Aragon PAU Technology and Engineering II - independent engineering foundations cheat sheet

Engineering stress σ = F/S₀ uses original area; E = σ/ε applies to the linear elastic region. Engineering stress itself is not confined to that region.

Toughness = whole curve area; resilience = elastic area

Hardness is not fundamental but correlates with strength

Grain refinement commonly increases yield strength in conventional metallic microstructures, subject to material and scale limits.

Selection needs specific indices (σ/ρ, E/ρ) plus cost and durability

In an ideal planar model: pin has two force components, roller one normal reaction, fixed support two force components and a moment.

I = b·h³/12, W = b·h²/6 for a rectangle

Simply supported beam, central load: M_max = F·L/4

Euler: P_cr = π²EI/L_k², with L_k depending on the end conditions

Planar DOF: G = 3(n−1) − 2j₁ − j₂

For the defined ideal lossless gear pair, speed and torque-magnitude ratios are inverse; losses reduce actual output torque.

For a sinusoid V_rms = V_peak/√2; the stated impedance magnitude is for a series RLC model.

Q_C = P(tan φ₁ − tan φ₂) for power-factor correction

Transformer: V₁/V₂ = N₁/N₂ = I₂/I₁

Induction motor: n = (1 − s)·60f/p

Thévenin voltage is open-circuit voltage; deactivate independent sources to obtain resistance while preserving dependent-source behavior.

Karnaugh: give the minimum sum of products

Sensitivity = Δoutput/Δinput; resolution = smallest detectable change

Closed-loop error compares reference and measurement; integral action can remove appropriate steady-state error only under suitable stability and operating assumptions.

PLC scan: read inputs → run program → update outputs

4–20 mA live zero: (I − 4)/16 of the span

Repeatability ≠ accuracy, resolution ≠ sensitivity

Robot DOF come from its joints; workspace is the reachable volume

p = F/A; 1 bar = 10⁵ Pa; 1 MPa = 10 bar

Q = A·v links flow, area and speed

Retraction force uses the annulus (bore minus rod)

Flow control depends on load and circuit; overrunning-load safety requires a properly engineered load-control system.

Hydraulic and pneumatic performance depends on the specified pressure, fluid, components, losses and operating conditions.

Read ISO 1219 symbols by the number of ports and positions

1 kWh = 3.6 MJ; 1 tep ≈ 41.86 GJ

Conversion efficiency must use a consistent useful output and input; it differs from a heat pump coefficient of performance, which can exceed one.

Carnot heat-engine efficiency is1−T_cold/T_hot using kelvin and the stated hot/cold reservoirs.

Hydro: P = η·ρ·g·Q·H

Wind power grows with v³; Betz limit C_p = 0.593

Sustainability is assessed per kWh: CO₂, life cycle, energy mix

State the system boundary and assumptions before calculation.

Units, sign conventions and uncertainty are part of the answer.

Verification against a specification differs from validation for an intended use.

Drawings need a declared convention and controlled revision.

Classroom models do not authorize physical operation or structural approval.