KSE Professional Engineer cheat sheet

Stress σ = F/A; axial strain ε = ΔL/L; Hooke's law σ = Eε holds only in the linear-elastic range below yield strength.

Factor of safety FS = failure stress / allowable stress; for static ductile design FS is typically 1.5-3, higher where loads are uncertain.

Beam bending: σ = Mc/I and deflection scales with wL⁴/(EI); doubling span increases deflection 16× for uniform load.

Thermodynamics first law for a closed system: Q − W = ΔU; for steady-flow open systems use enthalpy, Q − W = Δh + ΔKE + ΔPE.

Carnot efficiency η = 1 − T_cold/T_hot with absolute temperatures; no real cycle exceeds it.

Ohm's law V = IR; power P = VI = I²R = V²/R; three-phase real power P = √3 V_LL I_L cos φ.

Fluid continuity A₁V₁ = A₂V₂; Bernoulli p/γ + V²/2g + z = constant along a streamline for steady, incompressible, frictionless flow.

Reynolds number Re = ρVD/μ; flow is generally laminar below Re ≈ 2,000 in pipes and turbulent above ≈ 4,000.

Unit conversions: 1 hp = 550 ft·lbf/s = 0.7457 kW; 1 psi = 6.895 kPa; 1 Btu = 1.055 kJ.

Design for static ductile failure uses the von Mises (distortion energy) criterion; brittle materials are assessed with the maximum principal stress or Mohr-Coulomb criterion.

Stress concentration factor K_t multiplies nominal stress at geometric discontinuities; fatigue notch factor K_f = 1 + q(K_t − 1), where q is notch sensitivity.

S-N curve: fatigue life is finite above the endurance limit and effectively infinite below it for steels; nonferrous metals often lack a true endurance limit.

Miner's rule for variable amplitude fatigue: Σ(n_i/N_i) = 1 at predicted failure, where N_i is cycles to failure at stress level i.

Shaft design under combined bending and torsion: τ_max = (16/πd³)√(M² + T²) for a solid round shaft (maximum shear stress theory).

Gear ratio = N_driven/N_driver = ω_driver/ω_driven; torque ratio is the inverse of the speed ratio for an ideal gear pair.

Welded joint throat thickness t = 0.707w for a 45° fillet weld of leg size w; weld capacity = allowable stress × throat × length.

Bolted joint preload should exceed the external separating load to maintain clamp force; joint separation occurs when external load exceeds preload divided by the joint constant complement.

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

Critical path is the longest-duration path through the network; it determines minimum project duration and has zero total float.

Total float = LS − ES = LF − EF; a critical activity has total float of zero.

Earned value: CV = EV − AC (positive is under budget); SV = EV − PV (positive is ahead of schedule).

Earned value indices: CPI = EV/AC and SPI = EV/PV; values below 1.0 indicate cost overrun or schedule slippage respectively.

Estimate at completion EAC = BAC/CPI when current cost performance is expected to continue; EAC = AC + (BAC − EV) when remaining work proceeds at planned rate.

PERT expected duration t_E = (O + 4M + P)/6; standard deviation σ = (P − O)/6.

Risk exposure = probability × consequence; risk response options are avoid, mitigate, transfer, and accept.

Scope change control requires a documented change request, impact assessment on cost and schedule, and formal approval before implementation.

ASME Boiler and Pressure Vessel Code Section VIII governs pressure vessel design; Section I covers power boilers; Section IX covers welding qualification.

ASME B31.3 applies to process piping; B31.1 applies to power piping; the applicable code is selected by service and jurisdiction, not preference.

ASME Section IX welding procedure qualification is documented by a PQR supporting a WPS; welder performance qualification is separate and documented by WPQ.

ISO 9001 is a quality management system standard with process approach and risk-based thinking; certification is by accredited third-party bodies.

ISO 14001 specifies environmental management system requirements; ISO 45001 covers occupational health and safety management systems.

API 510 covers in-service inspection of pressure vessels; API 570 covers in-service piping inspection; API 653 covers aboveground storage tanks.

OSHA 29 CFR 1910 Subpart H regulates hazardous materials including compressed gases and flammable liquids in general industry.

ASME BPV Code Section VIII Division 1 maximum allowable stress values are tabulated by material and temperature in Section II Part D.

Jurisdictional requirements (state or local) can be stricter than the referenced national code; the more stringent requirement governs.

Hierarchy of controls, most to least effective: elimination, substitution, engineering controls, administrative controls, personal protective equipment.

Permit-required confined space: hazardous atmosphere, engulfment potential, internal configuration entrapment, or other recognized serious hazard; entry requires permit, atmospheric testing, attendant, and rescue plan.

Lockout/tagout (29 CFR 1910.147) requires energy isolation, verification of zero energy state, and removal only by the authorized employee who applied the lock.

Flammable liquid flash point and autoignition temperature determine storage and electrical classification; Class I locations require appropriately rated equipment.

LEL and UEL define flammable range in air; gas detection alarms are typically set at 10% and 25% LEL for combustible gas.

Hazardous waste generator status under RCRA depends on monthly generation rate; large quantity generators must meet stricter accumulation and reporting rules.

Incident investigation root cause analysis distinguishes immediate causes from underlying management-system causes; corrective actions should address the latter.

Personal protective equipment is the last line of defense and must be selected based on hazard assessment, fit-tested, and inspected before use.

Destructive testing includes tensile, Charpy impact, and hardness tests; nondestructive testing includes visual, liquid penetrant, magnetic particle, ultrasonic, and radiographic methods.

Liquid penetrant testing detects surface-breaking discontinuities in nonporous materials; magnetic particle testing applies only to ferromagnetic materials.

Ultrasonic testing detects internal flaws and measures thickness; radiographic testing reveals internal density variations but requires radiation safety controls.

Hydrostatic test pressure for pressure vessels is typically 1.3 times the maximum allowable working pressure multiplied by the ratio of allowable stress at test to design temperature.

Measurement system analysis: gauge repeatability and reproducibility (GR&R) below 10% of tolerance is generally acceptable; above 30% is unacceptable.

Control charts: X-bar and R charts monitor process mean and variation; a point beyond control limits or a nonrandom run signals special-cause variation.

Process capability Cp = (USL − LSL)/(6σ); Cpk accounts for centering and equals the lesser of (USL − μ)/(3σ) and (μ − LSL)/(3σ).

Calibration traceability requires an unbroken chain of comparisons to national or international standards, with documented uncertainty.

First article inspection verifies that the initial production item conforms to all drawing and specification requirements before full production.

Engineers shall hold paramount the safety, health, and welfare of the public in the performance of professional duties.

Engineers shall perform services only in areas of their competence and shall not affix a seal to work not prepared or directly supervised by them.

Conflict of interest must be disclosed promptly; accepting compensation from more than one party for the same service without disclosure is prohibited.

Engineers shall not reveal confidential client information without consent except where required by law or where public safety is endangered.

Professional misconduct includes falsifying credentials, plagiarism, and issuing misleading public statements; many jurisdictions require reporting of violations.

Continuing professional development requirements vary by jurisdiction; licenses are granted by state boards and are not nationally portable.

Sustainable development and environmental stewardship are part of professional responsibility; designs should consider lifecycle impacts.

When a safety concern is ignored by an employer, the engineer's obligation is to escalate internally and, if unresolved, to the appropriate authority.

Technical reports should state purpose, methods, results, and conclusions, with assumptions and limitations explicitly identified.

As-built drawings reflect actual installed conditions and must be distinguished from design drawings; revisions are tracked through revision blocks.

A controlled document has an identified owner, revision status, distribution list, and retention period; obsolete copies are removed from use.

Record retention periods are set by contract, statute, and regulation; the longest applicable period governs.

Meeting minutes should record decisions, action items with owners and due dates, and dissenting opinions where material.

Email and electronic records are discoverable; professional communication should be factual, concise, and free of speculation.

Specifications define materials and workmanship; drawings define geometry and configuration; conflicts are resolved by the stated order of precedence in the contract.

Calculations should be checked and signed by a qualified second party; the checker's signature documents independent verification.