Ship Structures
Ship Structures deals with the hull girder as a beam, local panel strength, buckling and fatigue. GATE NM tests whether you can compute bending stresses from a section modulus and recognise the load cases that govern midship scantlings.
Core rules
- Still-water bending moment (SWBM) comes from weight and buoyancy distribution; wave-induced bending moment (VWBM) is added for the design case.
- Hull girder bending stress σ = M/Z, where Z = I/y is the section modulus and y is the distance from the neutral axis.
- For a symmetrical box girder with two flange areas A at ±d from the neutral axis, I ≈ 2Ad² and Z = I/d = 2Ad.
- Shear stress in the side shell is τ = QS/(It); maximum shear occurs near the neutral axis.
- Buckling depends on plate slenderness, boundary conditions and compressive stress; effective width accounts for post-buckling redistribution.
- Fatigue is driven by stress range and number of cycles; weld details and hot-spot stress matter more than static yield alone.
Worked example
A simplified box girder has deck and bottom flange areas of 2 m² each, at ±5 m from the neutral axis. I ≈ 2 × 2 × 5² = 100 m⁴. Z = I/c = 100/5 = 20 m³. For a design bending moment of 200 MN·m, deck stress σ = M/Z = 200/20 = 10 MPa. The calculation is linear: doubling the moment doubles the stress; moving the flange farther from the neutral axis increases I with d² and reduces stress.
Traps
Using the full depth instead of the distance to the extreme fibre overestimates Z and underestimates stress. Do not add still-water and wave moments without checking sign and phase; hogging and sagging reverse stress. A neutral axis assumed at mid-depth is invalid when deck and bottom areas differ. Buckling can occur below yield, so a stress-only check is incomplete. Fatigue cracks initiate at weld toes, not in uniform parent plate.