## Description

***********IMPORTANT NOTE**: Please send us your system ID upon download. The key for the app will be sent subsequently upon receiving the system ID*******************

**Purpose **

Hull girder vertical and along-ship deflections at ship frame locations along the main deck of a Tanker-shaped hull (as measured from Aft Peak) are calculated.

- These deflections are of interest in the design of supports of deck-mounted structures as well as in the monitoring of hull deformation during ship loading and unloading operations.
- Global Results forward a general mid-body frame (“Frame 41”) are reported as well as relative results for 15 Frames forward of a user-selected Frame (ie “Aft Frame of interest”)
- Tanker sizes from Suezmax to VLCC are accommodated. Selected spot input and output checks are included to alert user to inconsistencies in the data.

**Instructions**

1. All user input is entered in Worksheet “Inputs” in the cells highlighted in blue ie

2. Supplementary nomenclature/notes/ input instructions are provided and highlighted in yellow ie

3. Required user input includes the hull section properties, frame definition data and bending moment data

(Standalone calculation apps for these are available seperately at www.thenavalarch.com)

4. For the relative deflections calculation, an “aft frame of interest” is selected to be the “zero reference”.

5. The workbook calculations are executed by keying in “Ctrl-r”. After execution, the active worksheet is “Outputs”)

**Limitations**

Validity of calculation is restricted to ships having hull girder where Euler beam theory is applicable

ie prismatic cross section over most of its length, Lpp/ D is greater than 5 and

planar cross-sections remain plane in bending

**References**

1. MacMillan et al., “Effective FPSO/FSO Hull Structural Design”, Offshore Technology Conference, 2001

2. ABS FPI Rules Part 5A, Ch 3, Sec 2 -5.2/5.3 (for formulae for vertical/horizontal WBM for FPSO’s)

3. ABS Steel Vessel Rules Part 3, Ch 2, Sec 1 – 3.5 (for formulae for vertical/horizontal WBM for Tankers)

4, ABS Steel Vessel Rules, Part 3, Ch 2, Sec 1 – 3.3 (guidance on SWBM calculation)

5. Ship-Specific Stability Booklet (for SWBM data).

**Version**

Version 0.0

Release Date 9-Dec-19

For feedbacks, write to [email protected].com OR [email protected]

**Theory Notes **

The method employed assumes that the deflected shape of the Hull Girder when subjected to bending moment(s) conforms to a circular arc.

Here the arc-length along the the hull girder neutral axis between the AP and LP is considered to be the length bewteen perpendiculars, Lpp.

This arc-length is considered to be invariant when the hull is subjected to bending.

(Note that the straight-line distance between AP and FP work points on the Hull neutral axis “decreases” when the hull girder is subjected to bending.)

The following calculation steps are executed:

STEP 1. Find the max vertical deflection based on dZ = ML^2/8EI (ie ML2/8EI), where M is taken as Msag and Mhog. Msag =SWBM+WBM,sag & Mhog = SWBM+WBM,hog

STEP 2. Find radius of curvature “R” geometrically using the equation : dZ = R-R cos(0.5L/R) and Associated angular arclength Theta

STEP 3: Locate the x-z coords at the centre of the arc (of the circle with radius Rna), ArcCen (where “x” is along-ship, “z” is vertical)

STEP 4: Determine the displaced location of each Frame WP (at Hull neutral axis) and plus the associated deflections dx & dz (along-ship and vertical respectively)

STEP 5: Develop Relative support displacement INPUT in way of Frames of interest for design of deck-mounted (eg topsides) structures

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