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GATE Marine Engineering Applied Mechanics and Structures Flashcards
53 question-and-answer cards covering Applied Mechanics and Structures as it is examined in GATE Marine Engineering. 24 of them are printed below, taken from across the deck — no signup, no paywall on the preview.
24 sample cards from the Applied Mechanics and Structures deck
Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.
For a solid rectangular beam, where is the transverse shear stress maximum and what is its value?
Maximum at the neutral axis: $\tau_{max} = \dfrac{3}{2}\,\dfrac{V}{A} = 1.5\,\tau_{avg}$. It is zero at the top and bottom fibres.
State the torsion equation for a circular shaft.
$\dfrac{T}{J} = \dfrac{\tau}{r} = \dfrac{G\theta}{L}$, where $T$ is torque, $J$ the polar moment of area, $\tau$ shear stress at radius $r$, $G$ modulus of rigidity, $\theta$ angle of twist over length $L$.
Give the polar moment of area $J$ for solid and hollow circular shafts.
Solid: $J = \dfrac{\pi d^{4}}{32}$. Hollow: $J = \dfrac{\pi (d_o^{4} - d_i^{4})}{32}$.
Define the torsional stiffness of a shaft.
Torsional stiffness $k_t = \dfrac{T}{\theta} = \dfrac{GJ}{L}$ (torque required per unit angle of twist).
State Euler's formula for the critical buckling load of a column.
$P_{cr} = \dfrac{\pi^{2} EI}{L_e^{2}}$, where $L_e$ is the effective length and $I$ the least second moment of area.
Give the effective length $L_e$ for the four standard column end conditions.
Both ends pinned: $L_e = L$. Both ends fixed: $L_e = 0.5L$. One end fixed, one free: $L_e = 2L$. One end fixed, one pinned: $L_e \approx 0.7L$.
Define slenderness ratio and the validity limit of Euler's theory.
Slenderness ratio $\lambda = \dfrac{L_e}{k}$, where $k=\sqrt{I/A}$ is the radius of gyration. Euler's formula is valid only for long (slender) columns where the critical stress stays below the proportional limit; short columns fail by crushing.
State Castigliano's second theorem (energy method for deflection).
The partial derivative of total strain energy $U$ with respect to a load gives the displacement at that load in its direction: $\delta_i = \dfrac{\partial U}{\partial P_i}$, and $\theta_i = \dfrac{\partial U}{\partial M_i}$ for rotation.
Write expressions for strain energy stored in axial, bending, and torsional loading.
Axial: $U = \dfrac{P^{2}L}{2AE}$. Bending: $U = \displaystyle\int \dfrac{M^{2}}{2EI}\,dx$. Torsion: $U = \dfrac{T^{2}L}{2GJ}$.
Name the principal theories of elastic failure used in machine design.
Maximum principal stress (Rankine), maximum shear stress (Tresca/Guest), maximum principal strain (St. Venant), maximum strain energy (Haigh), and maximum distortion (shear strain) energy (von Mises–Hencky).
State the maximum shear stress (Tresca) failure criterion.
Failure occurs when the maximum shear stress reaches the shear yield value: $\dfrac{\sigma_1 - \sigma_3}{2} = \dfrac{\sigma_y}{2}$, i.e. $\sigma_1 - \sigma_3 = \sigma_y$. Best for ductile materials.
State the distortion energy (von Mises) failure criterion for plane stress.
Yielding begins when $\sigma_v = \sqrt{\sigma_1^{2} - \sigma_1\sigma_2 + \sigma_2^{2}} = \sigma_y$. It is the most accurate criterion for ductile materials.
Distinguish hardness, toughness, and a fatigue (endurance) test.
Hardness: resistance to indentation (Brinell, Vickers, Rockwell). Toughness: energy absorbed before fracture, often from an impact test (Izod/Charpy). Fatigue test: cyclic loading (e.g. rotating beam) to find the endurance limit/S–N curve.
Write the differential equation of free undamped single-degree-of-freedom vibration and its natural frequency.
$m\ddot{x} + kx = 0$, with natural frequency $\omega_n = \sqrt{\dfrac{k}{m}}$ (rad/s) and $f_n = \dfrac{1}{2\pi}\sqrt{\dfrac{k}{m}}$.
Define the damping ratio and classify systems as under-, critically, and over-damped.
$\zeta = \dfrac{c}{c_c} = \dfrac{c}{2\sqrt{km}}$. Under-damped: $\zeta<1$ (oscillatory decay); critically damped: $\zeta=1$ (fastest non-oscillatory return); over-damped: $\zeta>1$ (slow non-oscillatory).
Give the damped natural frequency in terms of $\omega_n$ and $\zeta$.
$\omega_d = \omega_n\sqrt{1-\zeta^{2}}$ (valid for under-damped systems, $\zeta<1$).
Define the logarithmic decrement and relate it to the damping ratio.
$\delta = \ln\dfrac{x_1}{x_2} = \dfrac{2\pi\zeta}{\sqrt{1-\zeta^{2}}}$; for small damping $\delta \approx 2\pi\zeta$.
What is resonance, and what governs the amplitude at resonance in forced vibration?
Resonance occurs when the forcing frequency equals the natural frequency ($\omega = \omega_n$), producing maximum amplitude. The peak amplitude is limited only by damping; the magnification factor at resonance is $\dfrac{1}{2\zeta}$.
How many natural frequencies and mode shapes does an $n$-DOF undamped system have?
It has $n$ natural frequencies and $n$ corresponding mode shapes (eigenvalues and eigenvectors of $[K]\{\phi\} = \omega^{2}[M]\{\phi\}$).
State Soderberg and Goodman criteria for design under fluctuating (dynamic) loads.
Soderberg: $\dfrac{\sigma_m}{\sigma_y} + \dfrac{\sigma_a}{\sigma_e} = \dfrac{1}{N}$. Goodman: $\dfrac{\sigma_m}{\sigma_u} + \dfrac{\sigma_a}{\sigma_e} = \dfrac{1}{N}$, where $\sigma_m,\sigma_a$ are mean and alternating stress, $\sigma_e$ endurance limit, $N$ factor of safety.
Write the ASME design equation for a shaft under combined bending and torsion.
Equivalent twisting moment $T_e = \sqrt{M^{2}+T^{2}}$ and equivalent bending moment $M_e = \tfrac{1}{2}\left(M + \sqrt{M^{2}+T^{2}}\right)$; diameter from $T_e = \dfrac{\pi}{16}\tau\,d^{3}$ or $M_e = \dfrac{\pi}{32}\sigma_b\,d^{3}$.
For a pair of meshing spur gears, give the velocity ratio and the law of gearing.
Velocity ratio $\dfrac{N_1}{N_2} = \dfrac{T_2}{T_1} = \dfrac{d_2}{d_1}$ (speeds inverse to teeth/diameters). Law of gearing: for constant velocity ratio the common normal at the point of contact must always pass through the fixed pitch point.
Compare rolling-contact and sliding-contact (journal) bearings.
Rolling (ball/roller) bearings: low starting and running friction, carry combined loads, need little lubricant, but are noisier and fail by fatigue. Sliding (journal) bearings: higher friction, quieter, better shock/vibration damping and high-speed capacity, and rely on a hydrodynamic oil film.
Compare bolted, riveted, and welded joints.
Bolted: non-permanent, allows disassembly, needs locking against loosening. Riveted: permanent, good for shear and fatigue (e.g. ships/structures), assembled hot or cold. Welded: permanent, strong and lightweight (no holes weakening the section), but introduces residual stresses and a heat-affected zone.
What this deck covers
The Applied Mechanics and Structures deck follows the GATE Marine Engineering Applied Mechanics and Structures syllabus — 4 chapters and 18 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 13.3 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 185 characters, which is long enough to carry the reasoning and short enough to say out loud.
A deck like this earns its keep on the second and third pass. Read the syllabus first so you know the shape of the subject, then use the cards to find the specific facts that have not stuck.
Applied Mechanics and Structures flashcards FAQ
How many Applied Mechanics and Structures flashcards are in this GATE Marine Engineering deck?
53 cards. This page previews 24 of them, sampled evenly across the deck so you can judge the difficulty before installing anything.
Are these GATE Marine Engineering flashcards free?
Yes. The preview here is free to read with no signup, and the full 53-card deck is free inside the Examius app.
What do the Applied Mechanics and Structures cards cover?
They follow the GATE Marine Engineering Applied Mechanics and Structures syllabus — 4 chapters and 18 topics — so the questions track what is actually examinable.
How should I use these flashcards?
Read the syllabus first so you know the shape of the subject, then drill the deck. Examius schedules each card with spaced repetition, so cards you keep missing come back sooner and ones you know drift further apart.