Chartered Membership of IMechE (CEng MIMechE) Core Mechanical Engineering Knowledge Syllabus

Core Mechanical Engineering Knowledge syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Core Mechanical Engineering Knowledge in Chartered Membership of IMechE (CEng MIMechE), not a summary of it.

1. 1

   Engineering Mechanics and Materials

   4 topics

   • Statics and dynamics
     • Equilibrium, free-body diagrams and reactions
     • Kinematics and kinetics of machines
   • Stress analysis and strength of materials
     • Direct, bending, shear and torsional stress
     • Combined loading, Mohr's circle and yield criteria
   • Material selection and behaviour
     • Metals, polymers, ceramics and composites
     • Fatigue, creep and fracture mechanics
   • Failure analysis
     • Stress concentration and crack propagation
     • Corrosion and degradation mechanisms
2. 2

   Thermodynamics and Fluid Mechanics

   4 topics

   • Thermodynamic principles
     • First and second laws and entropy
     • Power and refrigeration cycles
   • Heat transfer
     • Conduction, convection and radiation
     • Heat exchanger design and effectiveness
   • Fluid statics and dynamics
     • Continuity, Bernoulli and momentum equations
     • Laminar and turbulent flow, losses in pipes
   • Applied energy systems
     • Pumps, compressors and turbomachinery
     • HVAC and energy efficiency
3. 3

   Design, Manufacturing and Control

   5 topics

   • Engineering design process
     • Requirements capture and specification
     • Conceptual, embodiment and detail design
   • Machine elements and CAD
     • Bearings, gears, fasteners and seals
     • Parametric modelling and tolerancing (GD&T)
   • Manufacturing processes
     • Casting, forming, machining and joining
     • Additive manufacturing and process selection
   • Control and mechatronics
     • Feedback control and system response
     • Sensors, actuators and embedded systems
   • Vibration and noise
     • Single and multi-degree-of-freedom systems
     • Resonance, damping and isolation
4. 4

   Analysis, Modelling and Emerging Technology

   3 topics

   • Computational engineering
     • Finite element analysis fundamentals and validation
     • Computational fluid dynamics application and limits
   • Reliability and statistics
     • Probability, distributions and tolerancing
     • Reliability, availability and maintainability
   • Digital and sustainable engineering
     • Digital twins, IoT and Industry 4.0
     • Decarbonisation and low-carbon technologies

Core Mechanical Engineering Knowledge flashcards for Chartered Membership of IMechE (CEng MIMechE)

19 of 60 cards from the Core Mechanical Engineering Knowledge deck — real questions with worked answers.

1. State the three scalar equations of static equilibrium for a coplanar (2D) rigid body.

   $\sum F_x = 0$, $\sum F_y = 0$, and $\sum M_z = 0$ (sum of moments about any point in the plane is zero).

2. What is Newton's second law for a particle, and how does it extend to rotation of a rigid body about a fixed axis?

   Translation: $\vec{F} = m\vec{a}$. Rotation: $\sum M = I\alpha$, where $I$ is the mass moment of inertia and $\alpha$ the angular acceleration.

3. For uniform circular motion, give the centripetal acceleration in terms of speed/radius and of angular velocity.

   $a_c = \frac{v^{2}}{r} = \omega^{2} r$, directed toward the centre.

4. Define the coefficient of static friction and write the limiting friction condition.

   $\mu_s = \frac{F_{max}}{N}$, so impending slip occurs when $F \leq \mu_s N$; at the point of slipping $F = \mu_s N$.

5. State the work–energy theorem and the principle of impulse–momentum.

   Work–energy: $W_{net} = \Delta KE = \frac{1}{2}mv_2^{2} - \frac{1}{2}mv_1^{2}$. Impulse–momentum: $\int F\,dt = \Delta(mv) = m v_2 - m v_1$.

6. Define normal (direct) stress and engineering strain for an axially loaded bar.

   Stress $\sigma = \frac{F}{A}$ (force per unit area). Strain $\varepsilon = \frac{\Delta L}{L}$ (change in length per original length, dimensionless).

7. State Hooke's law in 1D and define Young's modulus.

   $\sigma = E\varepsilon$, where $E$ (Young's modulus) is the slope of the linear-elastic stress–strain curve, with units of $\text{Pa}$ (typically $\text{GPa}$).

8. Write the engineering bending (flexure) formula and identify each term.

   $\frac{\sigma}{y} = \frac{M}{I} = \frac{E}{R}$, where $\sigma$ is bending stress at distance $y$ from the neutral axis, $M$ the bending moment, $I$ the second moment of area, $E$ Young's modulus, $R$ the radius of curvature.

9. Write the torsion equation for a circular shaft.

   $\frac{\tau}{r} = \frac{T}{J} = \frac{G\theta}{L}$, where $\tau$ is shear stress at radius $r$, $T$ torque, $J$ polar second moment of area, $G$ shear modulus, $\theta$ angle of twist over length $L$.

10. Define Poisson's ratio and give a typical value for metals.

    $\nu = -\frac{\varepsilon_{lateral}}{\varepsilon_{axial}}$, the negative ratio of transverse to axial strain. For most metals $\nu \approx 0.3$.

11. Give the relationship linking Young's modulus $E$, shear modulus $G$, and Poisson's ratio $\nu$ for an isotropic material.

    $G = \frac{E}{2(1+\nu)}$.

12. State the Euler buckling load for a pin-ended (both ends pinned) column.

    $P_{cr} = \frac{\pi^{2} E I}{L^{2}}$, where $L$ is the column length and $I$ the minimum second moment of area.

13. Distinguish the yield strength, ultimate tensile strength (UTS), and proof stress on a stress–strain curve.

    Yield strength: stress at onset of plastic deformation. UTS: maximum stress reached. Proof stress (e.g. 0.2%): stress giving a defined permanent strain, used when no sharp yield point exists.

14. Define ductility and toughness, and how toughness is read from a stress–strain curve.

    Ductility: ability to deform plastically before fracture (e.g. % elongation). Toughness: energy absorbed before fracture, equal to the total area under the stress–strain curve.

15. What is the difference between ductile and brittle fracture?

    Ductile fracture involves significant plastic deformation, necking, and a fibrous/cup-and-cone surface. Brittle fracture occurs with little plastic deformation, fast crack propagation, and a flat, often crystalline surface.

16. State the fracture-mechanics criterion using stress intensity factor and fracture toughness.

    Fast fracture occurs when $K = Y\sigma\sqrt{\pi a} \geq K_{IC}$, where $K$ is the stress intensity factor, $a$ the crack size, $Y$ a geometry factor, and $K_{IC}$ the plane-strain fracture toughness.

17. Define fatigue and the endurance (fatigue) limit. What does an S–N curve plot?

    Fatigue is failure under cyclic loading below the static strength. The endurance limit is the stress amplitude below which (for steels) failure does not occur for infinite cycles. An S–N curve plots stress amplitude $S$ against number of cycles to failure $N$ (log scale).

18. What is creep, and in which regime of homologous temperature does it become significant?

    Creep is time-dependent plastic deformation under constant load, typically significant above about $0.4\,T_m$ (homologous temperature, with $T_m$ the melting temperature in kelvin). It progresses through primary, secondary (steady-state), and tertiary stages.

19. List the main mechanical-property factors driving material selection in design.

    Stiffness ($E$), strength (yield/UTS), ductility, toughness/fracture toughness, fatigue resistance, hardness, density, plus cost, corrosion resistance, and processability.

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