9<4-VCJSO
CLASSIFICATION NOTES
NOTE NO. 32.2
STRENGTH ANALYSIS OF
CONTAINER SECURING
ARRANGEMENTS
JULY 1983
DETNORSKE
VERITAS
VERITASVEIEN 1,
1322 H0VIK,
NORWAY
TELEPHONES: +47 2 47 99 00
TELEX: 76192
INTRODUCTION
General
• Classification Notes are publications which give practical information on classification of ships and other objects. Examples of design solutions, calculation methods, specifications of test procedures, quality assurance and quality control systems as well as acceptable repair methods for some components are given as interpretations of the more general rule requirements.
•
An updated list of Classification Notes available is given in the latest edition of
the Introduction-booklet to the «Rules for Classification of Steel Ships».
e
The present edition of this Classification Note supersedes the May 1980 edition of
the same CN.
Major Changes.
• General
All formulae for calculating deflections and forces have been extended to take care of variable container mass and variable horizontal forces from the containers.
•
1.4 Container standards
Existing item 1.3.3 has been extended to give all relevant strength data for the normal ISO containers. In addition we have introduced the possibility to design the
securing system for a higher strength container standard termed «Class A» - containers, which may be used by owners carrying a large number of uniform and
high quality closed-box containers on their vessels. Guidelines for the evaluation
of such containers have been given in Appendix I.
•
2.2 Lashing and similar arrangements
2.2.2 The racking stiffness for the container door ends has been increased from
3,33 to 3,85 kN/mm. Higher values have been given for Class A-containers.
2.2.J 0-12 The formulae for vertical forces and racking forces in the containers have been clarified in relation to lashing arrangement and the tension or compression side of the stack. On the tension side we have introduced the perpendicular
component of the gravity force by multiplying by cos <p (<p = roll angle), which
means a small increase in tension force.
•
2.5 Container blocks
This part has been modified and the arrangement of the securing system has been
explained in more detail.
A reduction in horizontal support forces due to the vertical shear restraint in
blocks with a large number of stacks and bridge stackers at each level has been introduced.
3.1.2 The horizontal spring stiffness of lashing has been specified in more detail.
•
3. Derived calculation formulae
In order to cover the majority of lashing arrangements general formulae have been
added for:
stack with three rigid supports
- stack with one rigid and two flexible supports
- stack with three flexible supports.
e
4. Worked examples
The examples have been amended by introducing internal cross-lashing and by
making them more complete as to obtaining allowable forces on containers and
giving necessary strength values for securing equipment.
•
An Appendix 11 has been added in which methods have been given for calculating
lashing forces in case of tipping when locking cones are not used.
© Det norske Veritas 1983
Printed in Norway by Det norske Veritas
NV 7.83.2000
NV 9.86.500
CONTENTS
1. GENERAL
Page
1. I Introduction ............................................................................................................... 5
1.2 Definitions................................................................................................................. 5
1.3 Man ual for container sto wage and securing.............................................. ............ 6
1.4 Container standards.................................................................................................. 6
2.
BASIC ANALYSIS
Rigid container securing arrangements (Cellular containment or similar)......... 8
Non-rigid securing arrangements (Lashing and similar a rrangements).............. 8
Container stack with four flexible horizontal supports ....... ............................ ... l 0
Container stack with combined rigid and flexible horizonta l supports.......... .. 13
2.5 Container blocks ..................................................................................................... 14
2. 1
2.2
2.3
2.4
3. DERIVED CALCULATION FORMULAE
3.1 General........................ ............................................................................................. 16
3.2 Container stack with single rigid horiz ontal support.......................................... 17
3 .3 Container stack with tw o rigid ho rizontal supports............................................ 18
3.4 Container stack with three rigid horizontal sup ports.......................................... 19
3.5 Container stack with single fl exible horizontal suppo ti ..................................... 20
3.6 Container stack with one rigid and one fl exible horizontal support ................. 21
3.7 Container stack with two flexible horizontal su pports....................................... 22
3.8 Container stack with one rigid and t wo flexible horizontal sup ports............... 23
3.9 Container stack with three fl exible horizontal supports..................................... 24
4. WORKED EXAMPLES
4.1 Three tier stacks with single cross lashing............................................................ 26
4.2 Four tier stack with two cross lashings................................................................. 29
APPENDICES
Appendix I
Appendix II
Evaluation of «Class A» Containers...............................................
Fo rces on Container Stacks in Case of Tipping .............................
33
34
1.
GENERAL
I. l
Introduction
1.l.l For ships intended for container transport the «Rules for Classification of
Steel Ships» (henceforth refered to as «the Rules») require that approved securing arrangements for the cargo containers are fitted.
1.1.2 The purpose of this pub Iication is to serve as an aid to those responsible for the
planning and strength evaluation of securing arrangement's for cargo containers on
board ships. Acceptable assumptions and calculation procedures supplementing the
general requirements stated in the Rules are given.
l.l.3 Principles of analysis have been outlined for normal types of securing arrangements, including cellular containment structures.
l.l.4 For securing arrangements based on lashings or similar, calculation formulae
taking into account the interaction of containers and supports have also been included.
1.2
Definitions
1.2.l References to directions refer to the principal axes system of the ship. Thus the
terms vertical, horizontal, longitudinal and transverse when used refer to the ship's
axes.
1.2.2 With regard to terms used in this note reference is made to the Rules Pt.5 Ch.2
Sec.6.
l.2.3
The following symbols have been used:
bs
h
= distance between bottom supports of container in mm
= height of container in mm
nb
n
=
ij,k,m =
Kc
Ki
av
a1
a,
=
-
cp
go
-
M
Ma
=
-
Pw
Ph
Pha
=
number of interconnected stacks in container block
number of tiers of containers in stack or block
number of tiers of containers in stack or block below the level in question
racking stiffness in kN/mm of container wall
horizontal stiffness in kN/mm of container lashing connected to level i.
Similar at levels j, k and m
combined vertical acceleration in m/s 2
For details
combined transverse acceleration in m/s 2
see the Rules
combined longitudinal acceleration in m/s 2
Pt.3 Ch. I Sec.4B
angle of roll
standard acceleration of gravity
9,80665 m/s 2
specified maximum mass for containers (t), when constant
specified maximum mass in each container (t), when variable
wind force in kN for containers with exposed sides
17 ,5 k N for 20' containers
35,0 kN for 40' containers
7,0 kN for container ends
horizontal force in kN acting per half container, when constant
horizontal force in kN acting per half container, when variable
5
2
a
P1i
Pri
Psh
Pch
()ic
Oio
()ij
l.3
denominator of container in stack (from l ton)
lashing force in kN of lashing connected to level i.
Similar at levels j, k and m
horizontal support force in kN, acting at level i.
Similar at levels j, k and m
vertical support forces in kN acting at bottom of container stack due to horizontal loads
vertical forces in kN acting in side posts of lowermost container of stack
due to horizontal loads
= Psh - Ph 1 h/2bs
assumed fraction of horizontal load acting on container end, which is transmitted through the container wall. Normally a may be taken as 0,25 and 0,0
for end and side walls respectively
clearance in mm of rigid transverse support at level i.
Similar at levels j, k and m
calculated horizontal displacement in mm at level i of a horizontally unsupported stack of containers when subjected to a uniform horizontal load.
Similar at levels j, k and m
calculated horizontal displacement in mm at level i of a stack of containers
when subjected to a horizontal point load at level j.
Similar for other combinations of displacement and point load levels
Manual for container stowage and securing
1.3.1 For each ship intended for container transport, a container stowage and securing manual is to be worked out as stipulated in the Rules. The following should be
noted when preparing the Manual.
1.3.2 Container weight limitations may for rigid securing arrangements be expressed
as maximum weight per container and in addition as a maximum weight per container
stack. For non-rigid securing arrangements, weight limitations may also in special cases be expressed by so-called «stack weight diagrams», or similarly allowing an optimum stowage within given strength limits for the lashing and/or the containers.
1.4
Container standards
1.4.1 Container strength limits are normally to be in accordance with the required
minimum tested strength values and capabilities for containers given in ISO-standard
1496/ 1 and in the Rules for Certification of Freight Containers.
Applicable container strength ratings according to this standard are given in tahle I.
1.4.2 Containers with higher strength ratings than the minimum given in 1.4.1 may
be carried and used as basis for dimensioning of the securing system. Such containers
will be termed «Class A»-containers and are to he specially specified by the owners.
Stipulated minimum strength ratings are given in table 1. Such higher ratings are to be
demonstrated by strength tests. Selection of «Class A»-containers is to be based on
the standards and evaluation guidelines given in Appendix I.
Upon special considerations as to testing, securing and stowage manual, containers
with other specified ratings may also be carried in defined locations.
6
Table 1 Container strength ratings (in kN)
Standard ISO
Racking force:
Door ends
Doorless ends
Side walls
Vertical corner support force
Corner post compression
Corner post tension (top lift)
Vertical tension in bottom corner (from locking device)
Lashing loads in corner castings (in plane of
cont. wall):
Horizontal
Vertical
Horizontal shoring forces on corners (perp.
to cont. wall):
Lower corner, tension
Lower corner, compr.
Upper corner, tension
Upper corner, compr.
20'
40'
20'
40'
150
150
150
150
75')
540
450
IOO
810
675
150
200
200
150
640
550
200
200
200
150
900
750
250
200
250
250
300
150
300
150
300
250
300
250
300
200
300
200
200
250
350
250
250
250
350
250
250
300
400
300
300
l) May be taken 150 kN for closed box containers.
7
Class A
75'>
2.
BASIC ANALYSIS
2.1
2.1.1
Rigid container securing arrangements
(Cellular containment or similar)
The maximum vertical support force from corner base fitting may he taken as:
n
Ps = 0,25
r
Ma (&i
+
av)
1kN1
when Ma variable
a~ I
2.1.2
The maximum compressive force in container end posts may be taken as:
Pc = 0,25 (n-1) M (g0 +av)
n
Pc = 0,25 L Ma (g 0
+
a v)
{kNt
1kN1
when Ma variable
a-2
2.1.3 The stresses and forces in the securing structures for horizontal accelerations
and forces from wind, where relevant, are to be calculated for transverse and longitudinal forces per container equal (Ma a 1 + Pw) and (Ma a,+ Pw) kN , respectively.
2.1.4 The analysis required for a rigid con tainer securing arrangement depends on
the complexity of the arrangement. For com plex cellular securi ng structures, direct
(framework) analysis may be necessary. In other cases simple manual calculations will
be sufficient.
2.1.S Hull deformation s, if significant, are to be taken into account when determining the shoring forces.
2.2
Non-rigid securing arrangements
(Lashing and similar arrangements)
2.2.1 For non -rigid securing arrangem ents the vertical support forces, internal forces
of containers, horizontal support forces and las hing forces are all to be calculated if
relevant.
2.2.2 The analysis is to take into account the flexibility of the containers.
Unless otherwise specified, the racking stiffness Kc of container end walls for normal
closed-box ISO containers may be taken as:
Kc = l 0 (k N/ mm) for doorless ends
Kc = 3,85 (kN/mm) for door ends
Unless otherwise specified, the racking stiffness of container side walls may be taken
equal to doorless container end walls.
For containers with increased strength (Class A), possible increased racking stiffnesses should be verified by testing. Estimated obtainable values are:
Kc = 12 (k N/ mm) for doorless ends
Kc = 5 (kN/mm) for door ends
8
2.2.3 Calculations are to be performed for container stacks or blocks assuming both
doorless and door end walls. Normally maximum vertical and horizontal reaction forces at the stack base are found for doorless ends, whilst maximum horizontal support
forces and lashing forces are found for door ends.
2.2.4 The analysis is to be based on the elastic stiffnesses of lashings according to
their type and dimension.
2.2.S The analysis is to include effects of clearances. For individual container stacks,
clearances of stack fittings may be ignored. Stipulated clearances between container
stacks and horizontal supports are to be taken into account. For container blocks with
horizontal supports, clearances of bridge fittings within the block are to be taken into
account as outlined in 2.5.
2.2.6 The effects of vertical connections between the containers of a stack are to be
taken properly into account. The effects of possible tipping of container stacks without lock connection at bottom supports are of special importance. Calculation methods taking these effects into consideration are given in Appendix JI.
2.2.7 The calculations are to be based on methods of analysis applicable for structures in general. In the analysis the container walls may be considered as shear panels.
The interaction between the two ends (or sides) of containers may norma lly be assumed negligible.
2.2.8
as:
ah
Generally, the horizontal force of the container per end or side is to be taken
= a1or a 1 for transverse or longitudinal accelerations, respectively.
2.2.9 Maximum vertical support forces, racking forces, horizontal support forces
and lashing forces may normally be determined directly in accordance with Section 3.
2.2.10 The combined maximum vertical support forces may be determined as the larger of:
On compression side: (positive):
Psc = 0,25 n M g0
+
Psh
+ :EPst
lkN •
or
On tension side (negative):
If Pst becomes negative tipping will take place and Jocking cones or twist locks are to
be installed.
9
Psh
I.Psi
calculated vertical support force due to horizontal loads
sum of the vertical components of relevant lashing forces, according to Sect.
3 or similar.
On compression side L Psi is only added when internal cross-lashing is used.
On tension side L. Pst is only added when external lashing is used.
In case of variable container mass, (n M) is to be substituted by
L." Ma.
a= I
2.2.11 The combined maximum compressive force in the lowermost container posts
is normally determined as the larger of:
Pc = 0,25 (n-1) M (g0
+
!kNJ
av)
and
Pc= 0,25 (n-1) M g0
Pch
L Psi
+ Pch +
L Psi
1kN1
calculated compressive force in post due to horizontal loads
as given in 2.2. IO
11
In case of variable container mass, (n- 1) M is to be substituted by
L: Ma.
a=2
2.2.12 The racking force in the wall of the lowermost container of a stack is determined by:
(kN)
when Ph constant
or
ll
Sr =
L Pr
Phi
L. Pha
a=2
+
a Phi -.E Pr
lkNI
when
Pha
variable
sum of horizontal lashing or supporting forces (Prj, Prj etc.), calculated in
accordance with Sect. 3
horizontal force at end of lowermost container
In cases where there are two or more containers above the upper lashing or fixed support, the racking force in the lower of these containers should also be checked.
2.3
Container stack with four flexible horizontal supports
2.3.1 Consider a container stack suppo11ed by lashings at levels i, j, k and m in that
order from bottom. The stack may be subjected to:
a)
b)
A constant horizontal force Ph per half container.
A variable horizontal force Pha (Phi, P 112 ••• Phn) per half container.
For the analysis given in the following, reference is made to Fig. 2.1 .
lO
Disregarding the lashings, the free horizontal displacement at level i is given
2.3.2
by:
a)
Constant horizontal force Ph.
Oio
=
~( ~
Kc
(n-a)
a= I
+ i a)
and similar for the levels j, k and m.
Values of I: (n - a)
r (n-a) + 0,25 i
n
1
l
I
0,25
2
1
2
2
1,25
1,50
3
l
2
3
2,25
3,50
3,75
l
3,25
5,50
6,75
7,00
3
3
4
4
4
4
2
3
4
5
5
5
5
5
I
2
3
4
5
4,25
7,50
9,75
11,00
11,25
6
6
6
6
1
2
3
4
5
6
5,25
9,50
12,75
15,00
16,25
16,50
6
6
b)
+ i a are given in the following table for a.. =
Oio
= ic
(a a~
I
Pha
+
l
7
7
7
7
7
l
2
3
4
5
6
7
6,25
11,50
15,75
19,00
21,25
22,50
22,75
1
2
3
4
5
6
7
8
7,25
13,50
18,75
23,00
26,25
28,50
29,75
30,00
I
2
3
4
5
6
7
8
9
8,25
15,50
21,75
27,00
31,25
34,50
36,75
38,00
38,25
7
8
8
8
8
8
8
8
8
9
9
9
9
9
9
9
9
9
a~
1 b=
~+
and similar for other levels j, k and m.
ll
I
Phb)
L(n-a)
+ 0,25 i
n
7
Variable horizontal force Pha·
0,25:
2.3.3 The horizontal displacement at level i due to a horizontal force acting at the same level is given by:
8·· = i pi lmm}
n
Kc
and similarly for the levels j, k and m.
The displacement at levels below the force in question is proporsional to the level
number, e.g. the di splacement at level 1 due to force acting at level k is given by:
The displacement at levels above the force in question is equal to the displacement at
the force level.
2.3.4 The support force at level i is expressed as a function of the resulting horizontal displacement at the same level, i.e.:
and similar for the forc es at levels j, k and m.
2.3.5 The horizontal forces as mentioned in 2.3.3 must be equal to the corresponding
support forces given in 2.3.4. Consequently the following linear equations may be derived:
( ~: + m)
k Prm
j
Prrn
+(
+j
Prm + k
~~
P rk
+
+(
Prk
k) Prk
+j
Prj
+
+j
Prj
+ j p ri =
i
= Brno K c
Pri
~~ + j) Prj + i Pri
Oko
=
Kc
Ojo
Kc
J
i
Prm
+
i
Prk
+
i P rj
+ ( ~ +
i)
=
Pri
8ioKc
I
or in matrix form:
( ~+m)
Km
k
J
k
(
~
+
J
k)
J
Prm
Omo Kc
J
P rk
Oko
Kc
=
+ j)
( ___&_
K-
Prj
Ojo Kc
Pri
Oio Kc
J
( ~+i)
K·
I
12
From these equations the horizontal support forces Prm• Prk, Prj and Pri may be solved.
If the number of lashings is less than 4, the system is reduced correspondingly. E.g.,
for a system with two lashings the system reduces to
( ~+j)
K
Pr.i
Ojo Kc
Pri
Oj0 Kc
.I
+ i)
( __&__
Ki
Fig. 2.1 Four flexible supports, general case.
2.4
Container stack with combined rigid and flexible horizontal supports
2.4.1 Consider a stack of containers as in 2.3. Let one support be rigid, for example
at level j. A clearance Ojc at that support is assumed.
2.4.2 The support forces at level i, k and m are given by the formulae in 2.3.4. At level j the resulting displacement is given by:
Ojc =
oj 0
-(
~ omm +
l
okk
+ Ojj +
Oii)
Consequently the linear equations in 2.3.5 are modified as follows:
The diagonal element
-
The displacement Ojo
(~ + ·)
Kj
--+
J ~J
Bjo - Ojc
13
2.4.3 In this way the linear equat,ions may be set up for an arbitrary combination of
rigid and flexible supports.
For example, with four rigid supports the horizontal support forces are given by :
I:
l;
2.5
k
J
k
J
J
J
l l
Prm
Prk
Pr.i
J
Pri
!,(Omo -
r ~0;
(Oko - Okc) Kc
0
l
~me) ~
J
O;,) K,
(Bio - Djc) Kc
-
Container blocks
2.5.l Container stacks connected by horizontal bridge stackers (dual cone adapters)
may be regarded as a block with respect to lashing and rigid horizontal supports. It is
assumed that bridge stackers are fitted at each level of horizontal support and that the
clearances at stackers normally are negligible. The block may be calculated on the
basis of an analysis of single stacks with the same deflection (fixed support clearance).
The resulting horizontal support force will be the sum of all support forces from the
indi vid ual stacks.
If the horizontal stackers are fitted with a clearance 81i at each stacker, the support
clearances Oic• Ojc• Okc or Orne are for each stack away from the rigid support to be increased by ob. Arrangement with a single rigid support is shown in Fig. 2.2.
BRIDGE STACKERS
CLEARANCE: 6b
(n:. 6)
__..
-
_,..
___..,..
Ii" 5)
__..,.
-----
----
___..,.
___..,.
-.....
__...,.
~~
'I II
! II
I
: I
tI
I
I
:I
II
1/
_.,.
IJ
:1
t---~1+---..J+---...,,
_.,.
• I
I I
I I
~I•
I
_.,.
-
__....,
Oio
~
___..,.
_...,
II
,,
~
Fig. 2.2 Block with single rigid horizontal support.
14
Pr i
2.5.2 If the number of stacks in a block is greater than 4 and bridge stackers are fitted at all levels in the block, a reduction in the horizontal support forces may be introduced due to the stackers giving a certain vertical shear restraint. The final support
force may b e found as:
Pri
Cr
=
=
calculated horizontal reaction force for block
reduction factor as given in the table below
nb
4
5
6
7
8
9
Cr
t
0,97
0,90
0,80
0,67
0,50
;;?:
10
0,40
The racking force Sr in the end wall of the lowermost container is to be calculated according to 2.2.12 with the reduced Prif inserted in the formula. The vertical support
forces may b e calculated with the uncorrected Pri·
2.5.3 Ir. ord er to reduce the horizontal support forc es at rigid block supports, the
supp ort:; m ay b e arranged for absorbing both compression and tens ion. If the clearances at t11e individu al stackers are considered to be negligible, a 50% distribution between the compression and tension side may normally be used when calculating the
support forc es according to 2.5. l and 2.
Jn ca se of clearance at each horizontal bridge stacker, a redi stribution tow ards I 00%
compression will take place. A 50% distribution m ay b e achieved by omitting all
bridge stackers b etween middle stacks, thus obtaining two individual blocks.
15
3.
DERIV ED CALCULATION FORMULAE
3.1
General
3.1.1 The follow ing d escribes elementary for mul ae for the analysis of stacks of contain ers when subjected to horizon tal forces. In general, the formulae may be applied
fo r the d etermination of vertical support forces, horizontal support forces and lashing
forces. Note that the formulae fo r vertical support fo rces do not include the vertical
component ot possible lashing forces and vertical mass torces.
3.1.2
The calculation formulae have been based on the following assumptions :
The bending stiffness of the container walls is assu med > > than their shear stiffness. The container walls have therefore been consid ered as shear panels.
Interna l clearances in stacking and locking members of individual stacks are ignored.
Tens ile vertical support forces are assumed taken by lock stackers. If lock stackers
are not fi tted and containers may be su bject to tilting, the las hing forces will have
to be specially consi dered .
The flexibilities of container walls and lashings are assumed to be linear.
Prestressing of las hings is not incl uded in the consideration.
Containers subjected to horizontal acceleration forces are assumed homogeneo usly loaded with gravity centre in the centre po int of the container.
3.1.3 The horizontal spring stiffness of simple lashing devices su pporting the container stack at level i may be expressed as:
2
2
E1A 1 s1
E1A , sin 0
(h,2 + s12)3° or
11
V
lkN/ mm f
modulus of elasticity of lashing in kN/ mm2.
For ordinary lashing units with one turnbuckle or locking tensioner nominal E 1-values may be:
Wire lashing: 75 kN/mm2
C hain lashing: 100 kN/mm2
Rod las hing: E 1 = 0,04 (11 -1000) k N/mm2
cross-sectional area of lashing in mm2, to be taken as:
Wire lashing: N ominal area
Chain lashing: Area of one side of link
Rod lashing: Actual area of rod
lengths in mm, se also Fig. 3.1
angle of lashing, see also Fig. 3. l
For wire lashi ng E 1 A 1 may be substituted by a stiffness constan t C.
Unless otherwise specified, C may be taken as:
C
8000 k N for 12,5 mm dia meter steel wire rope
15000 k N for 16 mm diameter steel wire rope
2 1000 k N for 19 mm diameter steel wire rope
28000 kN for 22 mm diameter steel wi re rope
= 38000 kN for 25,4 mm diameter steel wire rope
For intermediate diameters C may be determined by linear inte rpolation.
For lashing devices consisting of different elem ents the spring stiffness may have to be
determined experimentally.
16
Ku
I
I
I
ht
I
I
I
I
I
I
Fig. 3.1 Stiffness of simple lashing.
3.2
Container stack with single rigid horizontal support.
3.2.1 The arrangement is shown in Fig. 3.2.
The clearance at the rigid support, oic. is assumed to be known. The unsupported displacement, Oj0 , may be calcul ated in accordance with the formulae in 2.3.2.
3.2.2 The horizontal support force derived from the general formul ae in 2.4.3 is given by:
Not valid for Oic > Oio·
3.2.3
The vertical support force due to the horizontal forces is given by:
Psh
=
for constant horizontal force
Ph
:E (a -0,5) Pha for variable horizontal force
Pha
n
a= l
5
17
~
ft
( n" 6)
{i : 6 )
I
._..
\
I
\
I
\
_...
I
'
I
\
I
\ :
._..
1 I
I I
I f
.....
I I
I I
II
fl
_,..
I/
II
'I
,,
/I
........
I I 'I
I
\
I
~
I I 'I
""
n 'IJ
Fig. 3.2 Single rigid horizontal support.
Container stack with two rigid horizontal supports
3.3
3.3.1 The arrangement is shown in Fig. 3.3.
The clearances at the lower and higher suppo11s, O;c and Ojcrespectively are assumed to
be known. The unsupported displacements, Oio and Oj0 , may be calculated in accordance with the formulae in 2.3.2.
3.3.2 The horizontal support forces derived from the general formulae in 2.4.3 are given by:
At level i:
j (C:.io - oic)J 1kN 1
Pri = Kc [i (ojo - (io~c)-ij)
At level j:
Kc [(O;o-Ojc)- (o;o- O;c)J
(j-i)
1kN1
If any of the support forces becomes negative, this support will not be engaged. The
calculation has to be repeated with the remaining support only, according to 3.2.
3.3.3
The vertical suppo11 force is given by:
1kN1
f (Pha) is as given in 3.2.3.
___.
I
Oic
~
___.
~
I
I Pri
Ii "4 I
I
I
I
I
I
I
___.
I
\ I
I
__.,.
I
II
__.
II I
l
I
I
//
II 'I
Fig. 3.3 Two rigid horizontal supports.
3.4
Container stack with three rigid horizontal supports
3.4.1 The clearances at the three supports, Oic, Ojcand okc are assumed to be known.
The unsupported displacements, Oj 0 , Oj0 and oko may be calcu lated in accordance with
the formulae in 2.3.2.
3.4.2 The horizontal support forces derived from the general formulae in 2.4.3 are given by:
At level i:
Pn·At level j:
P rj
=
Kc [
At level k:
Prk
JkNI
=
If any of the support forces becomes negative, this support will not be engaged. The
calculation has to be repeated with the remaining supports, accord ing to 3.3.
19
3.4.3
The vertical support forces are given by :
Psh
_ [f (Pba)-(iPri+j Prj+k Prk)]h
bs
-
l kN l
f (Pha) is as given in 3.2.3.
I
In : 61
~'
I
I
I
I
I
I
I
I
I
I
I
6io
Ii : 3)
..
I
Ki
I
I
I
I
I
1
I
I
I
........
I
I I
II
,
- = Pho
I/
//
//
l
~
tPsh
Fig. 3.4 Single flexible horizontal supports.
3.5
Container stack with single flexible horizontal support
3.5.1 The arrangement is shown in Fig. 3.4.
The horizontal spring stiffness of the lashjng, Ki, may be calculated in accordance
with the fo rmula in 3 .1.2.
The unsupported displacement, oi0 , may be calculated in accordance with the formula
in 2.3.2.
3.5.2 The horizontal support force derived from the general formulae in 2.3.5 is given by :
lkN l
20
3.5.3
The vertical support force may be calculated as given in 3.2.3.
Ojo
___I~ -1··;
I
I
\
\
I
I
\
I
I
I
I
I
I
\
I
I
I
I
I
I
I
K;
I
Ii; 3 )
I
I
I
Pri
I
,·fI
I
I
I I
II
I/
II
//
Fig. 3.5 One rigid and one flexible horizontal support.
3.6
Container stack with one rigid and one flexible horizontal support
3.6.1 The arrangement is shown in Fig. 3.5.
The horizontal spring stiffness of the lashing, Ki, may be calculated in accordance
with the formulae in 3.1.2.
The clearance of the rigid support, Ojc• is assumed to be known.
The unsupported displacements Oio and Ojo may be calculated in accordance with the
formula in 2.3.2.
3.6.2 The horizontal support forces derived from the general formulae in 2.3.5 and
2.4.3 are given by:
At level i :
tkNI
-
At level j:
tkNl
21
3.6.3
The vertical support forces may be calculated as given in 3.3.3.
,.
6jo
I
I
In:: 6l
I
I
'
I
I
I
JPrj
'·
I
I
j
I
I
I
I
I
I
I
,
H>io
Pri
I
I
I
I
I
I
,
I
I
I
I
I
I
I
I I
I I
I
I
1,
i
t
Psh
Fig. 3.6 Two flexible horizontal supports.
3.7
Container stack with two flexible horizontal supports
3.7.1 The arrangement is shown in Fig. 3.6.
The horizontal spring stiffnesses of the lashings, Ki and Kj, may be calculated in accordance with the formulae in 3.1.2.
The unsupported displacements,
formula in 2.3.2.
Bio
and Ojm may be calculated in accordance with the
3.7.2 The horizontal support forces derived from the general formulae in 2.3.5 are given by:
-
At level i:
Pri
-
1kN1
=
At level j :
Kc [ ( ~ +
(
i) ~jo - i Bio]
~~ + i)( ~; + j )-i2
1kN1
22
3.7.3
3.8
The vertical support forces may be calculated as given in 3.3.3.
Container stack with one rigid and two flexible horizontal supports
3.8.1 The arrangement is shown in Fig. 3 .7. The horizontal spring stiffness of the
lashings, Ki and Kj. may be calculated in accordance with the formula in 3.1.2. The
unsupported displacements Oio• Ojo and ~\ 0 may be calculated in accordance with the
formula in 2.3.2. The clearance of the rigid support, Okc. is assumed to be known.
Okc ..
1·
1
----..
~
~
In• 61
k
( k. 6}
\
\
\
\
I
I
I
\
I
I
I
Kj
I J• 3 I
I
I
I
I
I
I.,
J
I Pr
\
\
6
0
11 • 21
Fig. 3.7
Container stack with one rigjd and two fl exible supports.
23
3.8.2 The horizontal support forces derived from the general formul ae in 2.3.5 and
2.4.3 are given by:
At level i:
1kN1
At level j:
At level k:
.&+.
K 1
1
3.8.3 The vertical support forces due to the horizontal loads and forces may be calculated as given in 3.4.3.
3.9
Container stack with three flexible horizontal supports
3.9.1 The horizontal spring stiffnesses of the lashings, Ki, Kj and Kb may be calculated in accordance with the formul ae in 3. l.2.
The unsupported displacements, Oj 0 , Ojo and
the formulae given in 2.3.2.
ok0 may be calculated in accordance with
3.9.2 The horizontal support forces derived from the general formul ae in 2.3.5 are given by:
At level i:
p ri
= Kc
i8k0 U-ci) + i 8i0 U-ck) + Ojo(Cjck-j2)
Ci Cj ck - j2ci + i 2 (2j - Cj - ck)
At level j:
24
{kNJ
At level k :
Kc + ·
K-I
C·J
=
1
~:J + j
3.9.3 The vertical support forces due to horizontal loads and forces may be calculated as given in 3.4.3.
25
4.
4.1
WORKED EXAMPLES
Three tier stack with single cross lashing
4.1.1 General data, see also Fig. 4.1.
Single cross lashing to bottom of second tier.
40' x 8' ISO containers.
Container mass: JO t
Mean transverse acceleration: a 1 = 6,67 m/s 2
Vertical acceleration: av = 7,6 m/s 2
Roll angle <p = 27°
Ph= 0,5·30·6,67 = 100 kN
Lashing: 7 /8' diameter steel wire rope, stiffness constant C = 28000 kN
Horizontal spring stiffness of lashing (see 3.1.2):
K =
I
28000·22582 . . = 3 89 kN/mm
'
V(24382 + 22582)3
4.1.2 Calculation for doorless end walls.
End wall racking stiffness (see 2.2.2): Kc = 10 kN/mm
Free displacement at level i (see 2.3.2):
Horizontal support force of lashing (see 3.5.2) :
p.
=
10·22,5
( _lO
_ +l )
n
= 63 kN
3,89
Vertical support force (see 3.2.3) :
(0,5· 100.32_, ·63) 2438
2258
= 417,9 kN
Lashing force :
PIi = 63 .
2
J 243 82258
+ 2258 2
= 92,7 kN
Vertical component of lashing force :
Psi= 63·
2438
= 68 kN
2258
Combined vertical support forces (see 2.2.10):
Right support:
Psc
Psc
= 0,25·3·30(9,81 + 7,6) = 391,7 kN
= 0,25 · 3 · 30· 9,81 + 417,9 + 68 = 706,6 kN ( < 810)
26
Left support (P8 1 = 0):
Pst = 0,25·3·30·9.8 1 cos27°-417,9 = -221,2kN
The latter force is acceptable. A twist lock or similar with a s.w.I. of 225 kN will have
to be fitted.
Compressive force in lowermost container:
Pc= 0,25·2·30·9,81+417,9-
I00· 2438 + 68 = 579 kN ( <675)
2·2258
Racking force in lowermost container:
Sr= (3-1 + 0,25) 100-63 = 162 kN
This racking force is above the limit ( 150 kN) for a normal ISO container. Thus a reduction in the stack weight of 7,4 tor introducing a heavier lashing will be necessary.
A I" diameter steel wire lashing with stiffness constant C = 38000 kN will have a horizontal spring stiffness of Ki = 5,28 kN/mm. Repeated calculation with this value gives the following results:
Horizontal support force P ri = 77,7 kN
Vertical support force Psh = 402,0 kN
Lashing force Pli = 114,4 kN
Vertical component Psi= 83,9 kN
Right support force Psc = 706,6 kN
Left support force Pst = -205,3 kN
Racking force Sr = 147,3 kN
Now all forces are acceptable. Twist locks with s.w.L 205 kN have to be fitted.
4.1.3 Calculation for door end walls.
Wall racking stiffness: Kc= 3,85 kN/ mm
l" steel wire lashing.
Free displacement at level i:
010 =
100
3 85
'
2,25 = 58,4 mm
Horizontal support force from lashing:
p.rI -
3 85 58 4
' . '
( 3,85 +
5,28
l)
= 130 kN ( < 150)
Vertical support force;
(0,5 · l 00 · 32 - I · 130) 2438
2258
27
= 345,5 kN
Lashing force:
/24382 + 22582
2258
P1i = 130·
=
190 kN
+
140,4 = 706,6 kN
Vertical component of lashing force:
2438
Psi= 130·
2258
= 140,4 kN
Combined vertical support forces:
Right support :
Psc
0,25·3·30·9,81
=
+
345,5
Left support:
Pst = 0,25 · 3 · 30 · 9,8 l cos 27° - 345,5 = - 148,8 kN
Racking force:
Sr= 2,25· 100-130 = 95 kN
Also for door side all forces are acceptable. We find as expected that this side impose
the greatest requirement as to lashing wire strength. A wire with s.w.l. 190 kN has to
be used. According to the Rules (Pt. 5, Ch. 2, Sec. 6 G) the breaking strength is to be at
least 380 kN.
Finally we check the tipping moment of the two upper containers.
Vertical support forces:
Psh
=
0,5· 100·22 = 200kN
Combined support forces:
n•3
; • 1
I • l
P1
t .t
2258
Ps
Fig. 4 .2 Example no. 2.
Fig . 4.1 Example no. 1.
28
Right s u pport :
P 5c = 0,25·2·30 ·9,8 1
+
200 = 347,2 kN
Left su pport:
Psi = 0,25 ·2 · 30 ·9,8 1cos27° -200 = -68,9 kN
Thus tipping will take place and twist locks have to be fi tted . In general twist locks
should be fitted for all free containers on weather decks.
Racking force in secon d container :
Sr = 1,25 · 100 = 125 kN
4.2
Four tier stack with two cross lashings
4.2. t G eneral data. See a lso fig . 4.2.
Double cross lashing to botto m of second and third tier.
40' x 8'6" 1SO containers.
Container mass : 30 t maximum, however variable.
Vertical acceleration : av = 4,2 m/ s2
Vari able transverse acceleration accord ing to t able below.
Roll angle <p = 25° .
Horizonta l container loads are given as foll ows , assuming up per container empty .
Mass (M)
Transv. accel. at
Pha
30 t
6,10 m/ s 2
9 1,5 kN
2
30 t
6,25 m/s 2
93,7 kN
3
30 t
6,40 m /s 2
96,0 k N
4
3t
6,55 m/ s 2
9,8 kN
Tier (a)
Lashings at both levels: 25 mm diameter stee l rod. Horizontal spring stiffnesses (see
3.1.2):
~ =
/
25902 + 22582 = 3436 mm
~ =
/
4. 25902
+ 22582 =
5650 mm
Ei = 0,04 (3436 - 1000) = 97,44 kN/ mm2
Ej
=
Ki =
0,04 (5650 - 1000)
=
186 k N / mm2
97,44 ·3, 14 · 12,52 ·22582
V (25962 + 22582)3
2
2
186 ·3, 14 · 12,5 · 2258
/ (4 · 25902 + 22582)3
=
6,01 kN/ mm
= 2 ,SS kN/ mm
29
4.2.2
Calculation for doorless end.
End wall racking stiffness (see 2.2.2): Kc
IO kN/mm
=
Free displacements at levels i and j (see 2.3.2):
1
Oio
= TO (0,25 · 91,5 + 93,7 + 96,0 + 9,8) = 22,2 mm
Bjo
= 10 (0,25 (91,5 + 93,7) + 96,0 + 9,8 + 93,7 + 96,0 + 9,8)
1
= 35,2 mm
Horizontal support forces from lashing (see 3.7.2):
10 [I ·35,2-( _!Q_
+ 2) 22,2]
2
Pn-
12- ( _!Q_ + 1')( _lQ_ + 2)
65 kN
2,58
6,01
10
=
[(_!Q_
+ 1)35 2-1·222]
6 01
'
'
= 48,8 kN
Vertical support forces (see 3.3.3):
(0,5·91,5
+
1,5·93,7
+
2,5·96 + 3,5·9,8-1·65-2·48,8)2590
2258
= 341,8 kN
Lashing forces:
I
P1J·
=
48,8
2
2590 + 2258
2258
2
= 98,8 kN
V 4. 25902
+ 22582
2258
= 122,1 kN
Ve1tical components of lashing forces:
Ps1i
= 65
2590
= 74,5 kN
2258
Ps1j
= 48,8
2·2590
= 111,9 kN
2258
Combined vertical support forces (see 2.2.10):
Right support:
Psc = 0,25 (3 · 30 + 3) (9,81 + 4,2) = 325,7 kN
Psc = 0,25 ·93 ·9,81 + 341,8 + 74,5 + 111,9 = 756,3 kN ( <810)
30
Left support:
Psc = 325,7 kN
P81 = 0,25·93·9,81cos25° -341,8 = -135,1 kN
Compressive force in lowermost container (see 2.2.11):
+ 3) 9,81 + 341,8-
Pc = 0,25 (2·30
91,5·2590
2·2258
+ 74,5 + 111,9
= 630,2 kN ( <675)
Racking force in lowermost container:
Sr= 0,25·91,5
+ 93,7 + 96,0 + 9,8-65-48,8 =
108,6 kN
We should also check the possible tipping and racking of the second container:
Vertical support forces due to horizontal forces:
Psh2
2590
= 2258 (0,5·93 ,7 + 1,5·96 + 2,5·9,8 -48,8)
=
Left support vertical force:
Ps12 = 0,25·63·9,81 cos 25°-l91 = -51 kN
Racking force:
Sr2 = 0,25 · 93,7
+ 96 + 9,8-48,8 = 80,4 kN
4.2.3 Calculation for door end.
End wall racking stiffness: Kc = 3,85 kN/mm
Free displacements at levels i and j (modify values from 4.2.2):
Oio = 22,2 ·
Ojo =
35,2·
IO
= 57,7 mm
3 85
'
10
3 ,85
91,4 mm
=
Horizontal s upport forces from lashing:
~·~~
3,85[9t,4-(
P ri
+1)s1,1]
= - - - - . - - - -....•-,..-----.-- = 89,6 kN
1- (
w_+
6,01
1)( 2,58
3,85
+ 2)
Jss[(
3~85+ 1)914577]
6,01
'
'
'
Prj =
(
3,85 + I )
6,01
(
3,85
2,58
+ 2) - I
3l
191 kN
Vertical support force:
P sh
= 2590 (0,5·91,5 + l,5·93,7 + 2,5·96 + 3,5·9,8-89,6-2·75,l)
2258
= 253,3 kN
Lashing forces:
Pu= 122,l ·
~~:~
= 187,9 kN
Vertical components of lashing forces:
Psu = 89,6·
PSJ1•
=
751·
'
2590
= 102,8 kN
2258
2 2590
"
-- 1723kN
2258
'
Combined vertical support forces:
Right support:
Psc = 325,7 kN
Psc = 0,25-93·9,81
+
253,3
+
102,8
+
172,3 = 756,5 kN
Left support:
Psc = 325,7 kN
P51 =0,25·93·9,81 cos25°-253,3 = -46,6kN
Compressive force in lowermost container:
Pc = 0,25 (2 · 30
+
3) 9,81
+ 253,3 -
91,5 . 2590
2·2258
+
102,8
+ 172,3
= 630 kN
Racking force in lowermost container:
Sr= 0,25·91,5
+
93,7
+
96
+ 9,8-89,6-75,1 =
57,7 kN
4.2.4 Comments.
All forces at both ends of the container stack are within allowable limits. The following strength requirements are to be fulfilled by the lashing equipment:
-
-
Lower lashing: SWL > 136 kN
Upper lashing: SWL> 188 kN
Twist lock or locking cone at lower corners: SWL > 135 kN
32
APPENDIX I
1.
EVALUATION OF «CLASS A» CONTAINERS
General guidelines
1.1 Class A containers are to be constructed according to the ISO standard or equivalent.
1.2 The containers are to be certified by a recognized classification society and to be
approved according to the CSC-convention.
2.
Age and type
2.1 Existing containers of less than 5 yea rs of age may normally be considered for
re-rating.
2.2 Closed-box containers with steel framing and steel or aluminimum wall panels
are considered best suited for re-rating. Other types and materials may, however, be
applicable based upon satisfa ctory test results.
3. Testing
3.1 For existing containers at least two representative containers in a series should
be proof tested according to the ISO test specifications, with increased loads as given
in table 1. Other containers in same series should be carefully examined by competent
surveyor.
3.2 For new containers prototype testing according to the ISO specification a nd as
outli ned in our « Rules for Certification of Freight Contain ers» is to be performed,
with increased loads as give n in table 1.
4.
Marking
4.1 A special marking clearly identifying the container as a class A container is to be
added to the normal marking.
5.
Inspection and repair
5.1 In order to maintain the contain er standard and quality the II CL (Institute of International Container Lessors) guides and manuals for inspection and repair of freight
containers or equiva lent regulations should be fo llowed.
6.
Application
6.1 It is generally recommended that the application of class A containers as basis
for dimensioning of the container lashing system is limited to ships intended for regular transport of higher strength containers, either fo r the whole cargo compartment or
in restri cted parts of the shi p .
33
APPENDIX II
1.
FORCES ON CONTAINER STACKS IN CASE OF TIPPING
General
1.1 Container stacks without lock connections at the lower corners may be subject to
tipping, i.e. lifting of the corners opposed to the load .direction. Horizontal supports
o r lashings will be subject to additional forces. Estimation of these forces is outlined
in this Appendix.
1.2 In order to prevent the container stack from sliding, stacking cones are normally
to be applied (see also Rules).
2. Container stack with only one rigid horizontal support or one flexible support
(lashing)
2.1
The arrangement is shown in Fig. l.
PrJ
..-----.....---
lid }
In• l I
Fig. 1
2.2
Container stack with one horizontal support.
The horizontal support force is given by :
f (Pha) = 0,5 Ph n 2 for constant Ph
n
1: (a-0,5)
Pha
for variable
P ha
a- I
f (Ma) = 0,5 n M for constant M
n
= 0,5 L Ma for variable Ma
a~I
S
= ih when rigid support or internal lashing
= ih + t:fJ · when external lashing
0
angle of lashing as shown in Fig. 3.1
34
2.3
The total verti cal support force will be given by:
Ps = f (Ma) g0
P81
3.
+
Psi lkNJ
vertical component of lashing force when lashing
0 when rigid horizontal support
Container stack with several horizontal supports where the upper support is rigid
3.1 An example is given in Fig. 2. The upper support is assumed rigid, the others
may be rigid or flexibl e.
3.2 The horizontal support forces Pri. Prj and Prk and the vertical support force Psh
due to the horizontal forces are to be calculated in accordance with Part 3 of the main
text. For the example 3.8 is relevant.
(k • 6 I
~
. - -.......
\
I
\
\
I
I
\
I
l
I J• 3 I
I
I
I
:
/Pr
\
'
i
Fig. 2
I
I
60
tp~h
Container stack with one rigid and two flexible supports.
35
3.3
When tipping occurs, the upper support fo rce will increase:
f ( Ma) as given in 2.2.
3.4
The total vertical support force will be given by:
!:P51
sum of the vertical components of relevant lashing forces.
3.5 T he fo rmula given in 3.3 is in principle valid for any number of supports more
tha n one. In each case the subscript k bas to be substituted by the subscript of the upper, rigid support.
4.
Container stack with several flexible horizontal supports
4.1 The fo rmulae given bel ow are valid for arrangements with two and th ree flexible
horizontal supports.
4.2 The horizontal support fo rces (Prh Prj and , in case of three, Prk) and the vertical
support force Psh due to t he horizontal forces are to be calculated in accordance with
3.7 or 3.9 of the main text.
4.3
When tipping occurs, the horizontal support forces will increase:
In case of two :
Pr/ = Prj
..1..Pr
+ ..1..Pr
(Psh-0,5 f (Ma) g 0 )
(
~+
!)
~
lkNl
f (Ma) = as giv en in 2.2.
0
In case of three (see Fi g. 3) :
Prk'
..1..Pr
=
Prk
+ ..1..Pr
(Psh- 0,5 f(MJ go) (
~ + 1+ +) .![;-
36
1kN1
4.4
LP51
The total vertical suppo rt force will be given by:
sum of the vertical components pf relevant lashing forces
___
.,_
Prk
Pr J
t J• 2)
Pr1
tl•ll
1---~ ~
t - - - - - f. -
Fig. 3
(le• 41
Container stack with three flexible horizontal supports.
37