1. Eng. 6002 Ship Structures 1 Hull Girder Response Analysis
Lecture 3: Estimation of weight distribution and still water bending moment

2. Overview
A method for determining the distribution of buoyant forces was described in the previous lecture.
Today we will look at a method for estimating the distribution of weight along the ship.
We will also discuss still water bending moments

3. Estimation of Weight Distribution
For ships with parallel middle body (cargo ships)
If the weight distribution is unknown and we need to estimate the distribution, the Prohaska method can be used
The weight distribution is a trapezoid on top of a uniform distribution

4. Estimation of Weight Distribution cont.
The weights are distributed as shown, with:

5. Estimation of Weight Distribution cont.
Note that since a and b average to we can say:

6. Estimation of Weight Distribution cont.
To move the lcg, the fore and aft ends of the load diagram must be adjusted by equal and opposite amounts

7. Longitudinal Strength of Ships: Murray’s Method for SWBM
Although computer methods have emerged as a practical way of calculating the still water bending moment, it makes sense to discuss Murray’s Method for hand calculations
Based on the idea that forces and moments in a ship are self balancing (no net forces transferred to world)

8. Longitudinal Strength of Ships: Murray’s Method for SWBM
He proposed that any set of weight and buoyancy forces are in balance

9. Longitudinal Strength of Ships: Murray’s Method for SWBM
Furthermore, for any cut at x, the moment at the cut can be determined by:

10. Longitudinal Strength of Ships: Murray’s Method for SWBM
Applying this idea to a ship

11. Longitudinal Strength of Ships: Murray’s Method for SWBM
The bending moment at amidships is:
The estimate of max bending moment can be improved by averaging these

12. Longitudinal Strength of Ships: Murray’s Method for SWBM
The bending moment at amidships is:
We can simplify the buoyancy part by:

13. Longitudinal Strength of Ships: Murray’s Method for SWBM
Murray suggested a set of values for the average moment arm, as a function of ship length,CB, and the ratio of draft to length

14. Example using Murray’s Method
Tanker with L = 278m, B=37m, CB=0.8

15. Example using Murray’s Method
To find BMB we need the draft
So T/L = 16.68/278 = 0.06

16. Example using Murray’s Method
Murray’s table gives a=0.179 and b=0.063
And the buoyancy bending moment is

17. Example using Murray’s Method
The still water bending moment is then
Assuming the wave bending moments are: WBMsag= t-m and WBMhog= t-m

18. Example using Murray’s Method
The total bending moment is