Advanced Machine Design

MEPP 436 is a new course, so only one previous paper exists (Feb 2025). That paper is your single most reliable guide to style and weighting. These notes cover every question type on it, plus the surrounding theory in case the examiner varies things. Instructor: Dr. Surendra Sujakhu.

Structure of the paper (from the 2025 exam)

Where the marks concentrate

Design = the application of creativity to planning the optimum solution of a given problem, and the communication of that plan to others.

1.1 The design process

Stages (iterate as needed):

Need → Problem definition → Synthesis → Analysis & optimisation → Evaluation → Presentation

Design considerations the engineer juggles: functionality, strength/stress, distortion/deflection, wear, corrosion, safety, reliability, manufacturability, cost, weight, life, noise, styling, environmental impact.

1.2 Standards and codes

Bodies to know: NBSM (Nepal), NBC 105:2020, BIS, AISI, ASME, ASTM, ASHRAE, SAE.

1.3 Design economics

• Cost is almost always the governing factor. Using standard sizes is the first principle of cost reduction.
• Close (tight) tolerances raise cost — extra processing, extra inspection, slower machines.
• Break-even analysis compares two production methods: below the break-even quantity the low-setup method wins; above it the high-rate method wins.

1.4 Design factor & factor of safety — a favourite MCQ

The design factor \(n_d\) is a margin applied to load or strength to cover uncertainty in material properties, loading and analysis:

\[ n_d=\frac{\text{loss-of-function parameter}}{\text{max-allowable parameter}}\qquad\Longrightarrow\qquad n=\frac{S}{\sigma}=\frac{\text{Strength}}{\text{Stress}} \]

• Stress & strength must be the same type, same units, same critical location.
• The factor of safety is the realised design factor after rounding up to standard sizes/components.

1.5 Reliability (introductory)

\[ R = 1 - p_f,\qquad p_f=\frac{\text{number of failures}}{\text{total instances}},\qquad 0\le R\le 1 \]

Series system (all must work): \(R=R_1\cdot R_2\cdots R_n\). E.g. bearings 0.95 & 0.98 → \(R=0.931\). (Full treatment in §9.)

1.6 Dimensions & tolerances

Choosing the material is one of the earliest and most important design decisions — usually made before dimensions are fixed. Properties come from specimen testing (standardised, e.g. ASTM) or, when risk is high, component testing under real service loads.

2.1 The tensile test (ASTM E8) & key properties

A load–elongation curve is converted to a stress–strain curve, giving: elastic limit / yield strength, elastic modulus \(E\) (Hooke's law), ultimate tensile strength (UTS), ductility (% elongation, % area reduction), tensile toughness, Poisson's ratio \(\nu\).

📄 From slides✏️ Clean redraw

Slide: Material Properties, p.5

ℹ︎ Slide vs redraw: the slide shows all four classes — (a) metal, (b) thermoplastic, (c) elastomer, (d) ceramic/glass/concrete. My redraw isolates just the two the exam contrasts (ductile metal vs brittle ceramic) so the "straight line → sudden fracture" point stands out. Same physics, fewer curves.

Slide: Material Properties, p.4 — full tensile stress–strain curve

2.2 Other mechanical tests

2.3 Heat treatment (effect on properties)

2.4 Material classes

2.5 Material-selection charts (Ashby charts)

An Ashby chart plots one property against another (e.g. Young's modulus vs density). Each material class occupies a "bubble." Add a guideline of constant performance (e.g. specific stiffness \(E/\rho=C\), or specific strength \(\sigma/\rho=C\)); materials in the top-left region are best for light-and-stiff / light-and-strong designs.

• Metals are heaviest; foams lightest; ceramics stiffest.
• Light-and-stiff bike frame: polymers too floppy, ceramics too brittle in tension → composites best, with Mg/Al/Ti competitive.
• Wood has surprisingly high specific stiffness/strength → used in construction.

Slide: Material Properties — Young's modulus vs density Ashby chart

3.1 Stress & strain as tensors

Stress = internal resistance per unit area developed against external load; strain = the resulting deformation. At a point, three mutually perpendicular planes fully describe the state of stress — the "stress cube."

📄 From slides✏️ Clean redraw

Slide: Stresses, Strains & Failure, p.14

ℹ︎ Slide vs redraw: the slide draws the element with the x-y-z axes and all nine \(\sigma/\tau\) face components; my redraw keeps only three normal stresses + one shear so the "6 independent components" idea reads at a glance.

Slide: Stresses, Strains & Failure, p.14

\[ \sigma_{ij}=\begin{bmatrix}\sigma_{xx}&\tau_{xy}&\tau_{xz}\\ \tau_{yx}&\sigma_{yy}&\tau_{yz}\\ \tau_{zx}&\tau_{zy}&\sigma_{zz}\end{bmatrix} \]

A symmetric 2nd-order tensor: 9 components, 6 independent (because \(\tau_{xy}=\tau_{yx}\), etc.).

3.2 Generalized Hooke's law (isotropic, linear elastic)

\[ \varepsilon_x=\frac{1}{E}\big[\sigma_x-\nu(\sigma_y+\sigma_z)\big]\quad(\text{cyclically for }\varepsilon_y,\varepsilon_z),\qquad \gamma_{xy}=\frac{\tau_{xy}}{G} \]

Lamé / tensor form: \(\;\sigma_{ij}=\lambda\,\varepsilon_{kk}\,\delta_{ij}+2\mu\,\varepsilon_{ij}\;\) (\(\lambda\) ↔ bulk resistance, \(\mu=G\) ↔ shear resistance). Anisotropic generalisation: \(\sigma_{ij}=C_{ijkl}\,\varepsilon_{kl}\).

3.3 Principal stresses, transformation & Mohr's circle

Principal planes carry no shear, only normal stress; those normal stresses are the principal stresses \(\sigma_1\ge\sigma_2\ge\sigma_3\).

\[ \sigma_{1,2}=\frac{\sigma_x+\sigma_y}{2}\pm\sqrt{\left(\frac{\sigma_x-\sigma_y}{2}\right)^2+\tau_{xy}^2}\;,\qquad \tau_{\max}=\sqrt{\left(\frac{\sigma_x-\sigma_y}{2}\right)^2+\tau_{xy}^2}=\frac{\sigma_1-\sigma_2}{2} \] \[ \tan 2\theta_p=\frac{2\tau_{xy}}{\sigma_x-\sigma_y} \]

📄 From slides✏️ Clean redraw

Slide: Stresses, Strains & Failure, p.23

ℹ︎ Slide vs redraw: the slide pairs the circle with the stressed element and shows the point-by-point construction (σ→right, τ→down); my redraw is a stripped-down single circle just to fix centre = σavg and radius = τmax in memory.

3.4 Bending & torsion (revision formulae)

\[ \text{Flexure: }\;\frac{M}{I}=\frac{\sigma_b}{y}=\frac{E}{\rho}\qquad\qquad \text{Torsion: }\;\frac{T}{J}=\frac{\tau}{\rho}=\frac{G\phi}{L} \]

3.5 Failure — the five classical theories

A part fails by fracture (brittle) or by onset of yielding (ductile). A failure theory predicts failure under combined stress by comparing it to a simple tension test.

\[ \sigma'=\sqrt{\tfrac12\big[(\sigma_1-\sigma_2)^2+(\sigma_2-\sigma_3)^2+(\sigma_3-\sigma_1)^2\big]}\;;\qquad \text{biaxial }(\sigma_3=0):\;\sigma'=\sqrt{\sigma_1^2-\sigma_1\sigma_2+\sigma_2^2} \]

📄 From slides✏️ Clean redraw

Slide: Stresses, Strains & Failure — failure-theory comparison

ℹ︎ Slide vs redraw: the slide overlays experimental yield data on the boundaries and often includes the max-principal-stress square too; my redraw shows only the hexagon-inside-ellipse relationship — the single fact you must be able to sketch.

Fracture mechanics studies the propagation of cracks. A crack is a sharp void that acts as a stress amplifier — cracks do not create stress, they intensify the far-field stress. The sharper the tip, the higher the local stress.

4.1 Why fracture mechanics? (the design shift)

Traditional design compares applied stress vs strength (2 parameters). Fracture mechanics adds a third: flaw size. The design is safe if stress + largest expected crack keeps \(Kwhich flaws are safe and which will propagate. It answers: what is the strength as a function of crack size? and what is the maximum tolerable crack size?

Slide: Introduction to Fracture Mechanics, p.4

4.2 Characteristics of a crack

• Connection to free surface: fully internal / internal-connected-to-surface / surface crack (surface cracks also risk oxidation & corrosion).
• Crack length — longer is more dangerous.
• Crack-tip radius — sharper is more dangerous (plasticity blunts tips in ductile metals).
• Crack orientation relative to loading.

4.3 Modes of loading — memorise cold

📄 From slides✏️ Clean redraw

Slide: Introduction to Fracture Mechanics, p.16–18

ℹ︎ Slide vs redraw: the slide uses the standard 3-D block drawings (arrows on a solid bar with x-y-z axes); my redraw uses flat plates with coloured arrows so the direction of pull/shear is obvious. Both show the same I-opening / II-sliding / III-tearing motions.

4.4 Cohesive stress & why real strength is low

Cohesive stress \(\sigma_c\) = the theoretical stress needed to break atomic bonds and separate atomic planes (estimated from the interatomic force–displacement curve, approximated as half a sine wave):

\[ \sigma_c=\sqrt{\frac{E\,\gamma_s}{x_0}}\qquad(\gamma_s=\text{surface energy},\; x_0=\text{atomic spacing}) \]

Real materials fracture far below \(\sigma_c\) because flaws concentrate stress. For an elliptical crack (semi-axes \(a,b\), tip radius \(\rho=b^2/a\)):

\[ \sigma_{tip}\approx\sigma\!\left(1+\frac{2a}{b}\right)\approx 2\sigma\sqrt{\frac{a}{\rho}}\qquad(\text{sharp flaw, }b\ll a) \]

Setting \(\sigma_{tip}=\sigma_c\) with \(\rho\approx x_0\) gives the fracture stress \(\;\sigma_f\approx\sqrt{\dfrac{E\gamma_s}{4ax_0}}\) — orders of magnitude below \(\sigma_c\) because \(a\gg x_0\). A micron crack gives \(\sigma_f\approx0.01\,\sigma_c\), matching experiment.

LEFM applies to brittle behaviour — sharp cracks, little tip plasticity. For a crack to grow, both criteria must hold: the global energy criterion (Griffith) and the local stress criterion (Inglis).

5.1 Inglis (1913) — local, stress-based

Stress concentration at a hole/notch depends on the tip radius of curvature. Crack grows if the amplified tip stress reaches the theoretical fracture stress: \(\sigma_{max}=\sigma_A\ge\sigma_f\).

5.2 Griffith (1920) — global, energy-based

Inglis assumes energy is available; Griffith asks whether it is. Condition for growth: strain energy released ≥ surface energy of the new crack faces.

\[ \frac{dU_s}{da}\ge\frac{dU_\gamma}{da}\quad\text{with}\quad U_s=\frac{\pi a^2\sigma^2}{E},\quad U_\gamma=4\gamma_s a \] \[ \sigma_f=\sqrt{\frac{2E\gamma_s}{\pi a}}\;\;(\text{plane stress})\qquad \sigma_f=\sqrt{\frac{2E\gamma_s}{\pi a(1-\nu^2)}}\;\;(\text{plane strain}) \]

5.3 Stress Intensity Factor K — the central quantity

Williams (1952) showed the crack-tip stress field always has an inverse-square-root singularity, scaled by \(K\):

\[ \sigma_{ij}=\frac{K}{\sqrt{2\pi r}}\,f_{ij}(\theta)\qquad\Longrightarrow\qquad \boxed{K_I=Y\,\sigma\sqrt{\pi a}} \]

• \(a\) = half-length for a fully internal (central) crack; full length for an edge crack.
• \(Y\) = geometry / shape factor. Units of \(K\): MPa·√m.
• Insight: quadrupling crack length ≡ doubling stress — \(K\) captures the combined effect.

5.4 Irwin's fracture criterion & fracture toughness K_IC

Fracture occurs in Mode I when \(K_I\ge K_{IC}\). \(K_{IC}\) = fracture toughness, a material property (like \(\sigma_y\)), microstructure-sensitive, measured under plane-strain (thick specimen → conservative, lowest value).

\[ \boxed{a_c=\frac{1}{\pi}\left(\frac{K_{IC}}{Y\sigma}\right)^2}\quad\text{(critical crack length)} \]

5.5 Energy release rate G and the K–G relation

\(G=-\dfrac{d\Pi}{dA}\) = potential energy released per unit crack area (the "crack driving force"). Crack grows when \(G\ge G_c\).

\[ G=\frac{K_I^2}{E'}\quad\big(E'=E\text{ plane stress};\;E'=E/(1-\nu^2)\text{ plane strain}\big) \]

Mixed mode: \(G=\dfrac{K_I^2+K_{II}^2}{E'}+\dfrac{K_{III}^2}{2\mu}\). Compliance view (\(C=\Delta/P\)): \(G=\dfrac{P^2}{2}\dfrac{dC}{da}\). K is local; G is global; for linear elasticity they are uniquely related.

5.6 Crack-tip plasticity (beyond pure LEFM)

LEFM predicts infinite tip stress — impossible; plasticity intervenes. Two corrections:

• Irwin model: plastic-zone size \(r_y=\dfrac{1}{2\pi}\left(\dfrac{K_I}{\sigma_{ys}}\right)^2\) (plane stress); use effective crack length \(a+r_y\).
• Strip-yield (Dugdale–Barenblatt): a thin plastic strip \(\rho\) at each tip; total crack \(=2(a+\rho)\).

5.7 Summary of fracture criteria

Fatigue (ASTM): the progressive, localised, permanent structural change under fluctuating stress/strain that may end in cracks or complete fracture after enough cycles — even when the peak load is below yield or ultimate strength. Fatigue life = cycles to failure.

Fatigue gives no warning (little deflection), is sudden (brittle-like), and is only partly understood — so life is estimated by empirical methods.

6.1 The five-stage failure mechanism

1. Cyclic plastic deformation → dislocations pile at the surface, forming slip bands (persistent slip bands) and micro-roughness.
2. Micro-crack initiation along slip bands, grain boundaries, second-phase particles or inclusions.
3. Micro-crack coalescence into a macro-crack (spanning several grains); some arrest at interfaces.
4. Macro-crack propagation — now governed by \(\Delta K\) (LEFM); plotted as \(da/dN\) vs \(\Delta K\).
5. Final failure — remaining section can't carry the load; rapid fracture.

Slide: Introduction to Material Fatigue, p.7

Slide: Introduction to Material Fatigue, p.12

6.2 Fatigue loading parameters — know all of these

\[ \sigma_a=\frac{\sigma_{max}-\sigma_{min}}{2}\;(\text{amplitude})\qquad \sigma_m=\frac{\sigma_{max}+\sigma_{min}}{2}\;(\text{mean}) \] \[ \Delta\sigma=\sigma_{max}-\sigma_{min}\;(\text{range})\qquad R=\frac{\sigma_{min}}{\sigma_{max}}\;(\text{stress ratio})\qquad A=\frac{\sigma_a}{\sigma_m}\;(\text{amplitude ratio}) \]

Slide: Introduction to Material Fatigue, p.15

Slide: Introduction to Material Fatigue, p.5

6.3 HCF vs LCF — a guaranteed question

6.4 Factors affecting fatigue

Cyclic load state (amplitude, mean, sequence, biaxiality) · geometry / stress concentration (cracks start at notches) · surface quality (rough = stress raisers) · residual stress (compressive helps, tensile hurts) · microstructure (finer grains → longer life) · temperature · environment (corrosion fatigue).

6.5 Fatigue testing & the S-N curve

Rotating-beam (R.R. Moore) test: a specimen rotates under bending so each point cycles tension↔compression sinusoidally; \(\sigma_{max}\approx5.09\,FL/d^3\). Data plotted as stress \(S\) vs cycles-to-failure \(N\) (usually \(\log N\)).

📄 From slides✏️ Clean redraw

Slide: Fatigue Analysis Approaches — S-N of tool steel vs aluminium

ℹ︎ Slide vs redraw: the slide plots real S-N data for tool steel (flattening to an endurance limit) against aluminium (still dropping); my redraw exaggerates the two shapes on one axis to make the "steel flattens, Al doesn't" contrast unmistakable.

• Endurance / fatigue limit: stress below which (ferrous metals) fatigue never occurs.
• Fatigue strength: stress to fail at a specified \(N\).   Fatigue life: cycles permitted at a given stress.
• Endurance ratio = endurance limit / UTS ≈ 0.3–0.4 for metals.

7.1 Stress-life: Basquin's equation

\[ S_a=a\,N^{\,b}\;(b<0)\qquad\text{Two lives: }\;\frac{S_1}{S_2}=\left(\frac{N_1}{N_2}\right)^{b} \]

7.2 Strain-life (ε-N)

For LCF, total strain amplitude = elastic + plastic parts. Cyclic curve in Ramberg–Osgood form with cyclic strength coefficient \(K'\) and cyclic strain-hardening exponent \(n'\).

7.3 LEFM crack growth & Paris' law — highest-yield numerical

\[ \Delta K_I=Y\,\Delta\sigma\sqrt{\pi a},\qquad \Delta\sigma=\sigma_{max}-\sigma_{min}\;\;(\textbf{use }\Delta\sigma,\text{ NOT }\sigma_{max}) \]

📄 From slides✏️ Clean redraw

Slide: Fatigue Analysis Approaches — sigmoidal crack-growth curve

ℹ︎ Slide vs redraw: identical structure — both mark thresholds \(\Delta K_{th}\) and \(K_C\) and the three regions I/II/III. The slide is the exact plot from your deck; my redraw just recolours the three regions.

Paris' law: \(\dfrac{da}{dN}=C(\Delta K)^m\). Integrating over region II gives the propagation life:

\[ N=\int_{a_i}^{a_f}\frac{da}{C\,(Y\Delta\sigma\sqrt{\pi a})^m}\;\xrightarrow{\;m=3,\;Y,\Delta\sigma\text{ const}\;}\; N=\frac{2}{C(Y\Delta\sigma\sqrt\pi)^3}\Big[a_i^{-1/2}-a_f^{-1/2}\Big] \]

7.4 Variable amplitude — Palmgren–Miner rule

\[ D=\sum_i\frac{n_i}{N_i};\qquad\text{failure predicted when }D\ge1 \]

\(n_i\) = cycles applied at level \(i\), \(N_i\) = cycles-to-failure at level \(i\). If one pass of the load block gives \(D_{block}\), then blocks to failure \(=1/D_{block}\).

7.5 Fatigue / damage design strategies

Design = create the optimum solution · Manufacturing = produce components from raw material · Assembly = join components into a product. DFMA = DFM + DFA: reduce time-to-market and total cost by making parts easy to make and easy to assemble — decided at the design stage.

8.1 Design–manufacturing paradigms → concurrent engineering

• Over-the-wall — traditional; almost no design↔manufacturing communication.
• Sign-off — manufacturing must approve drawings.
• Limited collaboration — teams interact only on critical points.
• Concurrent engineering — design & manufacturing work together from concept to launch. This is the basis of DFX (Design for X = any life-cycle stakeholder).

Key fact: 60–80% of product cost is fixed by design decisions, so addressing manufacturing early pays off most. (2025 MCQ Q13 quotes the 70–80% band.)

8.2 DFM vs DFA vs DFMA

8.3 The five principles of DFMA

Process (right process for the part) · Design (drawing suits the process) · Material (correct material) · Environment (survives its service environment) · Compliance/Testing (meets safety & quality standards).

8.4 Classic case — Ford vs GM

Boothroyd's DFA software saved Ford billions on the Taurus line (1988). GM traced 41% of its productivity gap vs Ford to manufacturability: Ford's front bumper had 10 parts vs GM's 100, fitting together more easily. GM then became a leading DFMA user.

8.5 DFM & DFA guidelines — learn ~4 of each for the essay

Assembly = handling (grasp, orient, position) + insertion & fastening. Three levels of automation: manual, automatic (parts feeder + workhead), robotic.

8.6 Process-specific DFM rules (one-liners)

DFX aspects to name: Manufacture, Assembly, Reliability, Safety, Serviceability/Maintenance, Environment/Sustainability, Cost, Quality, Ergonomics.

Reliability \(R(t)\) = the probability that a system performs its intended function, within tolerances, under stated conditions, for a specified time. \(0\le R\le1\).

Engineering design is a three-way trade-off: performance ↔ reliability ↔ cost. Adding components raises performance but lowers reliability (unless component reliability rises or redundancy is added). Reliability grows through a test–fix–test–fix prototype cycle.

9.1 The bathtub curve

📄 From slides✏️ Clean redraw

Slide: Design for Safety & Reliability, p.20

ℹ︎ Slide vs redraw: the slide labels the three regions with their Weibull shapes (β<1 infant mortality, β=1 steady state, β>1 wear-out); my redraw names the causes instead. Same curve.

9.2 Reliability functions & indices

\[ F(t)=\int_0^t f(x)\,dx\;(\text{unreliability, CDF})\qquad R(t)=1-F(t)\qquad \lambda(t)=\frac{f(t)}{R(t)}\;(\text{hazard}) \] \[ \lambda=\frac{\text{number of failures}}{\text{operating time}}\qquad \text{MTTF}=\int_0^\infty R(t)\,dt=\frac{1}{\lambda}\;(\text{non-repairable})\qquad \text{MTBF}=\frac1\lambda\;(\text{repairable}) \]

9.3 Three failure-time distributions

Slide: Design for Safety & Reliability, p.19

9.4 System reliability

\[ \text{Series (all needed): }R_s=\prod R_i=e^{-(\sum\lambda_i)t}\qquad \text{Parallel (any one): }R_s=1-\prod(1-R_i) \]

📄 From slides✏️ Clean redraw

Slide: Design for Safety & Reliability, p.23

ℹ︎ Slide vs redraw: the slide shows the generic (a) series / (b) parallel block topologies; my redraw plugs in the worked numbers so you can see redundancy jump 0.605 → 0.998.

9.5 Design for Reliability (DFR) & Safety (DFS)

DFR strategies: fail-safe (monitor the weak link), "one-horse-shay" (equal-life components), absolute worst-case (conservative → overdesign). DFR guidelines: margin of safety, derating, redundancy, durability, damage tolerance, ease of inspection, simplicity, specificity. Causes of unreliability: design mistakes, manufacturing defects, maintenance, exceeding design limits, environment.

Design for Safety — the hazard hierarchy

1. Design the hazard out (inherently safe).
2. If not possible, add protective devices (guards, cut-offs, relief valves).
3. If hazards remain, warn the user (labels, lights, sounds).

Fail-safe variants: fail-passive (drops to lowest-energy state, e.g. circuit breaker); fail-active (stays energised in a safe mode, e.g. standby redundancy); fail-operational (keeps its critical function, e.g. valve that fails open).

Slide: Design for Safety & Reliability — stress–strength interference

Human engineering / ergonomics = designing so the product fits human abilities and limits — "fitting the job to the man," not "the man to the job." Goal: optimise efficiency, health, safety & comfort. (Greek ergos = work + nomos = natural law.)

10.1 Four forms of human factors

Slide: Human Engineering Considerations, p.3

10.2 The 10 principles of ergonomics

(1) Work in neutral postures (keep the spine's S-curve, neck aligned, elbows in, wrists neutral) · (2) reduce excessive force · (3) keep everything in easy reach · (4) work at proper heights · (5) reduce excessive motions · (6) minimise fatigue & static load · (7) minimise pressure points · (8) provide clearance · (9) move / exercise / stretch · (10) maintain a comfortable environment.

10.3 The man–machine system

The machine receives instructions and displays progress; build in ergonomic measures at design (ISO safety colours, warning signals, standard controls). The man is the flexible controller: senses → perceives → judges → stores/recalls → decides → acts. Design must match task requirements to human capability.

Slide: Human Engineering Considerations, p.28

10.4 Guidelines: displays & controls

If you can do each from memory, you're ready. Ticks save automatically in this browser.

• State the purpose of a factor of safety and write \(n=S/\sigma\).
• Draw the Tresca hexagon inside the von Mises ellipse; state which is conservative.
• Write generalized Hooke's law and the stress tensor (6 independent components).
• Sketch a ceramic stress–strain curve (straight line → sudden fracture).
• Name the three crack modes (Opening/Sliding/Tearing); "rolling" is not one.
• Write \(K=Y\sigma\sqrt{\pi a}\); recall Y = 1.12 for an edge crack.
• Compute critical crack length \(a_c=\frac1\pi(K_{IC}/Y\sigma)^2\).
• Define G and the K–G relation; state Griffith & the Irwin–Orowan modification.
• Contrast HCF vs LCF (cycles, stress, elastic/plastic, S-N vs ε-N).
• Compute \(\sigma_a,\sigma_m,R\) from \(\sigma_{max}/\sigma_{min}\).
• Use Basquin ratio and integrate Paris' law (remember Δσ, a in metres).
• Apply Miner's rule; find blocks-to-failure = 1/D.
• List the four fatigue design strategies (infinite/safe/fail-safe/damage-tolerant).
• Explain concurrent engineering & give four DFM + four DFA guidelines.
• Do a Normal and a Weibull reliability calculation; series vs parallel.
• Sketch & explain the bathtub curve; define λ, MTTF, MTBF.
• Give the three DFS hazard-hierarchy steps & three fail-safe variants.
• Name the four human-factor types; state the letter-height & clockwise-increase rules.