A rectangular vessel is 15 m broad and 10 m deep and has deck plating 5 mm thick and sides and bottom 9 mm thick. It is subjected to a hogging bending moment of 65 MN-m. Determine the maximum tensile and compressive stresses.

 

Solution: 

Given,

Breadth, B = 15 m

And, Depth, D = 10 m

Thickness of deck plate, t_D = 5 mm = 0.005 m

Thickness of bottom and side plate, t_B = t_S = 9 mm = 0.009 m

 Let us assume the baseline to be the Neutral Axis. 

Item	Area (m2)	Lever (m)	Moment (m3)	Area x lever2 (m4)	Iabout own NA
Deck Plating (x1)	0.075	9.9975	0.75	7.496	1.5627 x 10-7
Side Plating (x2)	0.18	5.002	0.9	4.50	1.494
Bottom Plating (x1)	0..135	0.0045	0.00061	2.73 x 10-6	9.1125 10-7
	ΣA = 0.39		ΣM = 1.651	Σ=12	Σ=1.5

So, Distance of actual NA from assumed NA, `\overline y=\frac{1.651}{0.39}=4.23\;m`

So, centroid of deck from NA is, `y_1=(10-4.23-0.0025)=5.7675m`

Centroid of Keel from NA is, `y_2=4.23-0.0045=4.2255m`

`I_{O-O}=I_{own}+\sum_{Area\times Lever^2 } =1.5+12=13.5m^4` 

`I_{NA}=I_{O-O}-A\overline y^2=13.5-0.39\times\left(4.23\right)^2=6.52m^4`

Applied Hogging moment, M = 65 MN-m

So, Stress at deck = `\frac{My_1}{I_{NA}}=\frac{65\times5.7675}{6.52}=57.498MPa` In tension 

So, Stress at bottom = `\frac{My_2}{I_{NA}}=\frac{65\times4.2255}{6.52}=42.12MPa` in Compression