## Timber Cargo-2 (Calculations)

Rolling of a ship imparts tremendous accelerations on the cargo that is loaded on it. This is made worse if the object is heavy and gains momentum due the play available by the virtue of the kind of stow. With timber all the above stated factors join hands and can cause a dangerous situation in even moderate weathers. Most of the lashing ways are learnt through accidents. Though, a technical angle introduced to the securing arrangements will only enhance the awareness that is much needed.  Let us now understand the importance and technicalities about various lashing arrangements.

Hog Wires
The purpose of hog wires is to connect the uprights erected to the port and starboard of the stow. The broad idea being, with the load of stow, the uprights don’t fall apart.

Thus, to achieve a more secure stowage of logs when stowed on deck, hog wires may be utilized. Such hog wire should be installed in the following manner:

1. At approximately three quarters of the height of the stow, the hog wire should be rove through a padeye attached to the uprights to run transversely, connecting the respective port and starboard uprights. The hog lashing wire should not be too tight when laid so that it becomes taut when overstowed with other logs.

Thus, height of hog wire = 0.75 x Ht. of stow

2. A second hog wire may be applied in a similar manner if the height of the hatch cover is less than 2 m. Such second hog wire should be installed approximately 1 m above the hatch covers.

Thus, if the ht of hatch cover is h the ht of hog wire = (h + 1)m

The aim of having the hog wires applied in this manner is to assist in obtaining as even a tension as possible throughout, thus producing an inboard pull on the respective uprights.

Top-over and continuous wiggle lashings In addition to uprights and hog lashings, an arrangement with top-over and continuous wiggle lashings may be used. Top over lashings are laid athwartships over the top of stow, helps consolidating the stow between the uprights. Wiggle lashings on the other hand are zig zag lashings, involving continuous wire rope passed through the snatch blocks to cause the required athwartship change in direction. The wire is tightened initially with power of winch and later by tensioners on individual segments.

Formula for bridge visibility

Where:
KCKS    Horizontal distance from conning position to position ‘S’
KsKP    Horizontal distance from position ‘S’ to position ‘P’
AC        Airdraft of conning position
AS        Airdraft of position ‘S’

Density, SF, Coefficient of Friction and Racking Strength are important data for the calculations.

In Ch 4, table 4.1 gives typical values for density and stowage factors of different timber. Thus, fresh round wood of Coniferous, with bark on, the density is between  0.9 & 1.1 t/m3, volume factor [volume of hold space / volume of cargo] is between 1.5 & 2.0 and stowage factor is between 1.4 and 2.2 m3/t. The weight of uncovered timber cargo may change during a voyage due to loss or absorption of water (but in case of wrapped bundled cargoes it does not). Timber cargo stowed under deck may lose weight whereas timber stowed on deck may gain weight by absorption of water.

Cargo at rest is prevented from sliding by static friction. When movement has been initiated the resistance of the material contact is reduced and sliding is counteracted by dynamic friction.

The static friction may be determined by an inclination test. The angle r is measured when the timber cargo starts to slide. The static friction is calculated as: m = tan (r). Values are different for winter and non-winter conditions.

Table 4.2 gives typical values of static friction for different material combinations. Thus, m for coniferous round wood (bark on) against painted steel is 0.35, whereas against similar layers it is 0.75.

Static friction may be used for tight block stowage arrangements. Dynamic friction should be used for non-rigid lashing systems, which due to elasticity of securing equipment allows for minor dislocation of the cargo before full capacity of the securing arrangement is reached. The value of increased weight of timber deck cargo due to water absorption should be considered in accordance with the 2008 IS Code. Any increase in weight due to water absorption should be considered before calculating the increase due to the weight of ice.

The Racking Strength

The Racking Strength, RS, is taken as the applied force F cos α (see figure above) when the package collapses or when the deflection in the top is 10% of the package width, B, or maximum 100 mm. Racking strength measurements will have to be carried out by the shipper and the information should be provided to the Master.

Every lashing should pass over the timber deck cargo and be secured to suitable eyeplates, lashing bollards or other devices adequate for the intended purpose which are efficiently attached to the deck stringer plate or other strengthened points. They should be installed in such a manner as to be, as far as practicable, in contact with the timber deck cargo throughout its full height. All lashings and components used for securing should:

1. possess a breaking strength of not less than 133 kN;
2. after initial stressing, show an elongation of not more than 5% at 80% of their BS; and
3. show no permanent deformation after having been subjected to a proof load of not less than 40% of their original BS.

Every lashing should be provided with a tightening device or system so placed that it can safely and efficiently operate when required. The load to be produced by the tightening device or system should not be less than:

1.  27 kN in the horizontal part; and
2.  16 kN in the vertical part.

Upon completion and after the initial securing, the tightening device or system should be left with no less than half the threaded length of screw or of tightening capacity available for future use. Every lashing should be provided with a device or an installation to permit the length of the lashing to be adjusted. Lashings at each end of each length of continuous deck stow are positioned as close as practicable to the extreme end of the timber deck cargo.

Precautions in respect of wire rope clips (bulldog clip)

1. The number and size of rope clips utilized should be in proportion to the diameter of the wire rope and should not be less than three, each spaced at intervals of not less than 150 mm.
2. The saddle portion of the clip should be applied to the live load segment and the U-bolt to the dead or shortened end segment.
3. Rope clips should be initially tightened so that they visibly compress the wire rope and subsequently be re-tightened after the lashing has been stressed.
4. Greasing the threads of grips, clips, shackles and turnbuckles increases their holding capacity and prevents corrosion.
5. Bulldog grips are only suitable for a standard wire rope of right-hand lay having six strands. Left-hand lay or different construction should not be used with such grips.

General principle observed in planning regarding location and lashing system to be applied for deck load of timber

Uprights should be used for loose sawn wood. Uprights or stoppers (low uprights) should also be used to prevent packaged sawn wood loaded on top of the hatch covers only from sliding. The timber deck cargo should in addition be secured throughout its length by independent lashings.

The maximum spacing of the lashings referred to above should be determined by the maximum height of the timber deck cargo in the vicinity of the lashings:

1. for a height of 2.5 m and below, the maximum spacing should be 3 m;
2. for heights of above 2.5 m, the maximum spacing should be 1.5 m; and
3. on the foremost and aft-most sections of the deck cargo the distance between the lashings according to above should be halved.

As far as practicable, long and sturdy packages should be stowed in the outer rows of the stow and the packages stowed at the upper outboard edge should be secured by at least two lashings each. When the outboard packages of the timber deck cargo are in lengths of less than 3.6 m, the spacing of the lashings should be reduced as necessary or other suitable provisions made to suit the length of timber.  Rounded angle pieces of suitable material and design should be used along the upper outboard edge of the stow to bear the stress and permit free reeving of the lashings. This also applies to a timber deck cargo of cants. Timber packages may alternatively be secured by a chain or wire loop lashing system.

The round wood deck cargo should be supported by uprights and secured throughout its length by independent top-over or loop lashings spaced not more than 1.5 m apart. If the round wood deck cargo is stowed over the hatches and higher, it should, in addition to being secured by the lashings, be further secured by a system of athwartship lashings (hog lashings) joining each port and starboard pair of uprightseIf winches or other adequate tensioning systems are available on board, every other of the lashings may be connected to a wiggle wire system.

Alternative Design Principles
The development (and use) of new designs and securing arrangements, by providing functional based requirements on the securing of timber deck cargoes, which may be used as an alternative to the requirements in the code, for ships of less than 24 metres in beam is permitted. Any design risk assessment should be agreed with the Administration before being used. The operational risk assessments should be included within the ship’s safety management system.

Uprights (stanchions)
Uprights are supporting structures (permanently fixed or collapsible) rigged on the inside of bulwarks to keep timber cargoes secured and prevent them from shifting transversely.

Guard line and life line: Guard lines or rails, not more than 330 mm apart vertically, should be provided on each side of the deck cargo to a height of at least 1 m above the cargo. Where uprights are not fitted or where alternative to the guardlines are permitted, a walkway of substantial construction should be provided having an even walking surface and consisting of two fore and aft sets of guardlines or rails about 1 m apart, each having a minimum of three courses of guardlines or rails to a height of not less than 1 m above the walking surface. Such guardlines or rails should be supported by rigid stanchions spaced not more than 3 m apart and lines should be set up taut by tightening devices. As an alternative to above a lifeline, preferably wire rope, may be erected above the timber deck cargo such that a crew member equipped with a fall protection system can hook on to it and work about the timber deck cargo.

Calculations for top-over lashings

Ex. Following are details in respect of ship,
DWT of ship                                                                : 16,600t
Length between perpendiculars, LPP                         : 134 metres
Moulded breadth, BM                                                 : 22 metres
Service speed                                                              : 14.5 knots a
Metacentric height, GM                                               : 0.70 metres

The deck cargo has the dimensions L ´ B ´ H = 80 ´ 19.7 ´ 2.4 metres. The total weight of the deck cargo is taken as 1,600 tons. Sliding between the layers is prevented by packages of different heights in the bottom layer.

Dimensioning transverse acceleration With ship particulars as above and considering a stowage position on deck low, Annex 13 of the CSS Code gives a transverse acceleration of at = 5.3 m/s2, using the following basic acceleration and correction factors:

at basic   = 6.5 m/s2       = Basic transverse acceleration
fR1        = 0.81              = Correction factor for length and speed
fR2        = 1.00              = Correction factor for BM/GM

at = at basic × fR1 × fR2 = 6.5 × 0.81 × 1.00 = 5.3 m/s2

a. Calculate the number of lashings required to secure packages of sawn wood on deck as well as the required racking strength in the packages in the bottom layer

b. Calculate required strength of the bottom blocking devices for a deck load of packages of sawn wood. The number of lashings are in accordance with relevant sections of Code. c. Calculate the dimensions and moments for uprights, supporting packages of sawn wood on deck.

Ans. a)
m = 1,600 t = Mass of the sec. to be secured in t, incl. absorbed water and possible icing
μstatic = 0.45 = Coeff. of static friction bet, the timber dk cargo and the ship’s dk/hatch cover
H = 2.4 m  = Ht of dk cargo in metres
B = 19.7 m = Width of dk cargo in metres
L = 80 m = Length of the dk cargo or section to be secured in metres
PW = 192 kN  = Wind pressure in kN based on 1 kN per m2 wind exposed area, (CSS Code),
PS = 160 kN = Pr.from unavoidable sloshing in kN @ 1 kN per m2 exposed area, (CSS Code)
PTV = 16 kN = Pretension in the vertical part of the lashings in kN
a = 85° = Angle between the horizontal plane and the lashings in degrees
np = 18 pcs = Number of stacks of packages abreast in each row

Number of required top-over lashings
For pure top-over lashing arrangements with no bottom blocking, the friction alone will have to counteract the transverse forces so that the following equilibrium of forces is satisfied:

(m.go + 2 × n × PTv × Sin α) µstatic ≥ m × at + PW + PS Units denoted with a consider cargo units above the bottom layer only. Thus the required number of top-over lashings can be calculated as:

Ans. b
To calculate required strength of the bottom blocking

The required strength, MSL, of the bottom blocking devices is given by the following equilibrium:
m = 1,600 t = Mass of the sec. to be secured in t, incl. absorbed water and possible icing
μstatic = 0.45 = Co.eff. of static friction bet, the timber dk cargo and the ship’s dk/hatch cover
H = 2.4 m = Ht of dk cargo in metres
B = 19.7 m = Width of dk cargo in metres
L = 80 m = Length of the dk cargo or section to be secured in metres
PW = 192 kN = Wind pressure in kN based on 1 kN per m2 wind exposed area, (CSS Code),
PS = 160 kN = Pr.from unavoidable sloshing in kN @ 1 kN per m2 exposed area, (CSS Code)
PTV = 16 kN = Pretension in the vertical part of the lashings in kN
a = 85° = Angle between the horizontal plane and the lashings in degrees
np = 18 pcs = Number of stacks of packages abreast in each row
nb = 26 pcs = Number of bottom blocking devices per side of the deck cargo

The required strength, MSL, of the bottom blocking devices is given by the following equilibrium:

Ans. c
Calculation of uprights for packages of sawn wood

m = 1,600 ton = Mass of the sect. to be secured in t, incl. absorbed water and possible icing
μinternal = 0.30 = Co.eff. of internal friction between the timber packages
H = 2.4 m = Height of deck cargo in metres
b = 1.1 m = Width of each individual stack of packages
np = 18 pcs = Number of stacks of timber packages abreast in each row
q = 2 pcs = Number of layers of timber packages
RS = 3.5 kN/M = Racking Strength per timber package in kN/m
N = 36 pcs = Number of uprights supporting the considered section on each side
H = 2.4 m = Ht above dk at which hog lashings are attached to the uprights in metres
K = 1.8 = Factor for considering hog lashings
k = 1 if no hog lashings are used k = 1.8 if hog lashings are used

Bending moment in uprights
The design bending moment per upright supporting timber packages is to be taken as the greatest of the three moments given by the following formulae:

With cargo properties and acceleration as given above, the following bending moments are calculated:

The design bending moment, taken as the maximum bending moment calculated by the three formulae above multiplied with the safety factor of 1.35, thus becomes 106 kNm:

Mbending ≥ 1.35 × max (CMbending1, CMbending2, CMbending3) = 1.35 × 78.5 = 106 kNm

Suitable dimensions for uprights
With MSL taken as 50% of the MBL for steel with the ultimate strength 360 MPa (N/mm2 ), the required bending resistance, W, can be calculated as:

Thus, uprights made from either HE220A profiles or a cylindrical profile with an outer diameter of 324 mm and a wall thickness of 10.3 mm are suitable. Strength in hog lashings The required MSL of each hog lashing is calculated by the following formula:

In this case, the hog lashings are attached at a height of h = 3.5 m and the required strength is calculated as:

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