Upon starting the program, the following screen appears (make sure the macro security is set to medium to allow macros to be run).

Transcription

1 CCCP user mnul Strt of project Upon strting the progrm, the following screen ppers (mke sure the mcro security is set to medium to llow mcros to be run). (1.1) Figure 1: strting screen In figure 1 some of the terminology s used in the progrm is explined. The offset is defined s the horizontl distnce between the two points the ctenry shpe is to form between. Sgging is defined s the tolernce for the Ctenry to run below the preset depth. In other words, the lowest point of the Ctenry is llowed to be locted between the two end points. The progrm is strted by pressing the strt-button, (1.1). Select output After pressing strt, the following input screen ppers. (.1) (.) Figure : clcultion method 1

2 A project nme cn be supplied in the textbox. Excel will utomticlly generte worksheet nmed s the project nme supplied here, followed by the number of the worksheet tht is creted. An output vrible hs to be selected here. The progrm either clcultes the required tension for given nchor line length (Required Tension,.1) or the ctenry shpe t given tension (Ctenry Shpe,.). Input prmeters (3.1) (3.) (3.3) (4.1) (4.) (4.3) (3.4) (4.4) (3.5) Figure 3: input prmeters I Figure 4: input prmeters II After choosing which clcultion method is required, one of the two screens s depicted bove will show. These screens re plced on top of the output sheet. These screens show the input vribles to be entered. Figure 3 represents the input screen for the clcultion of the required tension, where figure 4 represents the ctenry shpe clcultion. The two screens only differ in tht one sks for the nchor line length (3.) while the other screen sks for the lterl force (4.4). A short overview of the other input prmeters is given below: - Wter Depth (3.1) The wter depth cn be clculted here. A depth lrger then 0 needs to be entered. To pproximte ship to quyside nchoring, or ship to ship nchoring from two points on the sme height, wter depth of 0.1 cn be selected where the llow sgging box needs to be ticked. - Anchor Line Type (3.) As given in figure 3 number of predetermined nchor line types re included in the progrm. Depending upon the line type chosen, other input vribles cn be entered, picked from list or will be clculted by the progrm. Should n nchor line type be required tht is not present in the list, user defined option is included s well. - Anchor Line Dimeter (4.1) Depending on the nchor line type tht is selected dimeter cn be entered or picked from drop-down box.

3 - Anchor Line Density (4.) For the predetermined nchor line types density is given which cnnot be ltered. For the user-defined option density hs to be supplied. - Ambient Density (4.3) The density of the medium (wter/ir) the nchor line is in cn be entered here. - Anchor Line Mss The nchor line mss is utomticlly displyed in mss per length. - Horizontl Offset (3.4) The horizontl offset is the horizontl distnce between two points in between which the Ctenry should be formed. If the horizontl offset is not set, the progrm will generte Ctenry tht ends horizontlly t the defined depth. - Allow Sgging (3.5) If you tick this box, the nchor line is llowed to sg. To evlute your project, press the clculte button. If you wnt to strt new project, press the new project button, if you press the bck button to chieve this, your excel results of your lst run will NOT be sved. 3

4 Output dt As mentioned before, the progrm genertes worksheet for ech project. Such worksheet provides ll the dt for nd from the clcultion, both numericlly nd grphiclly. The screen with numericl dt is given below: Figure 5: numericl output The input prmeters re given in the upper prt. The relevnt clcultion results re printed in the middle prt. Should the resulting stress be lrger thn the men breking lod (MBL) of the nchor line, (only for ) wrning is given s well. In the bottom prt the plot dt for the grphicl representtion is stored. 4

5 The ctenry shpe is represented in grph of which n exmple is given in figure 6. Figure 6: grphicl output Specil ttention should be pid to the xes s they re not on the sme scle. In some cses it therefore cn look like the nchor line does not stisfy ctenry shpe. One should therefore lwys check the scle of both xes. Constrints Within the progrm, some ssumptions nd simplifictions hve been mde. These result in list of constrints for the progrm which should be tken into ccount when performing clcultions. The following constrints re vlid: - The nchor line hs no bending stiffness. - No strin in the nchor line - The nchor line dimeter is constnt over the nchor line length - Homogeneous distribution of tension over the dimeter of the nchor line - When steel chin is selected s nchor line type, the dimeter entered represents the dimeter of the shckle, not the dimeter of the whole chin. - The wter depth hs to be greter thn zero. This lso counts for freehnging cble in ir. A mooring with zero verticl offset cn be pproximted by entering 0.1 wter depth. - Anchor lines re not soked. - If the input results in clcultion of more then one million steps (for instnce with very steep sg), the progrm will terminte to void Excel to crsh. 5

6 Underlying theory Introduction If flexible chin or rope is loosely hung between two fixed points, it hngs in curve tht looks little like prbol, but in fct is not quite prbol; it is curve clled ctenry, which is word derived from the Ltin cten, chin. The word flexible points out tht the rope or chin doesn t hve ny stiffness nd thus tht the direction of the resulting force cting on ny point of the chin is in the direction of the chin s orienttion t tht point. P ψ T ψ Angle between cble nd horizontl t P μ Density per length s Length of Cble T Cble Tension T0 g Horizontl Tension t A Grvity T 0 A μg s Figure 7: ctenry The Intrinsic Eqution to the Ctenry The intrinsic eqution describes the Ctenry long the pth of the Ctenry s. We consider the equilibrium of the portion AP of the chin, A being the lowest point of the chin. See figure 1. It is in equilibrium under the ction of three forces: The horizontl tension T 0 t A; the tension T t P, which mkes n ngle ψ with the horizontl; nd the weight of the portion AP. If the mss per unit length of the chin is μ nd the length of the portion AP is s, the weight is μgs. From equilibrium we cn simply see tht: > T0 Tcosψ > μsg T sinψ (1) With Pythgors nd some bsic geometry we cn derive the next two expressions: + b c > ( μsg) + T T 0 () 6

7 sin x tn x cos x μsg > tnψ T 0 (3) Introduce constnt hving the dimensions of length. With nd equtions () nd (3) we cn come to the intrinsic eqution (i.e. the s, ψ eqution). T0 μg μgs tnψ T0 s > tnψ μgs > T0 μg s ( μsg) + T0 T > s ( μg) + ( μg) T > T μg s + (4) Eqution of the Ctenry in Rectngulr Coordintes To get n expression for the Ctenry in rectngulr coordintes, we need to eliminte s from the eqution. Using equtions () nd (3) we cn come to n expression for the derivtive for ds/dx in terms of dx nd dy. dy s y ' tnψ dx d s d dy dx dx dx ds d y > dx dx (5) ds dy dx 7

8 The Pythgoren reltion between the intrinsic nd rectngulr coordintes for the Ctenry cn now be derived nd is the second expression for the derivtive for ds/dx in terms of dx nd dy. ds dy + dx ds dy + dx dx ( ) 1 ds dy d y ( ) 1 > + dx dx dx (6) Now tht we hve two equtions (5) & (6) for ds/dx in terms of dx nd dy, we cn eliminte s from the eqution. Doing this gives second order differentil eqution with boundry conditions. Solving this eqution (defining y s function of x, so tht it stisfies this eqution nd the condition y(0) 0) gives the Ctenry eqution in rectngulr coordintes. 1 y'' ( y') + 1 Boundry Condition: y '(0) 0 x y ' sinh x y cosh + C Boundry Condition: y(0) 0 x T0 > y cosh, μg (7) Note tht the eqution cn lso esily be rewritten in terms of x nd s: s dy dx dy x sinh( ) dx x T0 > s sinh( ), μg (8) 8