes2.1 The full locked rope2.2 The Warrington Seale rope

3 Properties of the wires at room temperature4 Properties of the ropes at room temperature5 The finite element model6 Setup and validation of the FE models6.1 Ropes structural behavior at room temperature6.2 The ISO 834 curve: Set up of the thermal FE model

7 Mechanical properties of the wires material at different temperatures8 Fire resistance of the ropes: experimental and numerical results8.1 The thermo-structural FE model8.2 Comparison between numerical and experimental results8.3 The ropes experimental response to fire scenarios

9 ConclusionsReferences