Question

A box shaped vessel is 20 m long and 10 m wide. The weight of the vessel is uniformly distributed throughout the length and the draught is 2.5 m. The vessel contains ten evenly spaced double bottom tanks. each having a depth of 1 m. Draw the shear force diagrams

(a) With No. 1 and No. 10 tanks filled

(b) With No. 3 and No. 8 tanks filled

(c) With No. 5 and No. 6 tanks filled.

Which ballast condition is to be preferred from the strength point of view. (16)

Answer 1

Shear-force diagrams for a box-shaped vessel with double-bottom tanks.

A box-shaped vessel is 20 m long and 10 m wide. The weight of the vessel is uniformly distributed throughout the length and the draught is 2.5 m. The vessel contains ten evenly spaced double-bottom tanks, each having a depth of 1 m. Draw the shear-force diagrams for (a) No. 1 and No. 10 tanks filled, (b) No. 3 and No. 8 tanks filled, (c) No. 5 and No. 6 tanks filled. Which ballast condition is preferred from the strength point of view?

The vessel is a box 20 m long, 10 m wide, draught 2.5 m. Displacement = 20 x 10 x 2.5 x 1.025 = 512.5 t. The weight is uniformly distributed (the light ship), and the ballast tanks add weight at their positions. Each tank is 2 m long (20/10), 10 m wide, 1 m deep, so each holds 2 x 10 x 1 x 1.025 = 20.5 t of water when full.

The buoyancy is uniform at 512.5/20 = 25.625 t/m. The light weight is uniform at (512.5 - ballast)/20. When tanks are filled, the weight in those sections increases.

Part (a)

No. 1 and No. 10 tanks filled: the ballast is at the two ends (0-2 m and 18-20 m). The weight is increased at the ends, so the ends are heavier than the middle, producing a hogging condition (the ends sag, the middle is buoyant). The shear force diagram shows a positive shear at the ends building up, reaching a maximum near the quarter points, and the bending moment is hogging (positive) with a maximum at midships.

Part (b)

No. 3 and No. 8 tanks filled: the ballast is at 4-6 m and 14-16 m, i.e. near the quarter points. This produces a more even distribution, with the weight concentrated near the quarters. The shear force diagram shows the shear building up and the bending moment is smaller than in (a).

Part (c)

No. 5 and No. 6 tanks filled: the ballast is at 8-10 m and 10-12 m, i.e. amidships. The weight is concentrated amidships, producing a sagging condition (the middle is heavier, the ends are buoyant). The shear force diagram shows the shear building up and the bending moment is sagging (negative) with a maximum at midships.

Preferred condition: from the strength point of view, the condition that produces the smallest bending moment is preferred. The condition with the ballast near the quarter points (No. 3 and No. 8) produces the smallest bending moment, because the weight is distributed to reduce the difference between the weight and buoyancy distributions. The end-filling (No. 1 and No. 10) produces a large hogging moment, and the midship-filling (No. 5 and No. 6) produces a large sagging moment. Hence the No. 3 and No. 8 condition is preferred.

✓ Verified Model Answer (Text Solution)

No. 3 and No. 8 tanks filled: the ballast is at 4-6 m and 14-16 m, i.e. near the quarter points. This produces a more even distribution, with the weight concentrated near the quarters. The shear force diagram shows the shear building up and the bending moment is smaller than in (a).