An extended approach should certainly
take account of the movement of cargo units associated with direct securing,
without which a deformation of the securing devices and thus the necessary
generation of force is not possible. If it is possible in this way to define
"acceptable" cargo movements, identical movements could also be
permitted for arrangements with frictional securing (tie-down lashings). This
could in turn lead to a re-assessment of this securing method, possibly with
more favorable results.
Cargo movements which result in necessary
deformation (usually changes in length) of securing devices, primarily involve
sliding or slight tilting and many and varied changes in the shape of the unit
itself which may be superimposed on the first two types of movement mentioned.
Sliding is generally irreversible, while slight tilting is reversed once the
external tipping moment has disappeared.
Changes in the shape of the cargo unit
may be elastic, but there is usually a considerable plastic component to the
change. Since extreme loads occur as individual events in road transport,
permanent deformation of the loading arrangement is more readily acceptable
because checking and remedying the securing arrangement is immediately and
This assessment may be explained by
making reference to maritime transport, where extreme loads are associated with
storms and rough seas. These conditions may last for an extended period, as a
result of which an unforeseeable succession of extreme loads may occur and checking
and remedying cargo securing arrangements during this period can often only be
carried out at risk to life.
Figures 13 and 14 show the basic cargo
movements, while some further cases could certainly be added to the
deformations shown in Figure 14.
Figure 13: Types of movement of rigid cargo units
14: Types of movement of flexible loading arrangements
Which kinds and amounts of movement of
secured cargo can be tolerated in road transport has not previously been specified
or recommended in any regulatory texts, guidelines or similar documents. Some
influencing variables which can play a part in such considerations will thus
firstly be mentioned.
The frequency of a load causing
cargo movement could influence the tolerable extent such, that rare events,
such as full braking or extreme centrifugal forces, are allowed larger movements
than would be accepted in normal travel, since it is reasonable after an
extreme event to drive into a parking place and check the securing
The nature of the movement
likewise has an influence on its tolerable extent. A sliding offset movement
shifts the center of gravity of the cargo and may moreover exceed the loading
area limit. Racking (shear deformation) of compact cargo units, on the other
hand, may remain within the elastic deformation range and is therefore less
critical. Racking of bundled units, however, is quasi-plastic and ought
therefore to be limited in a similar way to sliding offset. Tilting of a cargo
unit should be limited to very small angles due to the low damping of the
The direction of movement is
influential. Movements in the longitudinal direction are less critical than
movements in the transverse direction, because the latter may exceed the admissible
breadth of the vehicle and may also have a major effect on the transverse
center of gravity.
In order to gain an
impression of the magnitude of cargo movements which have not previously been
scientifically accepted, it is worthwhile analyzing direct securing methods
which have conventionally been regarded as "good". This does not, however,
mean that the identified movements may thus generally be recommended as being
The proper and
rational way of defining and recommending tolerable cargo movements should
ultimately proceed by applying numerical criteria:
- admissible sliding/racking in the longitudinal
direction and transverse direction with regard to cargo geometry and center of
- admissible tilting angle with regard to dynamic
loading of the securing devices,
- general dynamic overstressing the capacity of securing
If this is to be
achieved, typical loading situations must be fully calculated. In order at this
point to provide an initial impression of the order of magnitude of previously
accepted cargo movement, one example of conventional direct lashing will be
presented, using some formulae taken from section 3.2 below.
A cargo unit with the
dimensions breadth = 2.1 m, height = 2.5 m is secured in the transverse
direction onto the vehicle with diagonal synthetic fiber belts which are
attached to the upper corners of the unit. The geometric components of the
belts are X = 1.0 m, Y = 2.3 m, Z = 2.5 m, while the loaded length L = 3.54 m.
The belts have an LC = 25 kN and an elongation of 3.75% once the LC is reached.
The spring constant of the belt is thus:
The belts are
pre-tensioned to 2.5 kN. The sliding balance (not shown here) shows that LC of
the belts is just reached. The change in length of the belts must then be:
In order to achieve this elongation, the
upper corner of the cargo unit must be deflected to the side by the amountD
Y by undergoing a sliding or racking movement or by a combination of both movements:
The lateral movement of 0.18 m transverse
relative to the vehicle under extreme loading would appear to be acceptable
and, under certain circumstances, for example with elastic deformation, an even
larger deformation could be accepted.
Top of page
3.2 Deformation and force development of securing
Breaking the direction of action of
securing devices down into Cartesian components has already been presented in
section 2. In geometric terms, each securing device has the components X, Y and
Z assigned to it, with the Pythagorean relation to its length L:
Cargo movement or deformation is
expressed by specific, small changes DX, DY and DZ in these components.
Change in length DL is then precisely calculated by:
If the individual changes are small
relative to the total length L, the change in length DL may in most cases
sufficiently accurately also be determined by an approximation equation as follows:
This approximation equation should,
however, not be used if for example component Y is close to zero and a cargo
shift involving a DY is to be investigated. This case in particular applies to steep
If force development by securing devices
as a result of cargo movement or deformation is to be determined, it is
advisable to assign a "personal" factor to each securing device which
makes it possible to calculate the force change DF directly from the change
in length DL. This factor is the spring constant D conventionally used in
industrial mechanics. The relation
The spring constant includes the
cross-section, modulus of elasticity and length of the securing device as
influencing variables in accordance with Hooke's law:
DF = force change
in the securing device [daN]
cross-section of securing device [cm2]
modulus of elasticity [daN/cm2] or [kN/cm2]
loaded length of securing device [m]
DL = change in length of securing device [m]
The spring constant is not generally
stated in data provided by manufacturers of securing equipment. There are
several ways of determining the spring constant depending on the information
which is available about the securing material.
ropes, chains and belts often state that the elongation of the material is P %
when the material is loaded with a specific force F (LC is usually stated
here). The force F stated corresponds to the force
change DF starting from zero load and assuming approximately linear
load/elongation behavior, which is generally the case in the limited load range
between pretension F0 and admissible load LC. The spring constant is
If the length of the lashings is initially
unknown, a normalized spring constant DN for the unit length of 1 m
may be used for the lashing material, the following applying:
constants of pressure transferring element, e.g. squared lumber, may be estimated from the three variables cross-section A, modulus
of elasticity E and length L:
constant of end walls and stanchions on a truck
loading area may be estimated by regarding them as beams
clamped on one end. The spring constant is then calculated on the basis of the
bending equation for cantilevers:
E = modulus of elasticity [daN/cm2] or [kN/cm2]
I = geometrical moment of inertia in clamping
d = lever length of clamped beam [m]
In practice, however,
this solution will provide excessively large values for D, since the wall or
stanchion is not clamped absolutely rigidly, the load-bearing substructure
instead likewise deforming. It is therefore advisable to establish a correction
factor by making representative measurements or to determine the entire spring
constant experimentally. The same also applies to sidewalls
of truck loading areas which are differently designed and often receive some support
over their length from the roof structure. A simple formula can no longer be
stated in this case.
The following formula applies to devices
arranged in parallel: D = D1
+ D2 + ... + Dn
The following formula applies to devices
arranged in series: 1/D = 1/D1
+ 1/D2 + ... + 1/Dn
Top of page
Horizontal components of tie-down lashings
Almost all conventional approaches to
calculation disregard the horizontal components of an inclined tie-down
lashing. If identical pre-tensioning on both sides is assumed, these components
cancel each other out. A one-sided tensioning device provides a resultant
which, while acting favorably on one side, acts unfavorably on the other. If,
for safety's sake, the calculation is carried out with the unfavorable side,
the peculiarity occurs which does not correspond to reality, as was described
in section 2.2.2.
Tied-down cargo units do in fact move
under the influence of external forces, so changing the geometry of the
tie-down lashing with various consequences:
- The tie-down lashing is (slightly) lengthened with a (small)
increase in overall forces.
- In the event of transverse movement of the cargo unit, distribution
of forces on both sides of the tie-down lashing adapts to the ratio of forces
determined by friction at the deflection points. A "favorable"
resultant of the transverse components is inevitably obtained.
- In the event of longitudinal movement of the cargo unit (assuming a
transverse tie-down lashing), a "favorable" horizontal component of
the lashing force likewise arises on both sides, which increases continuously
with the movement and only remains constant when the belt slips on top of the
The smallest possible ratio of forces
between the two sides of a transverse tie-down lashing and thus the transverse
component with the greatest possible securing effect may be sufficiently
reliably calculated using the known Euler's relation.
F and F0
= forces on both sides of the tie-down lashing [daN] or [kN]
Euler's constant (2,718281828)
m = coefficient
of friction at the deflection point
g = angle of deflection (change of direction) of the tie-down lashing
The magnitude of the transverse
component, which has a securing effect, of a tie-down lashing is, however,
crucially determined by the vertical lashing angle a. At m = 0.25, the
transverse component is at its greatest with a = 45°
on both sides. The overall ideal vertical lashing angle a is, however,
always at distinctly higher values, since the main action of a tie-down lashing
depends on the friction-enhancing vertical component which, as is known, increases
with the sine of the lashing angle a.
There is no transverse component with a
purely vertical tie-down lashing. In such a case, only once an appreciable
displacement is reached, are favorable transverse components obtained on both
sides, the magnitude of which is, however, not limited by the friction between
lashing device and the cargo. This is a borderline
case of direct securing, i.e. it is based on a different effect compared to
the transverse component from Euler's friction.
15: Transverse components of transverse tie-down lashings
The transverse component of the tie-down
lashing on the left in Figure 15 amounts to F0 × (1 – e-m×2×a)
The transverse component of the tie-down lashing on the right in Figure 15 amounts to F0 × (1 + e-m×p) ×
cos g. In order to
clarify the orders of magnitude, an example with plausible values is obtained
with: F0 = 2 kN, m = 0,25, a = 75°, g
Transverse component on left in Figure 15
= 0.25 kN; transverse component on right in Figure 15 = 0.13 kN.
Neither value takes account of the
possible elongation of the lashing belt by the change in geometric conditions.
This entails more complex calculation, which is not shown here.
16: Securing effect in the transverse direction of a tie-down lashing with a = 80°
Using a tie-down lashing with a = 80° by way of
example, Figure 16 compares the securing effect according to a conventional
assessment and the enhanced securing effect taking account of the transverse
component and the increase in force due to a change in the geometry as a result
of a sliding or racking movement.
Up to a transverse movement of approx 1.9
cm, the effects differ depending on the direction of loading. In the event of
loading towards the pre-tensioned side, smaller values are initially obtained.
From 1.9 cm, the belt slips and the greatest possible transverse component, arising
from Euler's friction between belt and cargo, takes effect. In the event of
loading on the opposite side, the belt slips from the start, so providing the
greatest possible transverse component. It is thus clear that while the usual
one-sided tensioning device does overall impair securing, so entirely
justifying the k-factor, it does not bring about any detrimental asymmetry in
the securing effect.
The further increase is attributable to
increasing elongation of the belt. Already with a transverse movement of 15 cm,
the securing effect achieved in this example is a good twice that obtained in
the conventional assessment.
Top of page
Semi-dynamic approach to calculation
Taking account of cargo movement and
elastic deformation of the securing devices makes approaches to calculation
other than those conventionally used necessary, since the input variables for
simple equilibrium methods are initially unknown. They are only obtained in the
course of a relatively long calculation process. A distinction may be drawn between
a semi-dynamic and a fully dynamic approach.
The term "semi-dynamic" is here
intended to indicate that while cargo movements are indeed taken into
consideration, they are only used to determine the different loads assumed by
the securing devices up until equilibrium with the external force. Further dynamic
effects arising from the cargo having started to move are ignored and are still
to be covered by the safety margin between LC and breaking load.
In an iterative calculation method, the
cargo is moved stepwise under the action of an external force in a
predetermined manner (sliding, tipping, racking). For each step, on the basis
of this movement, the deformation of the securing devices involved and the
force it has developed is determined. The developed force is added to the
initial pretension and is broken down as a securing force into Cartesian
These components are included in the
securing balances against horizontal sliding/racking and against tipping.
Horizontal components act directly against sliding/racking and vertical components
act via the coefficient of friction, while against tipping the horizontal and
the vertical components are introduced into the calculation with the associated
levers to the applicable tipping axis. If the securing arrangement consists of
tie-down lashings, a similar procedure must be applied which also takes account
of Euler's friction at the edges of the cargo unit.
The calculation is terminated once
equilibrium with the external force or with the external moment is reached. It
may then be established which loads have been assumed by the individual
securing devices and how large the cargo movement or deformation has become.
The suitability or admissibility of the securing arrangement in question may be
assessed on the basis of these two items of information. In addition, the
results may point to possible improvements and increases in efficiency for a
If reliable experience relating to
additional dynamic loads is available, the iterative calculation procedure may
also be terminated a little later than when static equilibrium is reached. The
amount of this allowance could be selected to be approximately proportional to
the cargo movement which has occurred up to equilibrium. This would enable a
pragmatic step to be taken towards a dynamic approach to calculation.
Obviously, this calculation process can
only be carried out with a programmed computer and thus cannot be considered
for on the spot dimensioning or verification of a securing arrangement, but it
may be considered for individual planning of critical transport operations or
for designing standard securing arrangements for long-term use.
A selective approach to direct securing
starts from the securing device in the arrangement in question which is definitely
the first to reach its admissible load (LC). On the basis of the deformation of
the selected securing device, this loading is converted into a cargo movement/deformation.
The latter is used to determine the deformations and loads developed by all further
securing devices and these values are input into a balance.
The balance indicates whether the
securing arrangement is adequate or requires further improvement. It also makes
it possible to identify which securing means may possibly be only inadequately
contributing to securing.
For frictional securing, i.e. tie-down
lashing, the selective approach should be modified such that the calculation
starts from the maximum tolerable cargo movement and uses this as a basis for
determining the changes in length, forces and geometric components of the
lashings and inputs these values into the sliding and tipping balances.
These selective methods involve less
complex calculation and may in most cases also be calculated manually. They are
thus also suitable for staff training. A result, one has oneself calculated,
carries more weight than a result passively accepted from a computer.
Top of page
Fully dynamic approach to calculation
A fully dynamic approach to calculation
should not only determine the different loads assumed by the securing devices
until equilibrium with the external force, but should also identify the
additional forces which are required to bring a cargo unit which has started to
move/deform back to a standstill. Such an approach can virtually only be implemented
with the assistance of a simulation which models the limited time period of the
critical driving situation. The effects of buildup phases and of pitching and
rolling oscillations outlined in section 1
can be taken into account in this way.
One essential item of information from
typical, calculated cases is the magnitude of the stated additional forces and
their dependency on the parameters involved, such as friction coefficients and
the elasticity of cargo securing devices. Evaluating such items of information
should allow for all-inclusive allowances to be defined and recommendations for
laying out securing arrangements to be drafted.