25-Nav-A4 Ship Structure and Strength of Ships · May 2016
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — May 2016 — 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: six compulsory questions, marks indicated per sub-part, totalling 100; some formulae (beam bending relations, section modulus, shear flow, deflection/slope tables) and a Normal (cumulative) distribution table are supplied at the end of the exam and are used directly below. All six 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–strain behaviour and fatigue basics; Muckle, W., Muckle’s Naval Architecture (2nd ed., Butterworths) — hydrostatics, Bonjean curves and structural terminology; Ang, A.H-S. & Tang, W.H., Probability Concepts in Engineering (2nd ed., Wiley) — structural reliability, load/resistance margin; IACS Common Structural Rules — steel grades, fatigue design (S–N curves, Paris Law).
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 of these five items describes a distinct way a ship structure departs from the simple picture of a uniform elastic beam under pure bending, and each governs a different part of structural design.
i. Long plate theory. A simplified bending theory for a rectangular plate panel whose length is much greater than its width (aspect ratio a/b ≳ 2, e.g. plating between closely spaced transverse frames but widely spaced longitudinal girders). Because the panel is restrained against curvature along its long direction, it bends essentially in cylindrical (single-curvature) bending across the short span only, so it can be treated as a unit-width beam strip using plate bending stiffness $D=Et^3/[12(1-\nu^2)]$ in place of ordinary beam $EI$, avoiding a full two-way thin-plate solution.
ii. Sandwich panel. A structural panel built from two thin, stiff face skins (e.g. steel or FRP) bonded to a thick, light core (foam, balsa, or a honeycomb) that carries the transverse shear and keeps the faces apart. Because bending stiffness grows with the cube of the separation distance, a sandwich panel achieves a high bending stiffness-to-weight ratio compared with a solid plate of the same weight — used in composite ship superstructures, deckhouses and some lightweight bulkheads.
iii. Warpage in open sections. When a thin-walled open section (channel, angle, T, I with unequal flanges) is twisted, plane cross-sections do not remain plane — they distort out of their original plane, an effect called warping. Because an open section has very low torsional (St. Venant) stiffness, most of its resistance to twist actually comes from resisting this warping (bending of the flanges in opposite senses), which is why open sections are so much weaker in torsion than closed (box) sections of the same wall thickness and perimeter.
iv. Main deck shear lag. In an idealized hull-girder bending calculation, the full width of the deck plating is assumed to act as an effective flange, carrying uniform longitudinal bending stress across its breadth. In reality, deck plating far from a supporting longitudinal (e.g. mid-way between hatch coamings) picks up stress more slowly than plating directly over a stiffener, because the shear strain needed to transfer stress inward lags behind the bending curvature — the actual stress distribution is peaked over the longitudinals and diminished between them, an effect most pronounced across wide hatch openings.
v. Elastic–perfectly plastic. An idealized material stress–strain model in which the material behaves linearly elastic ($\sigma=E\varepsilon$) up to the yield stress $\sigma_y$, after which stress remains exactly constant at $\sigma_y$ for any further strain (no strain hardening) — i.e. an infinite plastic strain is permitted at constant stress. It is the standard idealization used in plastic collapse/limit analysis of steel structures (e.g. computing the plastic section modulus in Q3) because it makes the stress distribution at full plastification simply "$\sigma_y$ everywhere in tension, $-\sigma_y$ everywhere in compression."
i. Hot spot stress. The structural stress at a critical fatigue-prone detail (e.g. a bracket toe or stiffener end), obtained by extrapolating the stress field measured or computed just outside the highly localized notch region back to the weld toe, so that it includes the effect of the detail's overall geometry (stress concentration due to the gross shape) but excludes the very local, weld-notch-tip stress peak. It is the quantity plotted against the hot-spot S–N curve in fatigue design.
ii. Hogging. The hull-girder bending condition in which the ship curves upward in the middle relative to the ends — physically produced when the net upward (buoyancy − weight) load is concentrated amidships and net downward load is concentrated at the ends (e.g. riding a wave crest amidships, or a still-water condition with buoyant support concentrated amidships as in Q2b below). In hogging the deck is put into compression and the bottom hull into tension.
iii. Nil ductility temperature (NDT). The temperature, determined from a drop-weight test (ASTM E208), below which a steel specimen containing a small brittle crack-starter weld fractures in a fully brittle manner with essentially no ductile (shear-lip) fracture at all; it marks the lower bound of the ductile-to-brittle transition and is used to set minimum service-temperature limits and required Charpy V-notch toughness for hull steel grades.
iv. Lateral torsional buckling. An instability mode of a beam or stiffener bent about its strong (major) axis, in which — once the compression flange reaches a critical stress — the whole section suddenly deflects sideways (laterally) and twists simultaneously, rather than continuing to bend in-plane; it governs the design of slender, unbraced flanged stiffeners (e.g. deck longitudinals) where the compression flange is not continuously restrained against sideways movement.
v. Section modulus. The ratio $Z=I/c$ of a cross-section's second moment of area $I$ about its neutral axis to the distance $c$ from the neutral axis to the extreme fibre; it converts a bending moment directly to extreme-fibre bending stress via $\sigma=M/Z$, and is the quantity that classification-society longitudinal-strength rules directly specify a minimum value for (the "midship section modulus").
