STILL WATER BENDING MOMENT   Home     Menu     

Tim Lovett April 2004. Original Excel calculation by Jim King 2004

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STILL WATER BENDING MOMENT

Uneven Loading

If all the cargo was stored in the middle of the ship, the hull would experience bending (sagging) even without waves (still water). For this reason, the loading and unloading of a cargo ship must be carefully monitored to ensure the loads are within safe limits. In the case of Noah's Ark, the cargo is not very dense, (e.g. iron ore), so uneven loading is not much of a problem. The water and food storage would be the heaviest loads on the ark, and it would be prudent to distribute this cargo in sealed storage areas throughout each level. This saves handling and makes it easier to control vermin, with the added benefit of a controlled static loading as food is consumed during the voyage. 

 

Uneven Buoyancy

The ideal loading situation is when the cargo matches the buoyancy forces of the hull along its entire length. This can be difficult when the hull is a streamlined shape. Noah's Ark was probably not like this, so buoyancy is expected to be fairly constant throughout the length of the vessel.  

 

Still Water Bending Moment Conclusions

The following calculations (Jim King) indicate static loading is negligible compared to the wave bending moment. The highest static moment (2250 tf.m) does not occur near the center where the wave bending moment is maximum, but lower values of 1800 to 1900 tf.m. These are  calculated at station 9 should be added to the wave bending moment. 

Static Bending Moment = 1873 / 66750 = 2.8% of wave bending moment.

Hence the static bending moment adds only 3% to the wave bending moment in the worst case. However, since sagging dominates wave bending (ABS), the hogging effect of the static loading actually reduces the total bending moment slightly. The static loading acts to equalize the ABS wave loading.        

 

Summary

Maximum Bending Moments.

Type

Hogging (tf.m) Sagging (tf.m)
ABS Wave BM 67 009 - 65 071
Static BM 1 907 1 770
Net BM 66 979 -65 238

So in this arrangement, static bending moment is negligible.

 


CALCULATIONS

Estimated Ark Loading. For more details see Cargo

Hull 5333 tf
Water 2000 tf
Dry Food (grain) 2400 tf
Dry Food (Hay) 600 tf
Enclosures 4000 tf
Ramps 200 tf
Passages 200 tf
Animals 400 tf
Weight 15133 tf

Loads were estimated for 20 stations along the length of the Ark. This approximation assumes a more open area at bow and stern, where the structure is less critical. At this early design stage, this is assumed to be the best place to put access ramps, ventilation shafts, pumps, winches etc. Another advantage is that the ride is more comfortable amidships, so this is where the animals would be best located. 

Shear and Net Bending Moments 
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 6.86 680.985 266.65   240 60   50 10   626.65 -54.335 -372.738 8133.936 -8376.09 7761.198 -8748.83
2 13.72 765.0572 266.65   240 60   50 10   626.65 -138.407 -1322.21 16267.87 -16752.2 14945.66 -18074.4
3 20.58 755.7159 266.65   240 60 250   10 25 851.65 95.93414 -664.103 24401.81 -25128.3 23737.71 -25792.4
4 27.44 756.7538 266.65   240 60 250   10 25 851.65 94.89621 -13.1155 32535.75 -33504.4 32522.63 -33517.5
5 34.30 756.6385 266.65 200 240 60 250   10 25 1051.65 295.0115 2010.664 40669.68 -41880.5 42680.35 -39869.8
6 41.16 756.6513 266.65 200     250   10 25 751.65 -5.00128 1976.355 48803.62 -50256.6 50779.97 -48280.2
7 48.02 756.6499 266.65 200     250   10 25 751.65 -4.99986 1942.056 56937.55 -58632.6 58879.61 -56690.6
8 54.88 756.65 266.65 200     250   10 25 751.65 -5.00002 1907.756 65071.49 -67008.7 66979.25 -65101
9 61.74 756.65 266.65 200     250   10 25 751.65 -5 1873.456 65071.49 -67008.7 66944.95 -65135.3
10 68.60 756.65 266.65 200     250   10 25 751.65 -5 1839.156 65071.49 -67008.7 66910.65 -65169.6
11 75.46 756.65 266.65 200     250   10 25 751.65 -5 1804.856 65071.49 -67008.7 66876.35 -65203.9
12 82.32 756.65 266.65 200     250   10 25 751.65 -5 1770.556 65071.49 -67008.7 66842.05 -65238.2
13 89.18 756.65 266.65 200     250   10 25 751.65 -5 1736.256 56937.55 -58632.6 58673.81 -56896.4
14 96.04 756.65 266.65 200     250   10 25 751.65 -5 1701.956 48803.62 -50256.6 50505.57 -48554.6
15 102.90 756.65 266.65       250   10 25 551.65 -205 295.6557 40669.68 -41880.5 40965.34 -41584.8
16 109.76 756.65 266.65   240 60 250   10 25 851.65 95 947.3557 32535.75 -33504.4 33483.1 -32557
17 116.62 756.65 266.65   240 60 250   10 25 851.65 95 1599.056 24401.81 -25128.3 26000.86 -23529.2
18 123.48 756.65 266.65   240 60 250   10 25 851.65 95 2250.756 16267.87 -16752.2 18518.63 -14501.4
19 130.34 756.65 266.65   240 60   50 10   626.65 -130 1358.956 8133.936 -8376.09 9492.892 -7017.14
20 137.20 680.985 266.65   240 60   50 10   626.65 -54.335 986.2176 0 0 986.2176 986.2176
Tot   14989.24 5333 2000 2400 600 4000 200 200 400 15133 -143.764          

Data: Jim King 2004