The simplified approach of structural strength

  

The text below is just a brief review of the topic. 

The text provides few indications about the basis for a simplified estimation of the local structural strength of a rated deck therefore likely to be useful for the mobilisation of temporary equipment on board of Offshore Service Vessels (OSVs). 



Disclaimer:

This text represents only the author personal opinion about the engineering topics presented. This personal opinion is not comprehensive and definitive and it is rather an invitation for discussions, comments and feedback and shall be considered accordingly.

The author can’ take any responsibility for any type of use of this text. 

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Why a simplified estimation of the local structural strength?

The offshore operations request the mobilization of a large range of equipment. 

Sometime the deck spread is designed to around few large equipment e.g. a lay tower, a carousel, a large crane or A-Frame but every time the deck spreads include a variety of small and medium ancillary support equipment as containers (spares, workshops, control cabins, etc) or lifting appliances (knuckle cranes, LARSs) and pulling accessories (winches, sheaves, D-Rings).

A rough estimation of the proportion of small, medium and large items in the deck spread could be done based on Pareto law – the 80/20 principle that 80% of results are obtained with 20% of resources.

In this way can be estimated that it is likely that 80% of equipment will be small equipment, about 16% (so 80% of the 20% left) will be medium equipment and just 4% will be a large equipment.

Using a numerical example it can be said that in case of a 20 items spread, most probably 1 (one) will be a large equipment, 4 (four) will be medium and 15 (fifteen) will be small equipment.


Due to the multiple restrictions related to ship, operation and equipment, it is extremely unlikely that the large equipment will change the position on board of the vessel.


This is not the case with the small and medium ancillary support equipment.

The experience demonstrates that these equipment could keep moving until the very night before ship sails out of the mobilisation place.

However, the question is what does mean small, medium and large in the context of the strength of the vessel?


Considering that the largest number of equipment what could change often the position on board over the night (or better said during a shift) it is assumed that it will be handy having handy a simple method for assessing the impact of equipment on the strength of the vessel.

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The gold key for a simplified approach

The golden key for this simple method is having a rated deck.

What does mean a rated deck?

A rated deck is a deck properly documented having sufficient strength for a well and clearly specified set of loads.

In general the loads are just uniform distributed loads (UDL) but there are seldom cases when the deck elements may be rated for line loads or point loads (e.g. the case of decks were “strong points” as ISO blocks or D-Rings are installed and documented properly).

However, the equipment may transmit point load loads to the deck (e.g. via ISO blocs installed at containers corners) and not UDL type loads.

This means that the UDL rating shall be converted into point load ratings.

Converting UDL into point load

The formula for converting the UDL of a rated deck into point load capacity is:

F = 0.5*(g+av)*p*l*s where:

F [kN] = the point load (F) to be applied at the middle of a rated deck longitudinal;

Note:

F is the point load applied at the middle of a rated deck longitudinal, equivalent from local strength point of view with the application of rated UDL (p) on same longitudinal.

av [m/s2] = the vertical acceleration considered for the rating of deck at the specified position. 

Note: The probability of acceleration shall be calibrated with the load condition analysed (operational or survival); 

p [t/m2] = the documented UDL rating of the deck;

l [m] = the span of longitudinal; the length between the supports (girders, bulkhead, pillar);

s [m] = the average distance to the nearby longitudinal.  


A similar formula could be applied in certain conditions (see the note about l) also for girders, so:

The point load (F) to be applied at the middle of a rated deck girder and equivalent from local strength point of view with the application of rated UDL (p) is:

F = 0.5*(g+av)*p*l*s where:

F [kN] = the point load (F) to be applied at the middle of a rated deck girder;


av [m/s2] = the vertical acceleration considered for the rating of deck at the specified position (see the note above about the probabilities); 

p [t/m2] = the documented UDL rating of the deck;

l [m] = the span of girder;


Note: The formula is applicable only for the girders supported by bulkheads by pillars arranged on the span of girder. 

The formula is not applicable if:

· The girder is part of a grillage of girders; or 

· The segment assessed is an end segment supported at the “free” end by a pillar.

s [m] = the average distance to the nearby parallel girders or bulkheads. 


Note:

The formula for longitudinal is listed as well in DNVGL-CG-0156 Sec. 3.4.

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The estimation of vertical loads transmitted by equipment onto the deck by a simple equipment

The equipment is assumed supported on 4 (four) points arranged on the corners of a rectangle LxB where L is parallel with ship’s CL and B is parallel with the deck and normal to CL.  

SW is the selfweight of the equipment and CoG is the centre of gravity.

F is the operational force generated by equipment (if any).


The maximum vertical reaction into the deck is:

Vmax [kN]= V-SW+V-F  where


V-SW [kN] is the vertical reaction due to the inertia loads. 

V-F [kN] is the vertical reaction due to an active load (e.g. line load).


V-SW= SW*(al* fCoG-l*zCoG/L+ at* fCoG-t*zCoG/B+(g+av)*fCoG-l*fCoG-t)

fCoG-l, fCoG-t = the ratios of CoG position relative to L and B;

zCoG = the height of CoG above the deck; 

al, at, av = the combined accelerations on the main directions of ship’s.

Note:

The accelerations shall be combined in accordance with the requirements in applicable rules/codes.


V-F = Fl* fF-l*zF/L+ Ft* fF-t*zF/B+Fv*fF-l*F-t

fF-l, fF-t = the ratios of the point of application of the active force point relative to L and B; 

zF = the height of the point of application of the operational force above the deck;

Fa-l, Fa-t, Fa-v = the projections of the operational force on the main directions of ship’s.  


Strength criteria

The strength of the deck is sufficient if F ≥ Vmax.

Equipment complying with this criterion could be classified as small equipment.

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Examples

Standard values for OSV deck are:

Deck rating 10 t/m2, av= 0.3g, l= 1.8 m and s= 0.6 m.

F= 0.5*9.81*(1+0.3)*10*1.8*0.6= 68.86 kN


Deck container

Typical deck container has characteristics as: 

SW= 10 t; L= 6.0 m, B= 2.4 m, 

fCoG-l= 0.5; fCoG-t= 0.5; zCoG = 1.2 m

The applicable accelerations combinations are  

a) V+T: al=0; at= 0.5g and av=0

b) V+L: al= 0.4g; at=0; av= 0.3g

Vmax-a= 18*9.81*(0*0.5*1.2/6+0.5*0.5*1.2/2.4+(1+0)*0.5*0.5)= 66.2 kN

Vmax-b= 18*9.81*(0.4*0.5*1.2/6+0*0.5*1.2/2.4+(1+0.3)*0.5*0.5)= 64.5 kN

Vmax= max(Vmax-a, Vmax-b) = 66.2 kN

Vmax = 66.2 kN ≤ F = 68.86 kN therefore this container can be categorized as a small equipment.


Deck winch

Typical deck winch has characteristics as: 

SW= 5 t; L= 1.4 m, B= 0.6 m, 

fCoG-l= 0.5; fCoG-t= 0.5; zCoG = 0.6 m

Fl= 0; Ft= 6.5 t; Fv= 0

fF-l = 0.5, fF-t= 0.8

The applicable accelerations combinations are 

a) V+T: al=0; at= 0.3g and av=0

b) V+L: al= 0.2g; at=0; av= 0.3g

Vmax-a= 5*9.81*(0*0.5*0.6/1.4+0.3*0.5*0.6/0.6+(1+0)*0.5*0.5)= 19.62 kN

Vmax-b= 5*9.81*(0.2*0.5*0.6/1.4+0*0.5*0.6/0.6+(1+0.3)*0.5*0.5)= 18.04 kN

Vmax= max(Vmax-a, Vmax-b) = 19.62 kN

V-F = 0*0.5*0.6/1.5+6.5*9.81*0.8*0.6/0.6+ 0*0.5*0.8= 51.12 kN

Vmax= 19.62+51.12=70.74 kN

Vmax > F therefore additional actions shall be considered e.g. the equipment could be rearranged on deck or installed on spreader beams in such a way that B is increased from 0.6 m to 1.2 m.