JC Engineering cheat sheet

Static equilibrium requires ΣF = 0 and ΣM = 0 about any point; a two-force member carries load only along the line joining its pins.

Stress σ = F/A; axial strain ε = ΔL/L; within the elastic range σ = Eε (Hooke's law), where E is Young's modulus.

Thermal expansion: ΔL = αLΔT; restrained expansion generates σ = EαΔT when both ends are fixed.

Beam bending: σ = My/I and deflection scales with 1/EI, so doubling the second moment of area I halves bending stress and deflection.

Bernoulli (steady, incompressible, frictionless): p/γ + v²/2g + z = constant along a streamline.

Reynolds number Re = ρvD/μ; Re < 2000 indicates laminar pipe flow, Re > 4000 turbulent, between is transitional.

First law for a steady-flow open system: q − w = Δh + Δ(v²/2) + gΔz per unit mass.

Shaft power P = 2πNT, with N in revolutions per second and T in N·m; torque transmits power without changing angular speed.

Design factor (safety factor) n = failure strength / allowable stress; the allowable stress equals the limit stress divided by n.

A factor of safety below 1 indicates predicted failure; values are set by consequence of failure, load uncertainty and material variability.

Fatigue: alternating and mean stresses combine via the Goodman line σa/Se + σm/Su = 1 for a conservative infinite-life check.

Stress concentration factor Kt multiplies nominal stress at geometric discontinuities; Kt applies to the alternating component in fatigue.

Tolerance stack-up: worst-case assembly clearance = sum of individual tolerances; statistical (RSS) method uses the square root of the sum of squares.

A closed kinematic chain has one degree of freedom when mobility M = 3(n − 1) − 2j equals 1, with n links and j lower pairs.

Design reviews progress concept, preliminary and critical stages; each gate should have defined exit criteria and recorded actions.

Finite element results converge as mesh density increases; a mesh refinement check compares stress change between successive meshes.

Carbon content drives steel behaviour: low-carbon (<0.3% C) is ductile and weldable; above ~0.6% C hardness and crack sensitivity rise.

Quenching forms martensite; tempering afterwards restores toughness, so hardened parts are almost always tempered.

Annealing softens and relieves residual stress; normalising refines grain structure; both require controlled cooling rates.

Cast iron has high compressive strength and damping but low tensile ductility; it is unsuitable for shock tensile loading.

Welding: preheat reduces cooling rate and hydrogen cracking risk in thick or high-carbon joints; low-hydrogen electrodes limit diffusible hydrogen.

Heat-affected zone properties differ from parent metal; hardness peaks near the fusion line in many steels.

Machining surface finish improves with higher cutting speed, smaller feed and nose radius, and rigid tooling.

Additive manufacturing is anisotropic: properties along the build direction differ from in-plane properties, so orientation must be specified.

Critical path is the longest duration path through the network; its total float is zero, and any delay on it delays project completion.

Total float = late finish − early finish = late start − early start; free float is the delay possible without affecting any successor.

Earned value: CV = EV − AC and SV = EV − PV; CPI = EV/AC and SPI = EV/PV, with CPI < 1 meaning cost overrun.

Estimate at completion EAC = BAC/CPI when current cost performance is expected to continue.

Crashing shortens duration by adding resources to critical activities; fast-tracking overlaps activities and raises rework risk.

A milestone has zero duration and marks a significant event; it consumes no resources.

Risk response categories: avoid, mitigate, transfer, accept; a contingency reserve covers identified risks, management reserve covers unknown ones.

Scope change control requires documented approval before work proceeds; unapproved changes erode the baseline.

Quality assurance is process-focused and preventive; quality control is product-focused and detects defects after production.

Control charts distinguish common-cause variation (stable process) from special-cause variation (assignable, out-of-control signal).

A process is capable when Cp = (USL − LSL)/6σ ≥ 1.33; Cpk accounts for centring: Cpk = min[(USL − μ), (μ − LSL)]/3σ.

Cpk < 1 means the process produces nonconforming output even when centred poorly; Cp ignores centring entirely.

Seven basic quality tools: flow chart, check sheet, histogram, Pareto chart, cause-and-effect diagram, scatter diagram, control chart.

Pareto principle: roughly 80% of problems arise from about 20% of causes; prioritise the vital few.

Acceptance sampling risks: producer's risk (α) is rejecting a good lot; consumer's risk (β) is accepting a bad lot.

Nonconformance requires containment, root-cause analysis and corrective action; rework must be re-inspected to the same criteria.

Hierarchy of controls, most to least effective: elimination, substitution, engineering controls, administrative controls, PPE.

Hazard is a potential source of harm; risk is the combination of likelihood and severity of that harm.

Permit-to-work systems govern hot work, confined-space entry, excavation and energised work; isolation must be verified before entry.

Lockout/tagout requires energy isolation, dissipation of stored energy and verification of zero energy before work begins.

Confined spaces may have hazardous atmospheres; testing for oxygen, flammables and toxics precedes entry, with continuous monitoring and an attendant.

Noise exposure limits are time-weighted: as sound level rises, permissible exposure duration falls; hearing protection is the last resort.

Spill response follows contain, report, clean up, dispose; waste segregation and manifesting are required for hazardous waste.

Incident investigation seeks root causes (system and procedural) rather than blame; near misses are reported and investigated.

A code is a legally adopted body of rules; a standard is a consensus technical document that a code may reference.

Specification states project-specific requirements; it may be stricter than the referenced code but not less strict.

Design codes give minimum requirements for safety; compliance with a code does not by itself prove fitness for a specific service.

Standards are revised periodically; the edition adopted by contract or regulation governs, not necessarily the latest edition.

Pressure equipment design typically requires design pressure, design temperature, material specification and corrosion allowance to be defined.

Regulatory approval (permits, inspections, statutory certifications) is separate from contractual technical compliance.

Where documents conflict, the contract's order of precedence governs; typically the specification outranks general drawings.

Manufacturer's instructions and test certificates (material, pressure, weld) form part of the compliance record.

Present worth of a single future amount: P = F/(1 + i)^n; future worth F = P(1 + i)^n.

Uniform series present worth: P = A[(1 + i)^n − 1]/[i(1 + i)^n]; capital recovery factor is its reciprocal.

Net present value compares alternatives by discounting all cash flows to time zero; choose the higher NPV at the same discount rate.

Internal rate of return is the discount rate at which NPV equals zero; accept a project when IRR exceeds the required rate.

Payback period ignores the time value of money and cash flows after payback; use it as a screening indicator only.

Annual worth converts all cash flows to an equal annual amount using the capital recovery factor.

Cost estimate accuracy improves with project definition: order-of-magnitude estimates are ±30–50%, detailed estimates roughly ±5–10%.

Depreciation (straight-line: (cost − salvage)/life) is an accounting allocation, not a cash flow; tax effects must be modelled separately.

Paramount obligation is to protect public health, safety and welfare; this outranks loyalty to an employer or client.

Competence rule: accept only work within one's competence or obtain qualified supervision; disclose limitations.

Conflicts of interest must be disclosed and avoided; undisclosed benefits from suppliers or contractors are improper.

Confidentiality applies to client and employer information; exceptions exist for legal requirements and public safety.

Signing or sealing documents certifies personal responsibility for their content; never seal work not prepared or reviewed by you.

Bribery, kickbacks and facilitation payments are prohibited; gifts should be nominal and disclosed per policy.

When a safety concern is ignored internally, escalate through the chain of command and, if unresolved, to the appropriate authority.

Technical communication: state assumptions, units, sources and limitations; a recommendation should be traceable to evidence.

Reliability R(t) = e^(−λt) for a constant failure rate; mean time between failures MTBF = 1/λ.

Availability = MTBF/(MTBF + MTTR); reducing repair time raises availability as much as improving reliability.

The bathtub curve has three regions: infant mortality (decreasing rate), useful life (constant rate), wear-out (increasing rate).

Preventive maintenance is time-based; predictive (condition-based) maintenance acts on measured condition such as vibration or oil analysis.

Overall equipment effectiveness OEE = availability × performance × quality; world-class benchmark is about 85%.

Series systems multiply reliability, so system reliability falls below the weakest component; redundancy in parallel raises it.

Root cause analysis tools include 5-Why, fishbone and fault tree analysis; fix causes, not symptoms.

Criticality ranking (consequence × likelihood) directs maintenance effort to assets whose failure most affects safety and production.