Thin-Walled Structures 85 (2014) 332–340
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Thin-Walled Structures
journal homepage: www.elsevier.com/locate/tws
Stress analysis in contact zone between the segments of telescopic
booms of hydraulic truck cranes
Mile Savković a,n, Milomir Gašić a, Goran Pavlović b, Radovan Bulatović a,
Nebojša Zdravković a
a
b
University of Kragujevac, Faculty of Mechanical and Civil Engineering Kraljevo, Dositejeva 19, 36000 Kraljevo, Serbia
Colpart d.o.o-Beograd, Ćirovljeva 5, 11030 Beograd, Serbia
art ic l e i nf o
a b s t r a c t
Article history:
Received 16 April 2014
Received in revised form
11 September 2014
Accepted 13 September 2014
This paper presents the analysis of local stress increases at the contact zone between the inner and outer
segments of telescopic booms of truck cranes. A portion with a relevant length was singled out of the
outer segment and a mathematical model was created describing its stress–strain state as a function of
geometrical parameters. The obtained results were verified by the finite element method as well as by
experimental testing of the truck crane TD-6/8. Comparison of results revealed high compliance between
the analytical model and the results obtained by the finite element method and experimental testing,
which confirmed all the hypotheses. The presented methodology as well as the verified analytical
expressions give guidelines for optimum design of box-like telescopic segments and other structures
with local stress increase in contact zone.
& 2014 Elsevier Ltd. All rights reserved.
Keywords:
Hydraulic truck crane
Telescopic boom
Local stress
Experimental testing
Finite element analysis
1. Introduction
The most important element for payload lifting and transport
by telescopic hydraulic truck cranes is the boom. The telescopic
boom consists of segments that retract or extend during operation.
By changing its position in space, the boom of the truck crane
transfers load onto the substructure of the crane and the vehicle
and represents its most responsible part. Reduction of dead weight
of the boom opens the possibility for increasing the payload, the
lifting speed as well as the speed of retraction and extension of the
segments.
In recent years, world manufacturers of truck cranes have been
assigning great importance to the determination of an optimum
form of the boom cross section, which would provide an increase
in bending and torsional stiffness along with the reduction of
mass. However, during overhaul and regular checks of telescopic
booms of truck cranes, certain deformations and damages in the
characteristic zone of boom segments have been noticed. That
characteristic zone is located at the contact zone between the
inner and outer segments when the inner segment is extended to
the maximum position. This fact indicates that stresses at those
zones are considerably higher than the stresses along the boom
n
Corresponding author. Tel.: þ 381 36 383392; fax: þ 381 36 383380.
E-mail address: savkovic.m@mfkv.kg.ac.rs (M. Savković).
http://dx.doi.org/10.1016/j.tws.2014.09.009
0263-8231/& 2014 Elsevier Ltd. All rights reserved.
segment. Determination of values of those stresses is the subject of
this paper.
Two model types of telescopic booms of the truck crane can be
found in literature: mathematical models of the entire boom and
mathematical models of interaction in contact zones between
segments, which is the subject of this research, too.
Papers [1,2] pay special attention to the contact zones between
the segments as well as the connection between the first (outer)
telescope segment and the hydrocylinder. These models consist of
the corresponding equivalent masses and springs, where [1]
considers the boom with two telescopic segments, while [2] has
three telescopic segments and a modal analysis done.
Paper [3] points out the importance of contact zones between
the segments as well as the change of stresses at those points for
various boom crane designs. The model which covers the influence
of sliding and the inner telescope extended length at different
elevation angles of the boom is presented in paper [4]. The
location of sliding contacts in relation to the outer and inner
telescope segment is particularly emphasized. The paper [5]
analyzed the influence of the extension length on loads distribution through sliding contacts along the boom. Paper [6] analyzes
the problem of contacts between box-like segments of the telescopic truck crane by using the software package ANSYS, with the
presentation of the load transfer problem and buckling shapes.
The mentioned papers examine interaction between the segments
and load transfer from the inner telescope segment to the outer
M. Savković et al. / Thin-Walled Structures 85 (2014) 332–340
333
Fig. 1. Model of truck crane telescopic boom: (a) generalized, (b) simplified.
one. The generalized model of the telescopic truck crane (Fig. 1) is
frequently considered by a large number of authors.
Paper [7] presents the mathematical model of the truck crane
that defines the control mode for reducing the oscillations of the
system. It shows the global model of the boom and does not take
into account the influence of load transfer between the segments.
Paper [8] also presents a mathematical model of the truck crane,
which defines the way for reducing the oscillations and precise
positioning of payload. Paper [9] gives another mathematical model
of the truck crane and defines the influence of lifting the boom by a
hydro cylinder on dynamic reactions. Minimization of forces values
in the hydro cylinders as well as their control while lifting and
transporting the payload in the working position are presented in
paper [10]. Similar problems are discussed in paper [11], where the
accent is put on restricting the lifting load for the purpose of safe
crane operation. Paper [12]considers the influence of different
parameters on motion of the payload and structure load. The
influence of hydraulic drive system as well as the manner of its
control on dynamic behavior of truck cranes is the subject of paper
[13]. Paper [14] presents a dynamic model of truck crane emphasizing the control of change of the telescope length, change of the
angle of inclination and rotation of the boom. The influence of
flexibility of soil on dynamic stability of the truck crane as well as
on positioning of payload during rotation is presented in paper [15].
Dynamic stability of a laboratory model of a truck crane was
examined in paper [16]. The model presented in this paper enables
determination of load conditions and geometrical characteristics at
which there may occur a loss of stability. The paper [17] analysed
dynamic stability of truck crane depending on the angular ball
bearing deformation at connection between the substructure and
superstructure through dynamic model with five degrees of freedom. A discrete model of truck crane and examination of oscillations while lifting the payload, depending on the length and the
angle of inclination of the boom, are presented in paper [18].
Minimisation of load in relation to oscillation while lifting the
payload and rotation of the boom was presented in paper [19].
Papers [20,21] also present modelling and simulation of a truck
crane as a complex model which takes into account all motions
(load lifting, extension of the telescope, rotation of the boom
without damping) using the Bond Graph method. Experimental
testing and simulations were performed for the actual model and
the correctness of the created model was confirmed. Paper [22]
puts a special accent, in operation of cranes with the boom, on the
influence of wind, which is often neglected although it is very
important for the global stability of the crane in operation.
Paper [23] presents the manner of decreasing the load at the
tip of the boom by reducing payload pendulations, i.e. excitation
at the tip of the boom, by using two-dimensional and threedimensional models. It is shown that significant reduction can be
accomplished by appropriate selection of cable speeds and length.
Analysis of load transfer from the inner telescope segment
to the outer one is very important because it is the zone with the
highest stress values. This is also a conclusion of many investigations conducted not only on cranes but on other structures as well.
The conclusions obtained in those investigations are important
for the hypotheses and creation of the model presented in this
paper. The results in [24–33] show the approaches in modelling and influence of local stresses at the contact zones of various
types of beams. Also, they underline the importance of defining
maximum loads that will not cause any plastic deformations
of the beams and, hence, will not endanger the functionality of
the object.
The generalized and simplified models of truck crane telescopic
boom are presented in Fig. 1, with marked contact zones between
the inner and outer segments of the telescope (lines a–a and b–b).
2. Definition of analytical model
During payload lifting, load is transferred from the inner
movable segment to the outer segment through the corresponding
sliding pads, Fig. 2. The sliding pads are placed at the front end of
the outer segment and at the rear end of the inner segment.
Therefore, the sliding pads placed at the outer segment are treated
as stationary, while the sliding pads placed at the inner segment
are treated as movable. Taking into account that the segment is
considerably longer than the sliding pad, this paper starts with the
assumption that the load from the inner segment sliding pad is
transferred to the outer segment as continuously distributed load
of a constant value (Fig. 3).
As the inner segment moves, position of the sliding pads
changes in relation to the front end of the outer segment (coordinate x-Fig. 3). Therefore, the absolute value of continuous load
changes with the change of the coordinate x. Still, remains constant
on the sliding pads surface.
This paper considers the influence of local bending of the outer
segment during load transfer. To make a successful research of the
local stress increase due to contact load, the paper introduces the
following assumptions:
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M. Savković et al. / Thin-Walled Structures 85 (2014) 332–340
Fig. 2. Sliding pads locations on the outer and inner segment.
Fig. 5. Model for analysis: (a) before disassembling the plates (b) after disassembling the plates.
Fig. 3. Load transfer on the outer segment via sliding pads.
mutual influence is taken into account by using the corresponding
bending moments. The physical model, which includes the mentioned assumptions, is presented in Figs. 4 and 5.
Within the stress–strain analysis of flange plates, it is assumed
that the vertical web plates have sufficient stiffness and do not
considerably influence the local values of stress and deformations.
Also, in the stress–strain analysis of vertical web plates, the flange
plates represent the elastic support. External load input is presented in Fig. 5.
2.1. Bending equation for the top flange plate
According to real-life solutions, it is assumed that the flange
plates and the web plates have the same thickness (δ1 and δ2),
which does not affect the generality of consideration. After
disassembling the segment portion, the stress–strain analysis
starts from the top flange plate, upon which the external load
acts. The differential equation for the transversely loaded plate has
the form [34,35]:
∂4 wu
∂4 wu ∂4 wu qðx; yÞ
þ2 2 2 þ
¼
4
D
∂x
∂x ∂y
∂y4
ð1Þ
where:
3
D ¼ Eδ1 =12 1 ν2 —the bending stiffness of the plate.
The displacement function is assumed in the form:
mπ x
1
wu ðx; yÞ ¼ ∑ f u ðyÞ sin
a
m¼1
Fig. 4. The portion of box-like segment loaded via two sliding pads.
the zone of stress local increase does not extends beyond a
length equal to height of the segment cross-section per side of
the sliding pads (amax r2 h), Fig. 4;
the influence of transverse forces on stresses and deformations
of the plate is neglectable in comparison to external load and
reactive moments;
the influence of forces acting in the plate plane on normal
stresses is neglectable in comparison to other loads;
elastic deformations of the supports (x ¼0 and x¼ a) are
neglectable in comparison to the deformations that occur due
to the action of external load (Fig. 4).
The singled out portion of length a is disassembled to its
constituent flange and web plates. The disassembled flange and
web plates are considered as freely supported, whereby their
ð2Þ
and it satisfies the boundary conditions by which the values of
displacement and the bending moments at the beginning (x ¼0)
and end of the segment (x¼ a) are zero, i.e.:
wu jx ¼ 0 ¼ 0;
∂2 wu
j
¼ 0;
∂x2 x ¼ 0
wu jx ¼ a ¼ 0;
∂2 wu
j
¼ 0;
∂x2 x ¼ a
ð3Þ
If the following designations are introduced:
Δa ¼ a2 a1 ;
β¼
mπ
;
b
α¼
nπ
;
a
c ¼ coshðα bÞ;
P ¼ 2 ðα b c sÞ;
s ¼ sinhðα bÞ;
R1 ¼ α b ðc 2Þ þ s ð2 c 1Þ;
R2 ¼ 2 ðα b þ sÞ ð1 cÞ;
h
M ¼ ða1 a2 Þ cos ðα a2 Þ þ
i
a
ð sin ðα a2 Þ sin ðα a1 ÞÞ ;
mπ
N ¼ cos β b1 cos β b2 þ cos β b3 cos β b4 ;
and if it is assumed that the particular solution of Eq. (2) has the
M. Savković et al. / Thin-Walled Structures 85 (2014) 332–340
the values of constants for the left web plate are obtained:
form:
mπ y
f p ðyÞ ¼ K p sin
b
ð4Þ
qco
D ðα 2 þ β Þ2
2
;
Bl ¼
Em c Emb
;
2αDs
Cl ¼
Emb c Em
b;
2 α D s2
Dl ¼
Em
;
2αD
2.3. Bending equation for the bottom flange plate
where:
qco ¼
Al ¼ 0;
Differential calculus for the right web plate is identical, only
with index “r” instead of “l”.
the value of the constant K p is obtained:
Kp ¼
335
4
q0
MN
n m π 2 a2 a1
The function of deflection of the top flange plate can now be
written in the form:
1 1
wu ðx; yÞ ¼ ∑ ∑ f u ðyÞ sin ðα xÞ
ð5Þ
n m
The nature of supports and load transfer for the bottom flange
plate is the same as for the web plates. So, the bending equation
for the bottom flange plate has the same form (8). The displacement functions correspond to Eqs. (9) and (10), so that the solution
of the differential equation of displacement of the bottom flange
plate is obtained in the form:
1
wb ðx; yÞ ¼ ∑
m¼1
ðAb þ Bb yÞ chðαyÞ þ ðC b þDb yÞ shðαyÞ sin ðαxÞ
where:
ð12Þ
f u ðyÞ ¼ Bu y chðα yÞ þ ðC u þ Du yÞ shðα yÞ þ K p sin β y :
By using the boundary conditions:
ð6Þ
As this is the case with a symmetric plate which is symmetrically loaded, the change of bending moments at the ends of the
plate (for y¼0 and y¼b) can be written in the form:
1
M l;u ¼ M r;u ¼ ∑ Em ðyÞsinðαxÞ
ð7Þ
m¼1
wu jy ¼ 0 ¼ 0;
wu jy ¼ b ¼ 0;
m¼1
1
∂ wu
D 2 jy ¼ b ¼ ∑ Em ðyÞ sin ðαxÞ;
∂y
m¼1
Em
c1
Bu ¼
;
2αD
s
Em b
c1
Cu ¼
;
2αD
s
m¼1
the values of constants are obtained:
2
Em ¼
the values of constants in Eq. (6) are obtained in the following
form:
Au ¼ 0;
wb jy ¼ b ¼ 0;
1
∂2 w
D 2b jy ¼ b ¼ ∑ Emb ðyÞ sin ðαxÞ;
∂y
m¼1
2
Bb ¼
Emb ðc 1Þ
;
2αDs
Cb ¼
Emb ðc 1Þ
b;
2 α D s2
Db ¼
Emb
;
2αD
Using the condition of equality of slope and deflection of the
flange and web plates at the joints, the following values are
obtained:
1
D∂∂yw2u jy ¼ 0 ¼ ∑ Em ðyÞ sin ðαxÞ;
2
D∂∂yw2b jy ¼ 0 ¼ ∑ Emb ðyÞ sin ðαxÞ;
Ab ¼ 0;
If the following boundary conditions are used:
1
wb jy ¼ 0 ¼ 0;
Em
;
Du ¼
2αD
Q R1 cos ðβ bÞ
;
P R2
Emb ¼
Em P þ Q cosðβ bÞ
;
P
where:
Q ¼ 2 α D s2 K p β:
3. Presentation and verification of results
2.2. Bending equation for the web plates
3.1. Stress–strain analysis by using the analytical model
Box-like beam portion has two identically supported and
loaded web plates (Fig. 5). The differential equation of the left
web plate has the form:
∂4 wl
∂4 w
∂4 w
þ2 2 l 2 þ 4 l ¼ 0
∂x4
∂x ∂y
∂y
The displacement function is assumed in the form:
mπ x
1
wl ðx; yÞ ¼ ∑ f l ðyÞ sin
a
m¼1
ð8Þ
ð9Þ
where function f l ðyÞ is adopted in the form
f l ðyÞ ¼ ðAl þBl yÞ chðαyÞ þ ðC l þ Dl yÞ shðαyÞ
Based on the obtained expressions, the values of stresses and
deformations can be calculated for any point in any cross section of
the considered box-like portion with length a (Fig. 4). In order to
check the correctness of the calculation of stresses and deformations, the values of geometrical parameters that correspond to the
object subjected to experimental testing are adopted. Tested object
is the hydraulic truck crane TD-6/8 from the production programme [36], in Fig. 6.
The relevant cross section where stresses and deformations are
checked is above the moving sliding pad at the maximum
ð10Þ
The solution of the differential Eq. (8) reads:
1
wl ðx; yÞ ¼ ∑
m¼1
ðAl þ Bl yÞ chðαyÞ þ ðC l þ Dl yÞ shðαyÞ sin ðαxÞ
ð11Þ
If the boundary conditions are used (Fig. 5):
wl jy ¼ 0 ¼ 0;
1
∂2 w
D 2 l jy ¼ 0 ¼ ∑ Em ðyÞ sin ðαxÞ;
∂y
m¼1
wl jy ¼ h ¼ 0;
1
∂2 w
D 2 l jy ¼ h ¼ ∑ Emb ðyÞ sin ðαxÞ;
∂y
m¼1
Fig. 6. Hydraulic truck crane TD-6/8.
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M. Savković et al. / Thin-Walled Structures 85 (2014) 332–340
Fig. 7. Calculation model of the truck crane TD-6/8.
Fig. 8. Measuring points for testing the hydraulic truck crane TD-6/8.
extension of the inner segment—section a–a (Fig. 1). The dimensions of the cross section of the box-like boom segment of the
crane (Fig. 5) are: b¼ 350 mm, h¼350 mm, δ1 ¼10 mm,
δ2 ¼10 mm. In order to perform the analytical calculation, it is
necessary to define the value of force between sliding pad and the
outer segment of the boom. The value of this force directly
depends on the length of extension of the inner segment, i.e. the
coordinate x (Fig. 3).
Using Fig. 7, the force Pls can be determined in relation to
extension length of the moving inner segment of the boom, i.e.
coordinate x:
P ls ¼
Q ð2 Lts x 2 eμα hs Þ þGts ðLts xÞ þ Gko ð2 Lts xÞ
4x
ð13Þ
where: α—the wrap angle of the rope over the upper pulley at the
top of the boom (α ffi 901), μ-the coefficient of friction between the
rope and the pulley (μ ffi 0.15), Gko ¼0.4 kN-the weight of the pulley
blocks, Gts ¼4 kN-the weight of the inner boom segment [36].
While testing the truck crane TD-6/8, the following values were
established: Q¼8.5 kN, Lts ¼ 3750 mm, xmin ¼885 mm, hs ¼350 mm,
a2–a1 ¼250 mm, b2–b1 ¼80 mm. Based on these values and Eq. (13),
the value of the force per sliding pad is obtained: Pls ¼ 20 kN. The
value of continuous load (Figs. 4 and 5) is:
qo ¼
P ls
ða2 a1 Þ ðb2 b1 Þ
ð14Þ
Obtained results of stresses and deformations are presented
later on in comparative diagrams with experimental results and
results obtained by FEM.
The measuring point 1 (Fig. 8) is above the centerpoint of the
sliding pad surface and the positions of the other six measuring
points are determined in relation to this measuring point (Fig. 9).
The measuring point 1 corresponds to the position when the inner
segment is extended to the maximum, i.e. when the pressure force
of the sliding pad acting on the outer segment has the maximum
value: Pls ¼ 20 kN.
While measuring the strains, the inner segment is extended to
the maximum (x ¼xmin ¼885 mm)—the boom of the truck crane is
in the horizontal position, so the pressure force at the sliding pad
is maximum. The payload weighing Q¼8.5 kN is lifted from the
ground and is held in that position for about 5 s. After that period
of time, the inner segment of the boom starts retracting thus
increasing the distance between the sliding pads. It decreases the
pressure force at the sliding pad of the inner segment. At a
moment, the sliding pad passes below the measuring point 6,
and then also below 7, so that the gauges installed in them record
the stress increase. This stress increase is smaller in comparison to
the stress increase above the measuring point 1 because the
pressure force at the sliding pad is also smaller. Stresses in the x
and y directions were measured separately. During tests, the load
had a dynamic character. However, the analytical model did not
include dynamics. So, in order to make the comparison possible,
payload had been left to become motionless (0–8 s, Fig. 10b), after
it was lifted. Thus, it can be said that the load had a static character
at first test stage. In next test stage – retracting the telescope, the
load had dynamic character.
Obtained results of stresses are presented later on in comparative diagrams with the results obtained by the analytical method
and by FEM.
3.3. Stress–strain analysis by FEM
The FEM model of the boom outer segment consists of 10,175
four-node shell elements and 10,242 nodes with mesh refinement
in contact zones with sliding pads (Fig. 11a). The loads that are
transferred from the inner segment via the sliding pads are
presented in Fig. 11b.
Stress analysis of the boom segment is done with real crane
load in order to make a comparative analysis of results obtained
from experiment, FEM model and analytical model.
Equivalent stress is calculated by Huber–Hencky–von Mises
hypothesis and its maximum value is obtained at the zone of load
action, i.e. above the sliding pads (Fig. 12).
Fig. 13 presents the values of normal stress components in the x
and y directions in the contact zone.
3.2. Experimental determination of stress values in the physical
model
4. Comparative presentation of the stress–strain analysis
The object of testing, hydraulic truck crane TD-6/8, is shown in
Fig. 5, the measuring points in Fig. 8 and the layout of measuring
points and the connection scheme of measuring devices in Fig. 9.
The analytical expressions for calculation of stresses and deformations (Section 3.1) take into account only the local influence of
pressure of the sliding pad on the outer segment of the truck crane
M. Savković et al. / Thin-Walled Structures 85 (2014) 332–340
337
Fig. 9. Testing the hydraulic truck crane TD-6/8 (a) layout of measuring points (b) connection scheme of measuring devices.
Fig. 10. Measured stresses on the outer telescopic segment of the hydraulic truck crane TD-6/8 (a) stresses in the x direction (b) stresses in the y direction.
boom, whereas the experimental results and the results obtained by
FEM encompass also the influence of global bending of the box-like
segment of the boom. In order to eliminate this deficiency, the
expression for the force Pls takes into account the influence of the
boom segment weight as well as the weight of the pulley blocks, so
that the calculation model could completely correspond to the
conditions of the experiment and FEM. During experimental test, the
influences of boom self-weight and global bending were taken into
account in the following manner: before measuring, the boom tip with
pulley blocks on it was temporarily rested on a vertical support and
the measuring system was set to zero. After that, vertical support was
removed and the system recorded the influence of boom self-weight
and the testing proceeded further.
The maximum equivalent stress in the case of global and local
stress, by using analytical expressions, reads:
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
σ e ¼ σ 2x;l þ σ 2y;l σ x;l σ y;l þ 3τ2xy;l ¼ 88 ðMPaÞ
The corresponding stress components are:
σ x;l ¼
6 Mx
δ21
¼ 67 ðMPaÞσ y;l ¼
6 My
δ21
¼ 100 ðMPaÞτxy;l
¼
6 M xy
δ21
¼ 1:5 ðMPaÞ
The comparative presentation of stresses in the top flange plate
for all three methods is presented in Fig. 14.
The highest values of equivalent stresses obtained by FEM (σe,
E) and experimental testing (σe,T), are:
σ e;E ¼ 92:6 ðMPaÞ;
σ e;T ¼ 90 ðMPaÞ
The values of equivalent stress obtained by given analytical
model show high compliance with the values obtained experimentally and by FEM. This deviation at the point with the
maximum value of equivalent stress is:
Δ¼
σ e σ e;T
100 ¼ 2:2 ð%Þ:
σe
It is also necessary to verify the assumption that the zone of
stress local increase does not extends beyond a length equal to the
cross-section height per side of the sliding pads (Fig. 4).
Fig. 15 presents normal stresses distribution in section of
vertical plane for y¼29 cm (direction through measuring points
5-1-6-7, Fig. 9).
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M. Savković et al. / Thin-Walled Structures 85 (2014) 332–340
Fig. 11. Fem model (a) density of the finite element mesh (b) load acting on the outer segment.
Fig. 12. Stress state of the outer boom segment.
Fig. 13. Stress component values in the contact zone (a) normal stress in x direction (b) normal stress in y direction.
M. Savković et al. / Thin-Walled Structures 85 (2014) 332–340
339
Fig. 14. Comparative presentation of values of the corresponding component
stresses of the outer segment in the cross section (x ¼88.5 cm) (a) stresses in x
direction (b) stresses in y direction.
Fig. 16. Comparative presentation of the obtained values of deformations for each
plate in the cross section (x ¼88.5 cm) (a) top flange plate (b) web plates (c) bottom
flange plate.
Fig. 15. Comparative presentation of normal stresses distribution in section of
vertical plane for y¼ 29 cm (a) stresses in x direction (b) stresses in y direction.
Fig. 15 reveals that the assumption about the length of the
singled out segment was correct. The distribution of local stress σ x
from analytical model has some deviation but it occurs in zone
where this influence fades. This deviation can be eliminated
if functions (2) and (5) are replaced with ones of higher order.
However, this involves more complex expressions which are less
convenient for further analysis. Thus, this action would be not
justified.
The obtained deformations of each plate in the cross section are
presented in Fig. 16.
Considering the obtained results, it can be seen clearly that the
fading of the local stress increase occurs approximately at the
length of 35 cm, which corresponds to the height of the cross
section. Therefore, it was correct to single out a portion with the
length a (Fig. 4). Namely, outside this zone there is no influence of
the local stress increase, but only the influence of global bending.
This statement was verified by the results obtained experimentally and by FEM. The results show that there are no significant
deviations between the results obtained by analytical model,
experimental testing and FEM analysis in the zone of highest
stresses values, which was the goal of defining the analytical
model. There are some deviations at the end of the influence zone
of local stress increase, but the values of stresses are small and
have no importance for the design. The cross section of the
segment is calculated on the basis of maximum stress values (line
4-1-2-3, Fig. 9), which occur in the zone with highest compliance
of results obtained by the analytical model and results obtained by
experimental testing and FEM.
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M. Savković et al. / Thin-Walled Structures 85 (2014) 332–340
The proposed analytical model explicitly defines strain and
stress increase in contact zone of telescopic boom segments. In
addition, the model shows that the highest stress values are in the
contact zone, which gives them a key relevance in boom design
process. Finite element model and the tests confirm correctness of
model results.
Analyzing the measured results of stresses in point 6, it can be
seen that the stress value before and after the moment of sliding
pad passing was σ y ffi 4:7 ðMPaÞ(points A and B in Fig. 8b), while its
value at the moment of sliding pad passing was σ y ffi 7 ðMPaÞ. Such
increase can be noticed for other measuring points, too. This fact
indicates that the design of crane telescopic boom must include
the local stress increase.
5. Conclusions
The research conducted in this paper showed the methodology
for determination of stress and deformation local increase in the
segments contact zone. In adition, the size of zone of local increase
was defined. Based on the presented physical model, a portion of
segment relevant for carrying out analytical calculation was separated. The analytical expressions for stress and deformation distributions in contact zone were obtained in explicit form by using
the corresponding boundary conditions and the hypotheses.
Verification of the obtained analytical results was performed by
FEM—using the software package ansys and experimental testing
carried out on the truck crane TD-6/8.
The values of equivalent stress obtained from analytical model
show high compliance with the values obtained by experimental
testing and FEM. The deviation at the point with the maximum
values of equivalent stress is 2.2% in relation to the results obtained
experimentally and 4.9% in relation to the results obtained by FEM,
which confirms the hypotheses.
High accuracy of results of the analytical model in explicit form
can be of great importance for further research in the optimisation
of box-like cross sections of telescopic segments and other general
structures with pressure load in local contact.
Acknowledgment
A part of this work is a contribution to the Ministry of Science
and Technological Development of Serbia funded Project TR35038.
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