NATARAJAStresses in ships — shear force & bending moment
Learning outcomes & permitted supports
- Build the load diagram yourself: load per metre = buoyancy per metre − weight per metre, and read hog and sag straight off its shape
- Integrate once for shear force, once again for bending moment — and say why dM/dx = F puts the extreme moment at a zero of the shear
- State why both curves must close to zero at the free ends, and use that closure as the arithmetic's own check
- Show that the same total cargo makes wildly different stresses depending only on WHERE it sits
- Use the marine sign convention with a straight face: hogging positive, deck in tension
Supports in this lab: Calculator. Box-form hull floated exactly (drafts solved for weight AND centroid), then integrated piecewise-analytically; the golden suite checks ends ≈ 0, dM/dx = F, max|M| at a shear zero, and a 20 000-strip numeric cross-integration. Golden 878/878.
Glossary: shear force · bending moment · hogging & sagging · TPC
MV NATARAJA as a beam: box form 140 m × 20 m, light ship 4200 t spread evenly, five holds of 28 m. Load the holds and read the disagreement: load = buoyancy/m − weight/m, shear is its running total, the bending moment is the shear's. She floats first — the engine solves the drafts so buoyancy matches weight in total and in centroid — then the beam is integrated exactly, segment by segment.
| Condition | HOGGING |
|---|---|
| Max shear force | 720 t @ 112.0 m from aft |
| Max bending moment | 25200 t·m @ 70.0 m — at the shear's zero |
| Drafts A / F | 2.82 m / 2.82 m |
The beam's honesty: at the bow the running totals must return to zero (a free end carries nothing). This loading closes with |F(L)| = 5.1e-12 t and |M(L)| = 2.9e-10 t·m — machine-precision residue of the exact piecewise integration, not a rounding fudge.
Read the signs the sailor's way: cargo amidships presses her middle down — sagging, deck in compression; cargo at the ends leaves midship buoyancy unopposed — hogging, deck in tension (positive here, the marine convention). And watch the dashed thread: the extreme bending moment always stands where the shear force crosses zero, because M grows exactly as long as F keeps feeding it — dM/dx = F.