Static analysis of single-axle tractor trialer frame

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STATIC ANALYSIS OF SINGLE-AXLE TRACTOR TRIALER FRAME
Jan Dizo1, Miroslav Blatnicky1, Stanislav Semenov2, Evgeny Mikhailov2, Rafal Melnik3, Jakub Kurtulik1
1University of Zilina, Slovakia; 2Volodymyr Dahl East Ukrainian National University, Ukraine;
3Lomza State University of Applied Sciences, Poland
jan.dizo@fstroj.uniza.sk, miroslav.blatnicky@fstroj.uniza.sk, semenov@snu.edu.ua,
mihajlov@snu.edu.ua, rmelnik@pwsip.edu.pl
Abstract. A tractor trailer is a nonautomotive vehicle, which is in its construction itself intended for transport of
materials, mainly of agricultural commodities. We can recognize several types of tractor trailers. There are flat
trailers, which platform allows transporting many kinds of materials, however, it does not allow to unload without
an additional machine or manpower. A tipping trailer body significantly makes easier manipulation mainly with
bulk material, such as gravel, send, soil, etc., and, at the same time, if the tipping body is properly designed, it
allows also to transport palletised materials and more other commodities, which occur in agriculture. A possibility
of tipping trailer body makes such a trailer very universal. However, the design of such a trailer requires to take
into account certain specific facts, which do not occur in a case of a common platform-type trailer body. On the
one hand, these specific requirements consist in operational conditions, in which a set of a tractor and a trailer can
get to, and on the other hand, they result from different loading of a trailer frame in case of tipping. The authors in
the article present the static analysis of such trailer structure, namely its main body. The presented problem is a
part of the process of the design of a new type of a trailer, which a commercial producer wants to approve for
production and operation. As it is a three-way tipping trailer, from the static analysis point of view, designers of
the trailer have to take into account the limited loading case, which the trailer can be in. The part of the presented
work are numerical calculations and strength analysis of the trailer frame structure under defined loading cases.
Strength analyses were carried out by means of the finite element method. The article includes presentation of a
computational model of a frame, the definition of the boundary conditions and the results of analyses.
Keywords: single-axle trailer, static analysis, frame, finite element method.
Introduction
A term tractor trailer means tractor trailers and semi-trailers, which are intended to transport
materials, mainly agricultural commodities. Based on the technical construction, trailers and semi-
trailers can be divided in several types, such as flatbed trailers, tipper trailers or special trailers equipped
by a specific superstructure (bulk, tank etc.) [1; 2]. The article presents a design of a frame of a single-
axle tractor trailer, which will use a tipper superstructure. Such a system will allow to unload the
transported goods by an easy way to three sides. A tipping process is realized by a hydraulic cylinder,
which is located in the centre part of the frame. Changing of the tipping side is ensured by restraining
the particular ball joint. Also, an axle of the trailer will be mounted to the frame. As it is an agricultural
transport means, it will be usually used in rough terrain conditions. It means, the frame will be exposed
to considerable loads. Taking into account these facts, the designed trailer frame should meet the
requirements of structure integrity, reliability and lifetime [3-5].
Materials and methods
Defining of inputs is the basic step in designing of the structure. Another important elements related
with the design of the trailer frame come from it. Determining of input parameters is very important in
terms of boundary conditions and individual loads for the strength analysis.
The main goal of activities has been to design a middle-class tractor trailer with a single axle. All
dimensions, such as the total length, width and height, all weight (including curb weight, total weight),
the maximal speed and others, meet all requirements introduced in the promulgation [6], as well as
European regulations [7; 8]. The total length is of 4.497 m, the total width is of 1.960 m and the total
height including sidewalls is of 1.820 m. These dimensions are indicated in Fig. 1. The payload of the
trailer is designed of 3 000 kg and the total weight of the trailer will be of 4 500 kg. Hence, the curb
weight is of 1 500 kg. The trailer is proposed to be operated at the maximal speed of 40 km·h-1. The
trailer belongs to the R3a category [9]. Dynamical effects of the load are taken into account by the
dynamic coefficient δD = 1.5. This value represents driving of the trailer on fortified roads and on terrain
without considerable irregularities [10; 11]. In case of driving in rougher terrain, the driving speed must
be reduced according to the trailer manual.
DOI: 10.22616/ERDev.2021.20.TF117

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Fig. 1. Trailer main dimensions
The trailer structure consists of two basic frames, i.e. the chassis frame and the superstructure frame.
The calculations of strength are focused on the chassis frame. The chassis frame is formed by closed
and open profiles. They are made of S355J0 steel. Its yield of the strength Re is of 355 MPa and the
ultimate strength Rm is of 470 to 630 MPa [12]. Individual profiles are connected by welding joints.
The chassis frame includes the main carrying elements with dimensions of 70x70x5 mm. The
bottom part of these profiles is adjusted for mounting of suspension elements. In the centre part of the
frame, lateral and longitudinal stiffeners are welded. They also serve for mounting the hydraulic
cylinder. In front and rear parts of the basic structure, ball joints are located for mounting the tipping
superstructure. These ball joints allow three-way tipping. A drawbar is in the front part of the trailer and
an underrun protection in the form of a steel tube is in the rear part of the trailer. The frame structure
also includes other steel elements, which strengthen the frame structure. A CAD model of the designed
trailer frame is depicted in Fig. 2. Static analyses have been carried out in a commercial FEM software
[13; 14]. For these purposes, it has been necessary to determine the boundary conditions. They include
definitions of acting loads and definitions of degrees of freedom.
Fig. 2. CAD model of the analysed frame
Fig. 3. Reactions for the straight surface
Fig. 4. Reactions during back tipping
Fig. 5. Reactions during side tipping
Acting loads have been calculated for three basic load cases as following:

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• The trailer is on a straight surface (Fig. 3).
• The maximal back tipping angle of 50º (Fig. 4).
• The maximal side tipping angle of 45º (Fig. 5).
The first load case represents a situation, when the trailer is being in the static position on a straight
surface or when it is moving on a straight surface at a constant speed (Fig. 3). Hence, the chassis frame
is loaded by the goods weight and by the superstructure mass, both loads due to the gravitational
acceleration of 9.81 m·s-1. The superstructure rests on all four ball joints. The dynamic coefficient
mentioned above δD is taken into account.
The second load case is for the back tipping of the superstructure. The trailer is being at rest and the
superstructure is tilted to the maximal position of 50º (Fig. 4). During the tipping process the load of
3 000 kg is considered. It is due to the reason that in extreme winter conditions the load can freeze to
the superstructure, or, that the superstructure rear end will not work properly, and it will be closed. The
superstructure rests on two rear ball joints and on a pivot joint of the hydraulic cylinder placed in the
centre of the frame.
The third load case considers a situation, when the superstructure is tilted on the side (Fig. 5). For
this it does not matter on which one. The trailer is again in the static position. The maximal tipping angle
is 45º. All calculations consider the load of 3 000 kg. Again in this case, the most unfavourable case is
the extreme condition, i.e. the load is frozen to the superstructure bottom or that the sidewall is closed.
The superstructure rests on the two ball joints and the centre of the pivot joint. However, two ball joints
on one side in the longitudinal direction are considered.
Reactions are calculated analytically by means of a free body diagram method and related equations
of equilibrium. The general form is as following:
0
0
0
xi
i
yi
i
i
i
F
F
M
=

=

=

, (1)
where Fxi – forces acting in x-direction, N;
Fyi – forces acting in y-direction, N;
Mi – moments acting about the chosen axis, Nm.
The application of the mentioned method is well-known. Describing of analytical calculations of
reactions for all load cases would significantly extend the range of the article. Therefore, their details
are not included and important results are listed in Table 1. Individual rows include numerical values of
calculated quantities for the described load cases, which are marked as following:
• RAx – reaction in the x direction of the ball joint.
• RAy – reaction in the y direction of the ball joint.
• RHCx – reaction in the x direction of the hydraulic cylinder.
• RHCy – reaction in the y direction of the hydraulic cylinder.
It should be noted, that every load case has own coordinate system, i.e. x and y axes are considered
individually for every free body diagram (Fig. 3, Fig. 4 and Fig. 5). The last column includes indication
of individual figures containing a calculation scheme. Table 1
Calculated reactions for individual load cases
Load
case
Values of calculated reactions, kN
Calculating
scheme
RBx
RBy
RBx
RBy
RHCx
RHCy
per two ball joints
per one ball joint
First load case
-
25.640
-
12.820
-
-
Figure 3
Second load case
0.296
0.272
0.148
0.136
0.296
33.916
Figure 4
Third load case
4.477
23.379
2.239
11.690
4.477
10.809
Figure 5

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Within research of the described load cases, it is necessary to analyse individual structural units of
the designed trailer. The chassis frame is the most important carrying part.
Fig. 6. Illustration of FEM mesh
Fig. 7. Illustration of boundary condition (DOF) definition
Fig. 8. Illustration of load definition for the first load case
This work presents static analysis. Its procedure includes several important follow-up steps. Firstly,
it is necessary to create the geometry of the model. Subsequently, this geometry is imported to a
simulation software. In our research, we have used the Ansys software package, which works based on
the finite element method (FEM) [15; 16]. This simulation tool is suitable to perform considered

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analyses of the frame, because it allows well cooperation with the used CAD software Catia. A generated
FE mesh is shown in Fig. 6. The next step, the definition of boundary conditions followed. This step has
taken into account specifics of individual load cases. An example of the boundary conditions definition
is depicted in Fig.7. As it can be seen, degrees of freedom were restrained for translation movements.
The letter “f” means “free” motions and the number “0” means zero degrees of freedom. Rotational
movements were defined as “free”.
Figure 8 shows an example of definition of loads for the first load case. It comes from calculated
values listed in Table 1. In the first load case, all ball joints are loaded by the forces with the same value,
namely by the force of 12.820 N.
It should be noted, that in principle, the FEM mesh and related FE elements (type, size) can be in
our analysed structure defined in two ways. Either by volume elements or by shell elements using
median planes. In the development phase of the trailer, both methods are used including various element
sizes. This work presents just one way to analyse it with the reached results.
Results and discussion
For the first load case, degrees of freedom have been removed in the suspension system area and at
the end of the drawbar. Values of load forces correspond to Table 1 and its placing to Fig. 3. Graphical
output of the strength analysis is shown in Fig. 9.
Based on distribution of stress, calculated based on von Misses hypothesis, the maximal stresses in
the structure meet the criterion to be lower than the yield of strength, i.e. lower than 355 MPa. We can
observe that in weld location the stresses are acceptable except of one tight location, where the calculated
stress achieved the value of 722.42 MPa. This high value is unique and it is supposed as a numerical
error. Results achieved for other computational settings (type and size of finite elements) have shown a
similar stress distribution. The maximal values of stress calculated in the ball joint structure achieves
the value of 345.34 MPa. As this part is normalized and bought from a supplier, we suppose, this result
is not critical and can be accepted for our purposes.
Fig. 9. Distribution of von Misses stresses in the frame structure for the first load case
Another analysed situation is the second load case. It relates to back tipping manoeuvre. Force
values are defined according to the analytical results (Table 1) and locations of these forces are defined
in Fig. 4. The results of the strength analysis can be seen in Fig. 10.

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Fig. 10. Distribution of von Misses stresses in the frame structure for the second load case
The results show locations with maximal stress locations. As it can be seen on enlarged details, the
maximal stress values are mainly in joints of the drawbar profiles and two longitudinal profiles of the
frame (Fig. 10, left below) and in the structure of normalized ball joints (Fig. 10, right below). These
results are safely under the yield strength and the structure of the trailer frame for the second load case
can be evaluated as safe.
Finally, the third load case has been analysed. It is the side tipping process. The superstructure is
tilted to the left and the load forces act to the frame structure in two side ball joints and in the beams
carrying the hydraulic cylinder in the centre part. A stress distribution, as well as the chosen details
showing the most loaded location of the frame are shown in Fig. 11.
Fig. 11. Distribution of von Misses stresses in the frame structure for the third load case

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The stress distribution reveals the structural stress of the trailer frame under defined forces. The
most loaded locations are again in the connection of the drawbar profiles with the longitudinal profiles,
mainly on the left (where the superstructure is tilted). Even in the third load case the normalized ball
joints belong to the most loaded elements of the trailer frame structure. All detected stresses are under
the yield of strength of the used steel and, therefore, the structure is supposed as safe.
The performed strength analyses of the trailer frame have shown that the designed frame structure
is able to carry considered loads in the static or quasi-static operational states. Dynamic effects are
included by means of the dynamic coefficient δD. Therefore, it can be concluded that the frame structure
is safe.
Based on the reached results of the strength analyses of the frame, it can be concluded that the
structure of the trailer can be supposed to be applied to the operation. Although, some values of the
results are close to maximal permissible values of the yield of strength of the used material, however,
they are normalized parts, such as ball joints. These parts are bought from the external supplier and they
are also used for other producers for similar products and even for higher loads.
As the superstructure of the trailer there is also the newly designed part of the trailer, this should be
analysed in terms of the strength as well. These analyses will also include definition of important load
cases, in which the superstructure frame will be maximally loaded.
The future research will be mainly focused on analysing of the dynamic effects to the structure.
Despite of the considered dynamic coefficient, the state of art simulation tools are able to simulate
driving of the trailer on the various road surface qualities depending on the road irregularities level. The
multibody simulations serve for it [17]. As the geometry of the frame, as well as the FE models are
created, they can be suitable inputs to set-up the so-called flexible multibody model [18; 19]. Such a
model will be good way to identify the stress distribution during driving for various manoeuvres, during
tipping manoeuvers, or also for exceptional load cases, which can occur during the trailer long-term
operation.
Conclusions
1. A single-axle tractor trailer has been designed. It is primary intended to be used as a tipper trailer.
2. The trailer structure consists of two main substructures, i.e. a chassis frame and a tipping
superstructure frame.
3. The article presented the strength analyses of the chassis frame for the three particular static load
cases representing the typical load cases of the trailer during operation.
4. The results of the strength analyses have shown that the trailer chassis frame is suitable to carry the
loads for defined manoeuvres within prescribed limits.
Acknowledgements
This work was supported by the Cultural and Educational Grant Agency of the Ministry of
Education of the Slovak Republic in the project No. KEGA 023ŽU-4/2020: Development of advanced
virtual models for studying and investigation of transport means operation characteristics.
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