25-Nav-A4 Ship Structure and Strength of Ships · May 2013
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — May 2013 — 98-Nav-A4 Ship Structure and Strength of Ships. Three-hour, closed-book exam (no notes permitted); Casio/Sharp non-programmable calculator and simple drawing equipment allowed. Format: five compulsory questions, marks indicated per sub-part, totalling 100; some formulae (fixed-end loads, beam deflection/slope tables, 2D beam-element stiffness) are supplied at the end of the exam and are used directly below. All five are solved in full.
Reference texts: Hughes, O.F. & Paik, J.K., Ship Structural Analysis and Design (2nd ed., SNAME, 2010) — hull-girder strength, panel/plate structure, section properties and shear flow in thin-walled hull sections; Hibbeler, R.C., Mechanics of Materials (10th ed., Pearson) — beam bending/deflection, stress transformation and Mohr's circle; Muckle, W., Muckle's Naval Architecture (2nd ed., Butterworths) — structural terminology and conventions; IACS Common Structural Rules / classification-society rules — steel grades, structural detail classification and fatigue design (S–N curves).
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
Each element of a ship's structure is sized against the loads and failure modes that are locally dominant, not against every load the vessel ever sees; the table below states the two or three that actually govern design for each item.
| Element | Governing loads (≤3) | Governing failure mechanisms (≤3) |
|---|---|---|
| i. Hull girder, oil tanker | Still-water + wave-induced longitudinal bending (hogging/sagging); shear from cargo/ballast loading pattern; thermal/tank-pressure loads | Ultimate longitudinal (hull-girder) collapse via buckling of deck/bottom panels; fatigue cracking at hatch corners and longitudinal stiffener terminations; brittle fracture at low temperature |
| ii. Transverse frame, bow, container ship | Bow-flare slamming / green-water impact; local hydrostatic and hydrodynamic panel pressure; panting (in–out breathing of the bow plating) | Local plastic yielding/buckling of the frame under slam impact; fatigue at frame–bracket connections; panting-induced fracture of plating/frame welds |
| iii. Bottom plating, warship | Hydrostatic pressure; bottom slamming at speed in a seaway; underwater-explosion (UNDEX) shock loading | Plate yielding/buckling under pressure; shock-induced plate rupture/tearing; fatigue from repeated slam cycles |
| iv. Propeller shaft | Driving torque; bending from propeller overhang weight and hydrodynamic thrust eccentricity; cyclic (rotating) bending as the shaft turns | Torsional fatigue failure; rotating-bending fatigue (classic "beach-mark" shaft failure); wear/fretting corrosion at bearings and seals |
| v. Fore deck | Green-water/wave-impact loading; longitudinal hull-girder bending stress (deck is an extreme fibre); deck cargo/equipment loads | Compressive buckling of deck plating/stiffeners under hogging; fatigue cracking at hatch-corner and deck-fitting details; local denting from green water |
| vi. Hatch cover, bulk carrier | Green-sea wave-impact pressure on the cover; sea pressure when the cover is submerged in heavy weather; cargo/dynamic loads if cargo is stowed on the cover | Collapse/buckling of the cover panel under wave impact (the documented bulk-carrier loss mechanism); corrosion-driven thickness loss leading to overload failure; failure of cleats/securing allowing progressive flooding |
i. Collision bulkhead. A watertight transverse bulkhead located a specified distance aft of the forward perpendicular (per SOLAS/class rules), required to extend to the freeboard/bulkhead deck, whose purpose is to limit the extent of flooding if the vessel suffers a bow collision.
ii. Long plate theory. The simplified bending theory applied to a rectangular plate panel whose length is much greater than its width (aspect ratio a/b large): the panel bends essentially in cylindrical (single-curvature) bending across the short span, so it can be analysed as a unit-width beam strip with plate bending stiffness $D = Et^3/[12(1-\nu^2)]$ in place of ordinary beam $EI$, rather than by full two-way (thin-plate) theory.
iii. Grade A steel. The basic (mild) ordinary-strength hull structural steel grade defined by classification-society/IACS rules, with a specified minimum yield strength of about 235 MPa and a Charpy V-notch impact-toughness requirement at a stated (relatively mild) test temperature; used for ordinary hull structure not exposed to especially low service temperatures or high stress concentration.
iv. Double bottom girder. A longitudinal (centre or side) girder within the double-bottom structure, spanning between floors and running the length of the double bottom between the inner and outer bottom plating; it provides longitudinal strength/rigidity to the double bottom and subdivides it into tanks.
v. Holland profile. A rolled steel "bulb flat" stiffener section — an angle/flat-bar section with a rounded bulb formed at the tip of the flange instead of a sharp edge — widely used for ship secondary stiffeners because the bulb improves local buckling/torsional stability without the fabrication cost of a separate flange plate.
vi. IACS. The International Association of Classification Societies, the umbrella body of the world's major ship classification societies (ABS, DNV, LR, ClassNK, etc.), which develops Unified Requirements (URs) and Common Structural Rules that set common minimum structural and safety standards across its member societies.
A bracket is a triangular (or gusset-shaped) plate that ties two structural members meeting at an angle — e.g. a frame to a deck beam, or a girder to a bulkhead — so that moment as well as shear can transfer across the joint. The plain (unstiffened) bracket is a flat triangular plate welded along its two straight edges to the members it connects, adequate for lightly loaded connections. Where the bracket must carry more load without buckling along its free (hypotenuse) edge, a flanged bracket is used: the free edge is turned up (or a face-flat welded on) to form a stiffening flange, exactly as sketched below. A tripping bracket is a smaller bracket fitted specifically to prevent local torsional "tripping" (rotation) of a flange or stiffener rather than to transfer primary load. Bracket toes are typically tapered (scalloped) rather than square-cut, since a square toe is a severe stress-concentration/fatigue-crack initiation point.
