General Engineering & Cross-Discipline Cheat Sheet - WittyWriter

General & Cross-Discipline Engineering

📘 Key Concepts and Definitions

Safety Factor (FoS): A design margin applied to a system, defined as the ratio of the structure's ultimate strength to the expected load. It accounts for uncertainties in materials, loads, and analysis.
Geometric Dimensioning & Tolerancing (GD&T): A symbolic language used on engineering drawings to define the allowable variation in geometry for a part.
Critical Path Method (CPM): A project management algorithm for scheduling a set of project activities. The "critical path" is the longest sequence of tasks that determines the minimum project duration.
Earned Value Management (EVM): A project management technique for measuring project performance and progress in an objective manner.

🧮 Formulas and Equations

Project Management Formulas

PERT Expected Time: T_E = (O + 4M + P)/6 (O=Optimistic, M=Most Likely, P=Pessimistic)
Schedule Variance (SV): SV = EV - PV (EV=Earned Value, PV=Planned Value). Positive is ahead of schedule.
Cost Variance (CV): CV = EV - AC (AC=Actual Cost). Positive is under budget.

Standard Equations of Motion (Kinematics)

v_f = v_i + at
Δx = v_it + ½at²
v_f² = v_i² + 2aΔx
Where v_i=initial velocity, v_f=final velocity, a=acceleration, t=time, Δx=displacement.

🛠️ Symbols & Standards

Engineering Drawing Symbols (GD&T)

GD&T symbols control form, orientation, location, and profile of features.

Form: Flatness, Straightness, Circularity, Cylindricity.
Profile: Profile of a Line, Profile of a Surface.
Orientation: Perpendicularity, Angularity, Parallelism.
Location: Position, Concentricity, Symmetry.
Runout: Circular Runout, Total Runout.

🧭 Step-by-Step Guides: Critical Path Method (CPM)

List Activities: Break the project down into all required tasks.
Identify Dependencies: For each task, determine which other tasks must be completed first.
Draw Network Diagram: Create a flowchart showing the sequence and dependencies of all tasks.
Estimate Durations: Assign a time estimate to each activity.
Identify the Critical Path: Calculate the longest path through the network. Any delay on this path will delay the entire project. This involves calculating earliest start/finish and latest start/finish times for each task.

⌨️ Productivity Tips

Unit Consistency: Before starting any calculation, convert all values to a consistent set of base units (e.g., SI units: meters, kilograms, seconds, Pascals). This is the single most effective way to avoid simple errors.
Order of Magnitude Check: After a calculation, step back and ask if the answer makes sense. Is the stress in a reasonable range for the material? Is the project duration months when it should be weeks? This sanity check can catch major mistakes.

📊 Tables & Visual Aids

Common Greek Letters in Engineering

Letter	Uppercase	Lowercase	Common Uses
Alpha	Α	α	Angles, acceleration, coefficient of thermal expansion
Beta	Β	β	Angles, coefficients
Delta	Δ	δ	Change or difference (e.g., ΔT), deflection
Epsilon	Ε	ε	Strain, emissivity
Theta	Θ	θ	Angle
Mu	Μ	μ	Coefficient of friction, dynamic viscosity
Pi	Π	π	Mathematical constant (~3.14159)
Rho	Ρ	ρ	Density, resistivity
Sigma	Σ	σ	Summation (Σ), Normal Stress (σ)
Tau	Τ	τ	Shear Stress, torque
Omega	Ω	ω	Ohms (Ω), Angular Velocity (ω)

Typical Safety Factors

Application	Typical FoS	Reasoning
Static loads, ductile materials	1.5 - 2.5	Well-understood loads and material behavior.
Fatigue/dynamic loads	3 - 8	High uncertainty in load cycles and fatigue life.
Pressurized systems	3 - 5	High consequence of failure (rupture).
Lifting equipment (hoists, cranes)	5 - 12	Risk to human life, dynamic loading effects.
Aerospace components	1.1 - 2.0	Weight is critical; analysis is extremely thorough.

🧪 Use Case: Earned Value Calculation

Scenario: A project has a budget of $10,000 and is 50% of the way through its schedule. So far, $6,000 has been spent. A review shows that only 40% of the work is actually complete.

Planned Value (PV): 50% of $10,000 = $5,000.
Actual Cost (AC): $6,000.
Earned Value (EV): 40% of $10,000 = $4,000.
Cost Variance (CV): CV = EV - AC = $4000 - $6000 = -$2000 (Over budget).
Schedule Variance (SV): SV = EV - PV = $4000 - $5000 = -$1000 (Behind schedule).

🧹 Troubleshooting Common Issues

Problem: Drawings are misinterpreted by manufacturing.
- Fix: Your tolerancing may be ambiguous. Use GD&T to explicitly define functional relationships between features, rather than relying on simple +/- tolerances on dimensions. Ensure a clear datum reference frame is established.
Problem: Project is consistently late despite team working hard.
- Fix: The team may not be focused on the critical path activities. Use CPM to identify the critical path and prioritize resources for those tasks. Any effort spent on non-critical tasks does not shorten the project duration.

📚 References and Further Reading

"Machinery's Handbook" by Oberg et al. - The indispensable reference for mechanical engineers.
"A Guide to the Project Management Body of Knowledge (PMBOK Guide)".
ASME Y14.5 - Dimensioning and Tolerancing Standard.
"Engineering Mechanics: Dynamics" by Hibbeler or Meriam and Kraige.