CPE I cheat sheet

Statics equilibrium: 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 deformation δ = FL/(AE); factor of safety FS = failure stress / allowable stress.

Beam bending: σ = Mc/I with I = bh³/12 for a rectangle; maximum bending moment for a simply supported beam under a central point load P at span L is PL/4.

Thermodynamics first law for a closed system: Q − W = ΔU; for a control volume at steady state, energy in equals energy out plus work.

Ohm's law V = IR; series resistance adds, parallel conductance adds; three-phase real power P = √3·V_LL·I·cos θ.

Fluid continuity A₁V₁ = A₂V₂; Bernoulli along a streamline p/ρ + V²/2 + gz = constant for inviscid, steady, incompressible flow.

Reynolds number Re = ρVD/μ; pipe flow is generally laminar below Re ≈ 2300 and turbulent above ≈ 4000.

Material properties: Young's modulus E from the elastic slope of the stress–strain curve; yield strength at 0.2% offset for metals without a distinct yield point.

Design process order: define requirements, generate concepts, screen and score alternatives, develop the selected concept, verify against requirements.

A requirement is verifiable if it states a measurable quantity, a test condition, and a pass threshold; unverifiable adjectives ("robust", "user-friendly") are defects.

Pugh matrix: compare concepts against a datum concept using +, −, and S scores; use it to eliminate, not to produce a final weighted ranking.

Weighted decision matrix: normalize criteria weights to sum to 1, score each option per criterion, and multiply; document the scoring scale before scoring.

Tolerance stack-up: worst-case = sum of tolerances; statistical (RSS) = square root of the sum of squared tolerances, valid only for independent, centered distributions.

Failure modes and effects analysis ranks risk by RPN = severity × occurrence × detection; act first on high-severity items regardless of RPN.

Design of experiments: randomize run order, use replication to estimate error, and block known nuisance factors; a main effect is the change in response averaged over levels of other factors.

Verification confirms the design meets stated requirements; validation confirms the requirements reflect the user's actual need.

Critical path method: the critical path is the longest-duration path through the network; its total float is zero and it sets project duration.

Total float = late start − early start = late finish − early finish; free float = early start of successor − early finish of the activity.

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

Earned value: CV = EV − AC, SV = EV − PV, CPI = EV/AC, SPI = EV/PV; CPI below 1.0 means cost overrun per unit of work performed.

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

A milestone has zero duration and no effort; a hammock or summary task aggregates subordinate activities and carries no direct work.

Risk response types: avoid, mitigate, transfer, accept for threats; exploit, enhance, share, accept for opportunities.

Scope change control: no change to baseline scope, cost, or schedule without a documented, approved change request that updates the baseline.

PDCA cycle: Plan (set objectives and process), Do (implement on a small scale), Check (measure against objectives), Act (standardize or correct).

Control chart rules: a point beyond a control limit, or seven consecutive points on one side of the centerline, signals a non-random (assignable) cause.

Process capability Cp = (USL − LSL)/(6σ); Cpk = min[(USL − μ), (μ − LSL)]/(3σ); Cpk accounts for off-center processes, Cp does not.

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

ISO 9001 is a quality management system standard requiring documented processes and continual improvement; certification is by an accredited third-party registrar, not by ISO itself.

ISO 45001 addresses occupational health and safety management systems; ISO 14001 addresses environmental management systems.

In the US, OSHA requires employers to record work-related fatalities within 8 hours and in-patient hospitalizations, amputations, or eye losses within 24 hours.

Root cause analysis tools: 5 Whys, fishbone (Ishikawa) diagram, and fault tree analysis; distinguish root cause from the immediate trigger of the event.

Hold paramount the public health, safety, and welfare; this duty outranks obligations to clients and employers.

Competence rule: accept only assignments within your competence, or disclose limits and obtain the necessary expertise before proceeding.

Conflict of interest: disclose any financial or personal interest that could impair judgment; undisclosed conflicts are the violation, not the mere existence of the interest.

Confidentiality: client and employer information is confidential except where release is required by law or necessary to protect public safety.

Sealing and signing: a PE signs and seals only work they prepared or directly supervised; sealing drawings prepared by others without review is misconduct.

Bribery and gifts: giving or accepting anything of value to influence a professional decision is prohibited; nominal hospitality must be disclosed per employer policy.

Whistleblowing escalation order: raise internally first, then to the appropriate regulator, and go public only when internal and regulatory channels fail and harm is imminent.

Sustainable development and informed consent: present data and conclusions honestly, credit others' contributions, and avoid misleading selective reporting.

Technical writing structure: state purpose and recommendation first, then evidence, then limitations; keep one idea per paragraph.

Audience adaptation: match vocabulary and depth to the reader's technical level; define acronyms at first use in every document.

Status reporting: report progress against baseline, forecast to completion, and list blockers with owners and needed decisions.

Meeting discipline: publish an agenda in advance, record decisions and action items with an owner and a due date, and circulate minutes within one business day.

Constructive feedback model: describe the observed behavior, its impact, and the requested change; avoid attributing intent.

Team stages (Tuckman): forming, storming, norming, performing, adjourning; conflict peaks in storming and is resolved by clarified roles and norms.

RACI matrix: each task has exactly one Accountable, at least one Responsible, and defined Consulted and Informed parties.

Written communication is the record: verbal agreements that affect scope, cost, schedule, or safety must be confirmed in writing.