J Mar Sci Technol (2000) 5:101–106

Review article

Roll-on/roll-off semi-trailer models: a comparison of results

Stuart R. Turnbull

Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, UK

cause rooted in the use of web lashings, the authorwas asked to carry out tests on the relative strengthand stiffness of the two types of lashing, and to constructa mathematical model of a trailer on board a Ro/Roship.

A typical trailer is shown in Fig. 1, where the letters Land R refer to the left- and right-hand side of the trailer,and the numbers refer to the positions of the lashingsalong its axis. On board ship, the trailer usually rests ona trestle close to the “fifth wheel” (i.e. the part of thetrailer that rests on the motor unit) and its own suspen-sion. It is lashed to the deck using chain or web lashings,and these lashings are attached to anchor points on thedeck and special anchor points on the trailer’s chassis.Or at least that is the theory. In practice, very fewtrailers present themselves with anchor points fitted totheir chassis, and the deck crew have to find anywherethey can to attach the lashings to the trailers.

It can be seen from Fig. 1 that a typical trailer has ahigh centre of mass and the lashings are located wellbelow it. This unavoidable configuration can lead tolarge lashing loads and large movements of the traileracross the deck.

In order to “drive” the mathematical model of thetrailer, a model of a typical Ro/Ro ship was required. Itwas decided, after reading the recommendations of thevarious regulatory bodies (such as Lloyd’s etc.), that themodel of the ship could be greatly simplified if the twoangular movements, pitch and yaw, were combined withthe three translation movements, heave, surge andsway, to give three modified translations of the deck.The justification for this rests on the fact that the pitchand yaw motions, for most ships, are small (relative tothe roll motion) and do not give rise to significant angu-lar accelerations.

Figure 2 shows the ship’s simplified motion. Zin is thecombined heave and pitching motions of the deck, Yin isthe combined sway and yaw motions of the deck, andXin is the combined surge and pitching motions of the

Abstract A comparison is made of the various mathematicalmodels that have been constructed, over the past 15 years, ofa semi-trailer that can be carried on roll-on/roll-off ships, andsome results from five of the models developed by the authorare given. The purpose of this comparison is to show that evenin the absence of reliable experimental evidence, there is suchgood agreement between the models that the results fromeach of them can be relied upon. Problems resulting fromlarge lashing loads and deck loads are highlighted, and it issuggested that the present codes which govern the way semi-trailers are secured on board ship need further scrutiny.

Key words Semi-trailer · Roll-on/roll-off · Lashings · Ferries

1 Introduction

In 1981, an incident on board a dedicated trailer shipcrossing the North Sea introduced the author to theproblems of restraining semi-trailers (hereafter referredto as a trailer) on the deck of a roll-on/roll-off (Ro/Ro)ship. The incident, which involved some of the trailersbreaking free, nearly caused the ship to sink, and itprompted the owners to question the received wisdomof the day on how a trailer should be lashed to the deckand with what type of lashing.

Prior to 1981, there had been a steady move awayfrom the use of chain lashings toward web lashings, asthey were easier to apply and their strength appeared,superficially, to be adequate. The prime move for thischange came from the Swedish Ro/Ro ferry operators,who had an abundance of experience of their satisfac-tory use in the transportation of flat wooden sheeting.However, as the North Sea incident appeared to have its

Address correspondence to: S.R. Turnbull (stuart.turnbull@eng.ox.ac.uk)Received: January 28, 2000 / Accepted: December 6, 2000

102 S.R. Turnbull: Roll-on/roll-off semi-trailer models

deck. The axes OXYZ are fixed in space, and theaxes OX and OY are parallel to and coincide with thefree surface of the sea. The trailer was assumed to belocated on the weather deck of the ship, near to theforecastle (about 35m from the pitch axis of the ship),and in an outside lane (about 7 m from the roll axis ofthe ship). The deck was assumed to be 10m above thewater line.

The amplitudes for the roll and pitch (used in thesimulations) were 30° and 8°, respectively, and the rolland pitch periods were both 9s. These figures for thelikely maximum roll and pitch amplitudes were takenfrom the regulations published by Lloyd’s Register, DetNorske Veritas, and others.

2 The trailer models

2.1 General description

All of the models (apart from model Nos. 6 and 7)assumed the trailer chassis to be rigid in bending, and(apart from model 2, the rigid box-type trailer) it wasassumed that all chassis were torsionally flexible.

The trestle which supports the trailer at the fifthwheel end of the chassis was assumed to be linear/elastic

in all three directions, and the suspension at each side ofthe trailer was assumed to comprise a linear spring witha viscous damper in parallel. Friction was assumed toexist between the trestle and the trailer chassis, andbetween the tyres of the suspension and the ship’s deck.The friction model assumed no slip until a specified loadwas exceeded, and then slip took place and was accom-panied by a recovery (i.e., removal) of any transverseelastic deflection of the suspension.

An elastic/plastic model was used for the chainlashings. The model was linear (with a stiffness of 8MN/m/m) up to the yield-load of 110kN, and then againlinear (with a reduced stiffness of 1MN/m/m). If atany time the lashing load exceeded the yield, all exten-sions resulting from the loads above yield load wereassumed to give rise to a permanent extension of thelashing and a new yield load was then calculated (i.e.strain hardening).

2.2 Model No. 1

Figure 3 shows the first model of a trailer produced bythe author. It was developed in the early part of 1982,and it gave the first hint of two paradoxes associatedwith securing trailers safely to the deck of a ship (i.e. thelashing loads are almost independent of suspensionstiffness and of the friction forces between the trailerand the deck).

The model is a two-dimensional version of the trailer.Half of the 30-tonne load is assumed to be located overthe suspension and the other half is located over thetrestle, which in this case was assumed to be rigid andeach lashing was assigned the stiffness of two lashings inparallel.

The model of the ship was a simplified version of thatshown in Fig. 2 in that no surge (i.e. motion in the Xdirection) was present.

Fig. 1. Typical semi-trailer

Fig. 2. Simplified ship’s motion

Fig. 3. The first trailer model

103S.R. Turnbull: Roll-on/roll-off semi-trailer models

Fig. 4. Lashing load vs. friction between deck and trailer Fig. 5. Model 2, the rigid-trailer model

Fig. 6. Model 4, the two-mass flexiblemodel

The results for the lashing loads from this very simplemodel are shown in Fig. 4. It is clear that apart fromvery low values of the friction (which could not be at-tained in practice), the two lashings loads are almostcompletely independent of the value of the friction be-tween the tyres and the deck. Other results from thismodel also showed that the lashing loads were onlyslightly dependent on the stiffness of the trailer’ssuspension.

It should be noted that the values of the lashing loadsshown in Fig. 4 exceed those shown in Figs. 9–12 onlybecause in this case the lashings were assumed to beliner/elastic up to the breaking load of 200 kN. In theother cases, an elastic/plastic model was assumed for thelashings, with yield occurring at 110kN.

The results from this simple model have been con-firmed by all of the later trailer models, including thoseproduced by the only other investigation1 into this prob-lem. Thus it became evident that all previous efforts toincrease the friction between the deck and the trailerand to immobilise the trailer’s suspension in order toreduce the lashing loads had been in vain. They alsoshowed that the formulae shown in the then UK De-partment of Trade notice M849 grossly under estimated

the actual lashing loads owing to the assumed influenceof the friction forces.

2.3 Models Nos. 2 and 3

In 1983, the author was asked by the General Council ofBritish Shipping (GCBS) to construct a more accuratemodel of the trailer to give some idea of how the lashingloads varied along its length, and what its motion rela-tive to the deck was likely to be in severe weatherconditions.

As there are two distinct types of trailer in use (i.e.the “box-van” type, which is very stiff both in bendingand torsion, and the “flat-bed” type, which is quite stiffin bending but very flexible in torsion), it was decided toconstruct two trailer models. The box-van trailer2

(model No. 2) was modelled as a rigid box, and is shownin Fig. 5. The flat-bed trailer3 (model No. 3) was mod-elled as a structure which was rigid in bending, butwhich had a torsional stiffness of 1.5MN/rad/m. Thefirst “flexible” model had a single concentrated loadlocated at the centre of mass of the trailer (shown inoutline in Fig. 6), the lashings being attached to theflexible “spine” (i.e. chassis) via rigid spars.

Some of the results from the “rigid” trailer model areshown in Figs. 9 and 10 (under the legend Model 2), and

104 S.R. Turnbull: Roll-on/roll-off semi-trailer models

they show that the distribution of the load (among thelashings) is anything but uniform, and that both veryhigh lashing and trestle loads were present.

After the author had successfully constructed the twotrailer models, he and a co-worker presented their workto the IMO conference in London in 1984. Here, theytried to persuade the delegates to abandon their reli-ance on the formula method of calculating lashingloads, and to replace them with “look-up” tables orcharts for which the data were generated for typicaltrailer sizes and “worst case” weather conditions. Atthat particular time their suggestion fell on deaf ears.

2.4 Model No. 4

Shortly after the Zeebrugge disaster in 1987, the authorwas approached by the Ministry of Transport (MarineDirectorate), in London, and asked if he could expandon their idea of replacing M849 with a new guide whichincluded a set of charts that indicated the best way tolash a particular trailer to the deck. The two modelsused to generate the data for these new charts werethose shown in Figs. 5 and 6 (i.e. models 2 and 4).

The model shown in Fig. 64 is a modified version ofthe original flexible spine model, in that two concen-trated masses were used to represent a distributed loadrather than a single concentrated load. This was donebecause it was felt that it was more representative of thetype of load carried by a flat-bed trailer. Also, the onlyother mathematical model, constructed by Anderssonet al.1, modelled a distributed load in this way, and it wasfelt that in absence of experimental data, a comparisonof the results produced from these two models would gosome way to mitigate for their absence. Figures 9 and 10show some of the results from the “flat-bed” modelunder the legend Model 4.

The new Code of Practice5 was published in 1991, butthere is a class of trailer that was not covered, and theauthor decided to investigate this special class to see if itrepresented a serious omission. The trailer in questioncarries its load suspended from its roof, and this extradegree of freedom was the cause for concern.

2.5 Model No. 5

Figure 7 shows how model 4, shown in Fig. 6, was modi-fied to accommodate a swinging load6. The two “fixed”masses, Mt and Ms, represent the mass of the trailer, andthe two “swinging” masses, Mtm and Msm, represent thesuspended load.

Some of the results from this model are shown in Figs.9 and 10 (under the legend Model 5), and they showconsiderably larger values of lashing load than for theother models. This increase in lashing loads was tobe expected, as the energy of the live load has to be

Fig. 7. Model 5, the swinging-mass trailer model

Fig. 8. Model 6, the six-mass flexible model

absorbed by the lashings each time the swinging loadstrikes the side of the trailer.

2.6 Model No. 6

The penultimate model to be constructed7 is shown inFig. 8. It had been felt that the two-mass model of thedistributed load was too crude, and a further fourmasses were added to try and make the model morerepresentative of a trailer with a distributed load. Also,as the “flexible” models had only one degree of flexibil-ity (i.e. torsional), it was decided that as well as increas-ing the number of masses, the bending of the chassisabout the Y and Z axes should be included in the newmodel.

The results shown in Figs. 9 and 10 (under the legendModel 6) and in Turnbull and Dawson7 suggest that theoriginal two-mass model was sufficiently accurate for itspurpose, and that the original decision to assume thatthe chassis was rigid had been a valid one.

2.7 Model No. 7

The final model was a modified version of model 6 inthat an extra suspension unit was added, along with anadditional mass above it. These additions were madeto see if there would be any significant difference in

105S.R. Turnbull: Roll-on/roll-off semi-trailer models

Fig. 9. Left-hand lashing loads Fig. 10. Right-hand lashing loads

Table 1. The main characteristics of the trailers

Type of chassis used

Bending Torsional Mass distribution

Model 2 Rigid Rigid UniformModel 4 Rigid Flexible Two concentrated massesModel 5 Rigid Flexible Two concentrated masses

plus two swinging masseswith ±10° of free swing

Model 6 Vertically and Flexible Six concentrated masseshorizontally flexible

lashing loads by “spreading out” the suspension. Apartfrom the obvious reduction in suspension load (i.e. theload was halved), there was no significant difference inany of the loads when compared with model 6, so nofurther work was carried out on this model, and noseparate results are shown here.

3 Comparison of results

The results shown in Figs. 9–12 are for a trailer with acombined load of 30 tonne. To help with the interpreta-tion of these results, Table 1 gives a summary of themain characteristics of the trailers. The torsional stiff-ness of the chassis (unless otherwise stated) was 1.5 MN/rad/m, and the bending stiffness (given in terms of theflexural rigidity) was 10MNm2 about the pitch axis and200 MNm2 about the yaw axis.

Figures 9 and 10 show the left- and right-hand lashingloads for the four trailer models being compared. Thesefigures also show the suspension and trestle loads, andshould be read in conjunction with Fig. 1 so that thepositions of the lashings, trestle and suspension can beidentified.

For these two figures, the “flat-bed” trailers (models4, 5 and 6) have been set up with their chassis stiffnesses

set to the values supplied to the author by a major UKtrailer manufacturer. Also, for these two figures theswinging mass model (model 5) allows the suspendedmasses to have a free swing of ±10° before they strikethe sides of the trailer.

It can be seen from Figs. 9 and 10 that although thereis a general trend in the distribution of load, there areconsiderable differences between the loads carried by aparticular lashing and the types of trailer it is attachedto. Also, it should be noted that because the yield loadof the lashing was set to 110 kN, the maximum lashingload in any of the lashings is limited to about 110kN.This is because as the lashing yields, it starts to shed itsload onto those lashings which have not yet yielded.

In the calculations carried out by Andersson et al.1,the value of the yield load was set at 140kN (eventhough experimental data would suggest that 110kNwas a more likely figure), and it was for this reason thatthey were predicting lashing loads as high as 140 kN andare not included in Figs. 9–12.

Figures 11 and 12 show the left- and right-hand lash-ing loads also, but in these two figures the torsionalstiffness of the chassis used in models 4, 5 and 6 hadbeen increased by a factor of 50, and the free swingof the suspended masses (model 5) had been set tozero.

106 S.R. Turnbull: Roll-on/roll-off semi-trailer models

Figures 11 and 12 show that by giving the chassis avery high value of torsional stiffness, and thus mak-ing the “flat-bed” trailer models (4, 5 and 6) more likethe rigid “box-van” trailer (model 2), the differencebetween the loads carried by the individual lashingsbecomes very small. This would suggest that as there isvery good agreement between the four models, theaccuracy of the results from each of the models is alsogood.

Assuming that the last statement is true, there is theworrying suggestion that the deck of the ship is experi-encing point loads at the trestle of up to 350kN (i.e. 35tonne). Such loads would give rise to structural damageto the deck, and there is some anecdotal evidence toconfirm that this is happening to decks where the platethickness is in the region of 10mm.

It can also be seen from the results for model 5,shown in Figs. 9 and 10, that if the load is allowed tomove relative to the trailer carrying it (i.e. suspendedloads or tankers with a free surface), very large loadscan be generated at all of the lashings and at the suspen-sion and trestle.

In the light of this evidence, the author recommendedthat the Code of Practice5 should be altered to specifi-cally exclude trailers with free loads from its scope, andthat new guidelines should be produced specifically forthis type of trailer.

4 Conclusions

It would appear that even though there is little experi-mental evidence to verify the results from the math-

Fig. 11. Left-hand lashing loads (stiff chassis) Fig. 12. Right-hand lashing loads (stiff chassis)

ematical models of the semi-trailers described in thispaper (apart from some results from a one-tenth scalemodel, and an abortive attempt to carry out experi-ments at sea on a full-size trailer in 1982), there is suffi-cient agreement between the results produced by the sixmodels to suggest that the results produced by eachof them is reliable. This being the case, it is clear thatstructural damage is likely to occur to the decks of Ro/Ro ships when the ship’s roll is in the region of 30°. Itwould also appear that for trailers carrying live loads,there is every likelihood of one or more of the lashingsbreaking when experiencing the same severe weatherconditions.

References

1. Andersson P et al (1984) Securing of road trailers on board Ro/Roships. MariTerm AB, IMO Conference, London, February

2. Turnbull SR, Dawson D (1997) The securing of rigid semi-trailerson roll-on/roll-off ships. Int J Mech Sci 39:1–14

3. Turnbull SR, Dawson D (1984) The dynamic behaviour of roll-on/roll-off trailers on board ship. Proceedings of the BSSM Confer-ence, Lancaster, September

4. Turnbull SR, Dawson D (1995) The securing of vehicles on roll-on/roll-off ships. Trans RINA 137:37–51

5. HMSO (1991) Roll-on/roll-off ships: stowage and securing of ve-hicles. Code of practice. ISBN 0-11-550995-X. HMSO, London

6. Turnbull SR, Dawson D (1998) The effects of freely suspendedloads on the dynamic behaviour of semi-trailers on board Ro–Roships. Trans RINA, vol 140, paper 1434

7. Turnbull SR, Dawson D (1999) The dynamic behaviour of flexiblesemi-trailers on board Ro–Ro ships. Int J Mech Sci 41:1447–1460