Internatonal Journal of Engneerng and echnology Volume No. 9, September, Stablty Analyss for the Desgn of 5-onnes Offshore Work arge Ntonye Samson a, Ezenwa Ogbonnaya b, uve Ejabefo a a Department of arne Engneerng, Rvers State Unversty of Scence and echnology, Port Harcourt, Rvers State Ngera. b Department of echancal/arne Engneerng, Nger Delta Unversty, Wlberforce Island, ayelsa State, Ngera. ASRAC here have been several development or gant strdes made n the feld of marne engneerng n general and the desgn of barges n partcular. he desgn of a 5-tonne offshore work barge wth a deck crane s one of these feats. he determnatons of optmal scantlng to ensure good stablty characterstcs, estmaton of the prncpal dmensons and analyss of the stablty of the work barge when the crane s n offshore workng condton were carred out. he hydrostatc curves for the vessel were plotted and used to determne the optmal values for safe operaton of the work barge. Analyss of stablty of the entre barge to ensure that the lmt of load to be carred by the crane s not eceeded or ponts loads does not eceed a safe value for the vessel shows that the desgn s feasble. eywords: Stablty analyss; Deck crane; 5-tonnes offshore work barge; Volume dsplacement.. INRODUCION A barge s usually a flat bottom vessel manly used as cargo tanker, equpment supply carrers, crane platform and support accommodaton bases n offshore drllng. ost barges do not operate under ther own power but requre a tugboat to pull or push them to ther destnaton. Only n few cases do we see self- propelled barges []. herefore barges are specally desgned for specfc purposes, dependng on the type of barges, whch s characterzed by the functon of the sad barge, ts desgn procedures are slghtly dfferent or rather the chosen characterstc may dffer n one way or the other []. buoyancy may be consdered to act. he force of buoyancy always acts vertcally upwards. etacentre () s a pont n space where the vertcal lne upwards through the centre of buoyancy () of the nclned vessel cuts through the vertcal lne upwards through the centre of buoyancy () of the uprght vessel. etacentrc heght (G) s the vertcal dstance between the Centre of Gravty (G) and the etacentre (). If s above G the vessel wll want to stay uprght and f G s above the vessel wll want to capsze.e. G postve s Stable, G negatve s Unstable. he desgn of a barge follows almost the same process, but wth a lttle or smple varaton n choosng some parameter as to compensate for the servce that wll be taken care of. he desgn processes from [] of the barge under consderaton gave smlar nformaton as usng prncpal dmensons of the shp through varous ratos of dmensons. hs work barge wll serve a multpurpose offshore functon for ol ndustres, marne establshment and other companes that requre manpower to work offshore wthout possble return of the workers daly to shore.. Illustraton Defntons [4] Centre of gravty (G) s an magnary pont n the eact mddle of a weght where the entre weght may be consdered to act. he force of weght always acts vertcally downwards. Centre of buoyancy () s an magnary pont n the eact mddle of the volume of dsplaced water where the entre Rghtng lever (+GZ) or Overturnng lever (-GZ) s the (horzontal) dstance between the two (vertcal) lnes of acton of the buoyancy force (upwards), and the gravty force (downwards). he sze of GZ s the measure of how stable or unstable the vessel s at any partcular angle of heel. AERIAS AND EHOD o acheve ths procedure, the approach from the prncples of dynamc smlarty of vessel from [5], was used to obtan the prncpal dmenson of the barge.. Estmaton of asses and an Dmensons Estmatng the mass of the arge C () et the volume be epressed n terms of ISSN: 49-444 IJE Publcatons U. All rghts reserved. 849
Internatonal Journal of Engneerng and echnology (IJE) Volume No. 9, September, ρ C () From Equaton () (4) C (5) (6) C Hence the readth to Draught rato wll result to, from Equaton and 4, et (7) herefore substtutng Equaton 7 nto 6 becomes C (8). Dsplacement and Form Coeffcent ass Dsplacement ( ) Δ Δ Δ WO + Δ S (9) Volume Dsplacement Δ () ρ A C.5 ρ A C 5 g / m lock Coeffcent C. Stablty Analyss.5tonnes / m () Fg. s the nclned eperment used transversely to determne some stablty characterstcs of the work barge Fg.: ransverse stablty analyss dagram [6] For a pontoon shaped barge an appromaton for the metacentrc heght G can be obtaned from the rectangular block formula whch says:- G + - G () + t - h t () hs formula assumes the barge s a rectangular block wth the lghtshp centre of gravty at deck level. s the vertcal dstance from the keel to the centre of buoyancy, s the vertcal dstance from the centre of buoyancy to the metacentre, and G s the vertcal dstance (from the keel to the centre of gravty). he vertcal dstance between the centre of buoyancy () and the metacentre (), s the [7]. I (4) where I s the nerta of the water plane area*, and s the volume of dsplacement. [6] stablty analyss shows that for θ ( - ) V d (5) V w Volume of wedge g Centrod of wedge g Centrod of wedge gg d Weght g actng downwards uoyancy force actng upward herefore a couple of W GZ s formed ISSN: 49-444 IJE Publcatons U. All rghts reserved. 85
Internatonal Journal of Engneerng and echnology (IJE) Volume No. 9, September, GZ rghtng level G metacentrc heght From [6] analyss V d V gg From the trangle anθ tanθ tanθ For a work badge Consderng the trangle o O h tan θ tan θ Whle the area of the trangle o O wll be ( tan tan θ θ ) he dstance from g to centre O gg Fg. : Crane outreach [4] he greatest uplft or detachment force, acts at the pont of attachment (of the crane to the barge) furthest from the pont of suspenson. hs s the force tendng to turn the crane over and the moment of ths force s the product of the weght of the lfted load, and the (horzontal) dstance ( d ) of the pont of suspenson (p) from the pont of uplft (u). At zero lst and roll the crane s more effectve and the stablty of the barge s better than when t has a percentage of lst and roll. On the other hand, durng the analyss of the stablty of the barge when the crane s workng, an ncrease n the radus wll be followed wth a decrease n oom angle degree and also a decrease n the ratng of the load t s carryng. herefore a decrease n boom angle ncreases the barge stablty [8]. Hence analyss was taken n the followng poston as shown n Fg.. Postons A,, C, D, and E are consdered the lftng postons of the crane n the analyss of the stablty of the work barge when the crane s n offshore workng condton. he postons F, G, H and I are consdered the loadng postons when consderng the loadng condton of the barge n the analyss of the stablty of the work barge when the crane s n offshore workng condton at dfferent draft condton..4 Stablty of the arge when Crane s Workng From [4], when usng cranes and other lftng gear such as A- frames that are barge mounted, t must be noted that the weght of the lfted load acts at the pont of suspenson not at the base of the crane. he overturnng moment on the barge, tendng to cause t to capsze, s the product of the weght of the lfted load, and the (horzontal) dstance ( d ) of the pont of suspenson (p) from the centre of buoyancy () as shown n Fg. Fg.: Stablty analyss dagram wth the crane s workng For the work barge only poston A was consdered n the analyss of the stablty, because every safe value at ths locaton wll be safe at other locatons. ISSN: 49-444 IJE Publcatons U. All rghts reserved. 85
Internatonal Journal of Engneerng and echnology (IJE) Volume No. 9, September, Snce the amount of load lfted s drectly proportonal to the draft of the barge, hence, the analyss was based on dfferent levels of the draft to calculate other parameters. hese curves also vew to great etents locaton where weghts of larger tonnes could not be placed for the safety of the personnel on board the vessel. Snce the work barge floatng at many dfferent drafts when the crane s n workng condton, the analyss of the stablty of the barge n such condtons cannot be overemphass. Hence the hydrostatc curves of the barge n these condtons become very mportant. hese dagrams nclude the plottng of the draft versus several parameters that ther factor plays a sgnfcant role n the stablty of the barge. hey nclude amongst others:. Volume of dsplacement (Δ). Center of buoyancy (). etacentrc radus () 4. oment of nerta of water plane (I) 5. Center of gravty (G) 6. oment to change trm by cm (C.) 7. he metacentrc heght () Hence each graph has ts sgnfcant role to help analyze the stablty of the work barge at dfferent loads carred by the crane. For nstant, the graph of draft versus volume dsplacement s useful to fnd the dsplacement of the barge for any average draft when floatng. he loadng condton can also be determned for safe workng condton n seawater. All condtons of equlbrum were replaced durng the analyss. he laws of statc and dynamcs, transverse and longtudnal stabltes of the work barge were also strctly adhered to. he epermental analyss, calculatons etc, and the followng results are thus obtaned through the help of the hydrostatc curves.. ANAYSIS AND DISCUSSION OF RESUS here are many ways to estmate the shp mass and the man dmenson of the shp for the purpose of basc desgn. However these approaches are appromate and are ether based on eperence and performance characterstcs of estng desgns or on results obtaned from model testng carred out for years past [9]. For the mportance of ths arge under consderaton and ts advance mplementaton n the ol ndustry, a model work barge was desgned. he odel Shp Dmenson used; odel arge Dmenson ength ( ) 9.5m readth ( ) 7.5m Depth (D ) 6.m Draught ( ) 4.5m Deadweght ( Δ ) tonnes WO ght weght ( Δ ) tonnes S. Dsplacement and Form Coeffcent o calculate for a stable vessel, the followng consderatons have to be taken: ass Dsplacement ( Δ ) from equaton Δ ΔWO + ΔS + 5onnes ass Dsplacement 5onnes Volume Dsplacement ( ) From equaton, Volume Dsplacement Densty 5g/m.5 onnes/m Substtuton nto equaton 5.5.5 4855m lock coeffcent ( C ) 5. Δ ρ A From equaton, lock Coeffcent for the model barge s, C 5678 9.57.54.5 Deadweght Dsplacement Rato η 5 Δ W Hence from equaton 6 ( ) ( ) C.6 C.5 ( ) W W (6) ρ C ISSN: 49-444 IJE Publcatons U. All rghts reserved. 85
Internatonal Journal of Engneerng and echnology (IJE) Volume No. 9, September, From the estmaton C ρ 7.5. 9.5 4.5 9.5.5.49.5 tonnes / m 5tonnes Substtutng values nto equaton 6, we have 5.5..45.5 86. 49m Selected length for ths work barge under desgn s 8m to enhance compensaton n the wdth of the barge. Smlarly,... 86.49 6.m Selected breadth for the work barge s m though the compensaton was from the length overall and.49.49.49 86.49 4.5m Selected Draft for the work barge s 4.5m through the compensaton made from the length. hus the dmensons for the desgn of the work barge are as follow: 5 tonnes 8m m 4.5m olded readth 5 Whle tan θ tan.76 Calculated Area 9.8m Volume of wedge Area ength 586.4m he volume moved from one sde to the other by I tanθ y substtuton I 79,965.97m C I Snce t s a barge 4 7.m.5m + 486m 9.8m centre of gravty s at.84m, whch s G. G + G G ; D f () G 6.44m 4 (7) (8) o fnd the mnmum that wll cause an ncrease n draft, 5 C. 46 8 4.5. Determnaton of etacentrc Heght [6] Area of wedge Ref: tan ISSN: 49-444 IJE Publcatons U. All rghts reserved. 85
Internatonal Journal of Engneerng and echnology (IJE) Volume No. 9, September, d d + d + d +.5m rm s the dfference n draught forward and aft. If H A > H F rmmng by the stern Whle H A < H F rmmng by the ow H F Draught forward H A Draught Aft rm H A - H F () And angle of rm H A F () H ength between perpendcular F Centre of flotaton Snce the center of flotaton s not at dshp W W. ongtudnal Stablty Analyss [] W n W W W n W W Fg. 4 s the nclned eperment used longtudnally to determne some stablty characterstcs of the work barge. he smlar trangle W W F & Wn WW W n FW FW FW () n Wo o PP Fg. 4: ongtudnal stablty analyss dagram From trangle GZ n fgure 4, GZ tan θ G GZ tanθ G G 6.44 (9) Fgure. s the epermental procedure used when the barge s under rng parallel snkage to determne some stablty characterstcs of the work barge. W W s the alteraton of draught at the stern and W n s the total change n trm. On the other hand alteraton of draught forward s gven as () F PP W n ean Draught H A H F (4) d otal rm (t) length (5) d dstance of F from dshp dstance between parallel water lne td true mean draught Arthmetc mean draught + H A H F td y calculatng Angle of nclnaton tan t PP (6) Fg. 5: Parallel snkage stablty analyss dagrams 5 ISSN: 49-444 IJE Publcatons U. All rghts reserved. 854
Internatonal Journal of Engneerng and echnology (IJE) Volume No. 9, September, t PP tan tan GG G 6.56m ( total trm) b (7) W b C.cm d G G ρ d W G 6.4m 4. RESUS AND DISCUSSION 4. Results 64cm (8) he weght of 5, -tonnes off-shore work badge was estmated to be 6.-tonnes wth all necessary equpments. here by havng the capacty of carryng eternal load up to -tonnes wthn the vessel dependng on the safety factor and the avalable space. After desgn and estmaton, t was observed that the center of gravty s actng at.84m above the keel (bottom) of the barge,.9m fore of the chosen centre (longtudnally) and 9mm port of the chosen centre (transversely). hs s safe n shp desgn; t would have been unsafe f the centre of gravty acts above.m from the bottom of the shp. able shows the values of stablty characterstcs used to plot the hydrostatc curves of the work barge. he relatons used for hydrostatc curves are as follows: I I.. C. 4. ρ C. 5. + 6. I 7. G Z C able : Calculated values of stablty characterstcs of the work barge Δ G C I.5 55.5 54.5.8.5.5 45.68 7997.. 7 8.5 66.6 67..6 47.6 7998..5 66.5 6.75..85.945 49.57 7998.. 4 6. 8. 84..6 5.54 7998,.5 767.5 7.5 66.7 67.95.575 5.5 869.. 4.5 55.5 57..89 55.5 798..5 874.5 78.75 47.6 49.5,5 57.5 7998. 4. 448 4. 4.7 4.7.5 59.5 844. 4.5 498.5 486,5 7. 9.5.84 6.55 798. Wth these results we obtaned the hydrostatc curves, whch enable us to determne the varous analytcal results for the work barge under servce condton. 4. Dscussons In antcpaton of the barge floatng n an uprght condton at many dfferent water lnes (or draft) n the course of ts servces, t s usual to calculate, n advance, the man geometrcal characterstcs of the shp form at each draft []. hs data n able whch s plotted as curves aganst the draft are known as hydrostatc curves. hese hydrostatc curves are represented n Fgs. 6 to whch shows dfferent calculated values plotted aganst dfferent draft due to varaton of loads. Fg. 6 shows a graph of draft plotted aganst the dsplacement of the vessel. Result shows that the workng barge can carry a mamum load of 498.5-tonnes wthout the barge snkng. he ISSN: 49-444 IJE Publcatons U. All rghts reserved. 855
(eters) Dsplacement (onnes) G (eters) Internatonal Journal of Engneerng and echnology (IJE) Volume No. 9, September, result also shows that there s coherence between the loadng condtons (or confguraton) wth that of the draft. he perfect straght lne suggests that the draft vares drectly wth the dsplacement of the barge. Smlarly, fg. 7 shows that, the centre of buoyancy vares drectly to the draft of barge, whch s a good representaton n the totalty of shp desgn. Fg. 8 s a graph of the centre of gravty versus draft. hs s one of the most mportant representatons n a shp desgn as t relates to stablty of the barge and to prove the structural rgdty s correct. hs proportonal graph as dstorton at three dfferent locatons but t would not have so much effect on the entre desgn and the stablty of the offshore work barge. It s not a major threat to the safety of the vessel, personnel and equpment. 6 5.5 4.5.5 4 6 Draft (eters) 4 5 Draft (eters) Fg. 6: Dsplacement versus draft Fg. 8: Center of gravty versus draft From Fg. 7, the draft versus (dstance between the centre of buoyancy and the metacenter and the draft or smply represented at the metacentrc radus and the draft), ths shows that he draft s nversely proportonal to the metacentrc radus. hs suggests that as the draft s ncreasng the metacentrc radus s reducng. At draft 5m the metacentrc radus s less than. hs s a correct representaton n shp desgn. Fgure 9 s representaton of a graph of draft aganst the moment to change trm by.cm. hs s the value of the moment coursed by longtudnal shftng of a mass on a shp, whch nvolves the trm of cm, when a shp s mmersed up to the water lne. he graph shows that draft s proportonal to moment to change trm by cm. hs also s strategc n the desgn of shps. 5 5 5 5 4 6 Draft (eters) Fg. s a representaton of the dstance from keel to the metacenter. hs shows that the draft vares nversely to the dstance between the keel and the metacenter, whch s also a good representaton n general, shp desgn. 5. CONCUSION AND RECOENDAION From the desgn of the 5 tonnes work barge wth a deck crane, the stablty analyss of the vessel when the crane s at workng gves a representaton that at certan loadng, the vessel becomes unstable. Every necessary care has to be made not to carry such load at these stpulated locatons. hs s n order to make the vessel safe for the personnel. Fg. 7: etacentrc radus versus draft ISSN: 49-444 IJE Publcatons U. All rghts reserved. 856
(eters) C (eters) Internatonal Journal of Engneerng and echnology (IJE) Volume No. 9, September, 64 6 6 58 56 54 5 5 48 46 44 4 5 5 5 5 REFERENCES 4 6 Draft (eters) Fg. 9: oment per cm trm versus draft 4 5 Draft (eters) Fg. : etacentrc heght versus draft [] Ekwere I. W. (4) Desgn of 5 tonnes Self-Propelled arge. ech arne Engneerng Project, Faculty of Engneerng, Rvers State Unversty of Scence and echnology, Port Harcourt, Ngera. [] Intershp td. (996) Work arge Venture Desgn of Work arge (Onlne Seral) Avalable: Http/ / www.arge.com/venowork.htm (4, ay, 4). [] Robert,. Ed (98) Shp Desgn and Constructon. he Socety of Naval Archtect and arne Engneerng. New York Cty. [4] Drectory of artme NZ Dstrct Offces (6), arge Stablty Gudelnes, eadng Safety, Securty and Envronmental Protecton, Copyrght artme New Zealand, ISN -478-889-, www.martmenz.govt.nz [5] Ntonye, S. (996) Desgn of Power Plant of a tug oat, Fnal Year arne Engneerng Project, Engneerng Project, Faculty of Engneerng, Rvers State Unversty of Scence and echnology, Port Harcourt, Ngera. [6] Derrett, D. R. (999), Shp Stablty for asters and ates, Revsed by Dr C.., Reed Educatonal and Professonal Publshng td arrass, Oford Auckland oston Johannesburg elbourne New Delh. [7] Intershp td. () Offshore Supply Work Shp W 88 Desgn of Supply Work Shp (Onlne Seral) 4. Avalable: Http// www.arge.com/wb88.htm (4, ay, 4). [8] Ephram.E and Douglas, I. E. (99) echncal Report on Analyss and Desgn of Support System for Weatherford Gulf master G 5F Crane on the Ann- Rg. [9] Vncent, S.. And Grenadnes () Offshore Work- arge W 97. Desgn Of Work arge (Onlne Seral) Avalable Http:// www.arges.comwb97.html (4, Feb.). [] Edward, V.. Ed (988) Prncple of Naval Archtecture Second Revson: Stablty and Strength. Volume I. he Socety of Naval Archtecture and arne Engneers. New Jersey. []loyd s Regster, (997) Classfcaton of Shp Rules and Regulatons Part : Shp Structure, ondon. ISSN: 49-444 IJE Publcatons U. All rghts reserved. 857