# 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,

And, Depth, D = 10 m

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

Thickness of bottom and side plate, tB = tS = 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