How to use this under time pressure:
Skim the question for the trigger keyword (e.g. "hydraulic radius", "critical path", "void ratio") and jump straight to that card — don't read the section top to bottom.
Use the filter box above to search across every section at once (it temporarily ignores the sidebar tab); clear it to go back to browsing one topic at a time.
If a formula isn't triggering recall within ~20 seconds, flag the question and move on — hunting mid-problem burns time you don't get back.
Unit mismatches are the #1 silent time-sink: check the Conversions tab first whenever ft/in, lb/kip, or US/SI units are mixed in a problem.
Unit Conversion Quick-HitsNCEES Handbook (Ed. 10.6): Units and Conversion Factors, p.1
| Quantity | Conversion |
|---|---|
| Length | 1 ft = 12 in | 1 yd = 3 ft | 1 mile = 5280 ft |
| Area | 1 ft² = 144 in² | 1 acre = 43,560 ft² | 1 mile² = 640 acres |
| Volume | 1 ft³ = 7.48 gal | 1 gal = 3.785 L | 1 m³ = 1000 L = 264.2 gal |
| Gravitational acceleration | g = 32.2 ft/s² = 9.81 m/s² |
| Mass / weight (force) | 1 slug = 32.2 lbm | 1 lbm = 0.4536 kg | 1 lbf = 4.448 N | 1 kip = 1000 lbf |
| Pressure / stress | 1 psi = 6.895 kPa | 1 ksi = 1000 psi | 1 atm = 14.7 psi = 101.325 kPa |
| Energy / work | 1 Btu = 778 ft·lb = 1055 J | 1 N·m = 1 J |
| Power | 1 hp = 550 ft·lb/s = 33,000 ft·lb/min = 745.7 W |
| Temperature | °F = 1.8·°C + 32 | K = °C + 273.15 | °R = °F + 459.67 |
| Angle | 1 rad = 57.3° | 2π rad = 360° |
| Water properties (std.) | γw = 62.4 lb/ft³ = 9.81 kN/m³ | ρw = 1000 kg/m³ = 1.94 slug/ft³ |
| Length (metric/US) | 1 in = 2.54 cm | 1 m = 3.281 ft | 1 km = 0.621 mile |
1. Mathematics & StatisticsNCEES Handbook (Ed. 10.6): Mathematics p.36 · Probability & Statistics p.64
Quadratic Formula
x = (−b ± √(b²−4ac)) / 2a
Roots of ax²+bx+c=0
Law of Cosines
c² = a² + b² − 2ab·cos(C)
Use when you know 2 sides + included angle, or 3 sides
Law of Sines
a/sin A = b/sin B = c/sin C
Use when you know 2 angles + a side (AAS/ASA)
Straight Line
y = mx + b; m = (y2−y1)/(x2−x1)
b = y-intercept; perpendicular slope = −1/m
Circle
(x−h)² + (y−k)² = r²
Center (h,k), radius r
Derivative Power Rule
d/dx(xn) = n·xn−1
Basic differentiation for optimization problems
Integral Power Rule
∫xn dx = xn+1/(n+1) + C
n ≠ −1
Mean & Std Deviation
x̄ = Σx/n; s = √(Σ(x−x̄)² / (n−1))
s uses n−1 (sample); population σ uses n
Z-Score
z = (x − μ) / σ
Standard normal table lookup for probability
Permutations / Combinations
nPr = n!/(n−r)!; nCr = n!/(r!(n−r)!)
Permutation = order matters; combination = order doesn't
Vector Dot Product
A·B = |A||B|cosθ = AxBx+AyBy+AzBz
Result is a scalar; used for angle between vectors, projections
Vector Cross Product
|A×B| = |A||B|sinθ
Result is a vector ⊥ to both; used for moments, area
Linear Regression Slope
b = Σ(x−x̄)(y−ȳ) / Σ(x−x̄)²
Least-squares best-fit line y = a + bx
2. StaticsNCEES Handbook (Ed. 10.6): Statics, p.95
Equilibrium
ΣFx = 0; ΣFy = 0; ΣM = 0
Rigid body in static equilibrium (2D)
Moment of a Force
M = F·d
d = perpendicular distance from point to line of action
Friction Force
F ≤ μsN (static); F = μkN (kinetic)
N = normal force; μs > μk typically
Centroid (composite area)
x̄ = Σ(xiAi)/ΣAi; ȳ = Σ(yiAi)/ΣAi
Break shape into simple parts, use signed areas for holes
Parallel Axis Theorem
I = Ic + A·d²
I_c = centroidal moment of inertia, d = distance to new axis
Rectangle Moment of Inertia
I = bh³/12
About centroidal axis parallel to base b, height h
Circle Moment of Inertia
I = πd4/64 = πr4/4
About centroidal (diametral) axis
Polar Moment of Inertia
J = Ix + Iy
Circle: J = πd4/32
Resultant of Concurrent Forces
R = √(ΣFx² + ΣFy²); θ = tan−1(ΣFy/ΣFx)
Sum components first, then combine
Distributed Load Resultant
R = area under w(x) diagram
Acts through the centroid of the load-diagram area
Method of Joints / Sections
ΣFx=0, ΣFy=0 at each joint (joints); cut & ΣM=0 (sections)
Joints = all member forces; sections = fast for 1-2 target members
Belt / Wedge Friction
T1/T2 = eμβ
β = wrap angle (rad), T1 = tight side tension
Two- / Three-Force Members
2-force: forces collinear along member axis; 3-force: forces concurrent (or parallel)
Fast way to find force directions without full ΣM
3. DynamicsNCEES Handbook (Ed. 10.6): Dynamics, p.102
Linear Kinematics (const. a)
v = v0+at; x = x0+v0t+½at²; v²=v0²+2a(x−x0)
Use whichever equation skips the unknown you don't need
Projectile Motion
x: vx=const; y: vy=vy0−gt, y=y0+vy0t−½gt²
Decouple horizontal (no accel.) and vertical (a=−g) motion
Newton's 2nd Law
ΣF = ma
Apply in n-t or x-y directions; a can have normal + tangential parts
Work-Energy Theorem
W = ΔKE = ½m(v2²−v1²)
Work of net force equals change in kinetic energy
Power
P = F·v = dW/dt
Instantaneous power; F and v components along same line
Impulse-Momentum
FΔt = mΔv = m(v2−v1)
Use for collisions / impact, no need to know force-time detail
Conservation of Momentum
m1v1+m2v2 = m1v1′+m2v2′
Total system momentum conserved if no external force
Coefficient of Restitution
e = (v2′−v1′)/(v1−v2)
e=1 perfectly elastic, e=0 perfectly plastic (stick together)
Circular Motion Accel.
an = v²/r = ω²r; at = rα
a_n points toward center; a_t along path direction
Angular Kinematics (const. α)
ω=ω0+αt; θ=θ0+ω0t+½αt²
Rotational analog of linear kinematics
Torque / Angular 2nd Law
T = Iα
I = mass moment of inertia about rotation axis
Simple Harmonic Motion
ωn = √(k/m); T = 2π/ωn
Spring-mass natural frequency and period
Centripetal Force
Fc = mv²/r
Net force required to keep mass on circular path
4. Mechanics of MaterialsNCEES Handbook (Ed. 10.6): Mechanics of Materials, p.130
Normal Stress
σ = P/A
Axial load P over cross-sectional area A
Shear Stress (avg)
τ = V/A
Direct/average shear across a section
Hooke's Law
σ = Eε
Linear-elastic range only; E = modulus of elasticity
Axial Deformation
δ = PL/AE
Constant P, A, E along length L
Torsional Shear Stress
τ = Tr/J
Max at outer radius r; J = polar moment of inertia
Angle of Twist
φ = TL/JG
G = shear modulus; radians
Bending (Flexure) Stress
σ = Mc/I
c = distance from neutral axis to extreme fiber
Beam Shear Stress
τ = VQ/(Ib)
Q = first moment of area above/below point, b = width there
Thermal Deformation
δT = αLΔT
α = coefficient of thermal expansion
Poisson's Ratio
ν = −εlat/εax
Typically 0.2–0.3 for steel/concrete
Mohr's Circle (2D stress)
σavg = (σx+σy)/2; R = √(((σx−σy)/2)²+τxy²)
σ1,2 = σavg ± R (principal stresses)
Factor of Safety
FS = σyield / σallow
Also FS = load at failure / allowable load
Euler Buckling Load
Pcr = π²EI/(KL)²
K = effective length factor (0.5 fixed-fixed … 2.0 fixed-free)
Beam Deflection (center load, S.S.)
δmax = PL³/48EI
Simply supported beam, point load at midspan
5. MaterialsNCEES Handbook (Ed. 10.6): Materials Science/Structure of Matter, p.117
Engineering Stress/Strain
σ = P/A0; ε = (L−L0)/L0
Based on ORIGINAL area/length (vs. true stress/strain)
True Stress / Strain
σT = σ(1+ε); εT = ln(1+ε)
Accounts for instantaneous area/length during loading
Modulus of Elasticity
E = Δσ/Δε
Slope of linear-elastic portion of stress-strain curve
% Elongation / % Reduction in Area
%EL=(Lf−L0)/L0×100; %RA=(A0−Af)/A0×100
Ductility measures from a tension test
Concrete Modulus of Elasticity
Ec = 57,000√f′c (psi) or 4700√f′c (MPa)
f′c = 28-day compressive strength
Standard Material Moduli
Esteel ≈ 29,000 ksi (200 GPa)
Same for all structural steel grades regardless of Fy
Specific Gravity
SG = ρmaterial/ρwater
Reference: water at 4°C, ρ=1000 kg/m³
Modulus of Resilience
Ur = σy² / 2E
Elastic energy stored up to yield point
Toughness
Toughness ≈ area under σ-ε curve to fracture
Total energy absorbed before fracture (ductile > brittle)
Corrosion (Penetration) Rate
mpy = 534W / (DAT)
W=wt. loss (mg), D=density (g/cm³), A=area (in²), T=time (hr)
Fatigue / Endurance Limit
S-N curve: cycles to failure N vs. stress amplitude S
Steel has a true endurance limit; aluminum does not (use N=5×108 ref.)
6. Fluid MechanicsNCEES Handbook (Ed. 10.6): Fluid Mechanics, p.181
Specific Weight
γ = ρg
Water: 62.4 lb/ft³ = 9.81 kN/m³
Hydrostatic Pressure
P = γh
h = depth below free surface; Pabs = Patm + γh
Hydrostatic Force on Plane Surface
F = γh̄A
h̄ = depth to centroid of submerged area A
Continuity Equation
Q = A1V1 = A2V2
Incompressible steady flow, conservation of mass
Bernoulli's Equation
P/γ + V²/2g + z = const
Along a streamline; no friction/pump/turbine losses
Manning's Equation
V = (1.49/n)·R2/3·S1/2
Open channel; R=A/P (hydraulic radius), S=slope; k=1.49 US, k=1.0 SI
Hazen-Williams Equation
V = 1.318·C·R0.63·S0.54
Pipe flow, V in ft/s (US); use 0.849 coeff. for SI (V in m/s)
Reynolds Number
Re = ρVD/μ = VD/ν
Re<2100 laminar, Re>4000 turbulent (pipe flow)
Darcy-Weisbach Head Loss
hf = f(L/D)(V²/2g)
f = friction factor (Moody chart), major losses
Orifice / Weir Discharge
Q = CdA√(2gh)
C_d = discharge coefficient, h = head above orifice
Froude Number
Fr = V/√(gL)
Fr<1 subcritical, Fr>1 supercritical (open channel)
Pump Power
P = γQH / η
H = total dynamic head, η = pump efficiency
Specific Gravity (fluid)
SG = γfluid/γwater
Water at 4°C = reference (SG=1.0)
Manning's Q (combined)
Q = (1.49/n)·A·R2/3·S1/2
Multiply Manning V by area A directly for discharge
7. SurveyingNCEES Handbook (Ed. 10.6): Civil Engineering — Transportation (near Latitudes/Departures), p.313
Latitude & Departure
Lat = D·cos(bearing); Dep = D·sin(bearing)
D = course distance; N/S component=Lat, E/W component=Dep
Traverse Closure Error
Error = √((ΣLat)² + (ΣDep)²)
Should be ≈0 for a closed traverse; distribute by adjustment rule
Area by Coordinates (Shoelace)
A = ½|Σ(xiyi+1−xi+1yi)|
Sum around polygon in order, close back to first point
Interior Angle Sum
Σinterior angles = (n−2)×180°
n = number of sides of closed traverse polygon
Degree of Curve (arc def.)
D = 5729.58 / R
D in degrees per 100-ft arc, R in ft (US railroad/highway convention)
Horizontal Curve — Tangent
T = R·tan(Δ/2)
Δ = deflection (central) angle; T = PC to PI distance
Horizontal Curve — Length
L = R·Δ·(π/180)
Δ in degrees; arc length of curve
Horizontal Curve — Chord
C = 2R·sin(Δ/2)
Long chord from PC to PT
External & Middle Ordinate
E = R(sec(Δ/2)−1); M = R(1−cos(Δ/2))
E = PI to curve; M = midpoint of chord to curve
Curve Stationing
Sta PT = Sta PC + L
PC = Sta PI − T; always add along the curve, not the tangent
Differential Leveling
Elev = ElevBM + BS − FS
BS=backsight (+), FS=foresight (−); HI = Elev + BS
Vertical Curve Elevation
y = y0 + g1x + [(g2−g1)/2L]x²
Parabolic curve; g1,g2 = grades (decimal), L = curve length
Bearing ↔ Azimuth
Azimuth (from N, cw) converts quadrant bearings directly by adding/subtracting from 0°/180°/360°
NE quadrant: Az=Bearing; SE: Az=180−B; SW: Az=180+B; NW: Az=360−B
8. Environmental EngineeringNCEES Handbook (Ed. 10.6): Environmental Engineering, p.318
Mass Balance
Accumulation = In − Out + Generation
Steady state: Accumulation = 0 → In+Gen = Out
Hydraulic Detention Time
θ = V/Q
V = tank/basin volume, Q = flow rate
First-Order Decay
C = C0·e−kt
k = decay rate constant, t = time
BOD Exertion
BODt = BODu(1−e−kt)
BOD_u = ultimate BOD, k = rate constant (base e)
BOD Rate Constant Conversion
k(base e) = 2.303 × k(base 10)
Watch which base a given k is reported in
DO Sag (Streeter-Phelps)
Dt = [kdL0/(kr−kd)](e−kdt−e−krt) + D0e−krt
k_d=deoxygenation, k_r=reaeration; critical pt where dD/dt=0
Population Growth — Geometric
Pn = P0(1+r)n
Constant % growth rate r per period
Population Growth — Arithmetic
Pn = P0 + kn
Constant increment k per period
Surface Overflow Rate
vo = Q/As
Settling tank; particle removed if settling velocity vs ≥ vo
Weir Loading Rate
WLR = Q / Lweir
Flow per unit length of weir crest
Filtration Loading Rate
Filter rate = Q/A
Same form as overflow rate, applied to filter surface area
Ideal Gas Law
PV = nRT
Air quality/gas volume calcs; R=0.0821 L·atm/(mol·K)
Molarity / Normality
M = mol solute / L solution; N = M × (eq/mol)
Normality accounts for valence/equivalents
mg/L ↔ ppm (dilute water)
1 mg/L ≈ 1 ppm
Valid when solution SG ≈ 1.0 (dilute aqueous)
% Solids (sludge)
%solids = (mass dry solids / mass wet sludge) × 100
Used for sludge volume/thickening calcs
9. Geotechnical EngineeringNCEES Handbook (Ed. 10.6): Civil Engineering — Geotechnical, p.265
Void Ratio & Porosity
e = Vv/Vs; n = Vv/V = e/(1+e)
V_v=voids volume, V_s=solids volume, V=total volume
Degree of Saturation
S = Vw/Vv
S=0 dry, S=1 (100%) fully saturated
Water Content
w = Ww/Ws
Weight of water / weight of solids
Dry Unit Weight
γd = γ/(1+w)
γ = total (moist) unit weight
Specific Gravity of Solids
Gs = γs/γw
Typical range 2.6–2.8 for mineral soils
Effective Stress
σ′ = σ − u
u = pore water pressure; controls strength/settlement, not total stress
Darcy's Law
q = kiA; v = ki
k=hydraulic conductivity, i=hydraulic gradient=Δh/L
Mohr-Coulomb Failure
τf = c + σtanφ
c=cohesion, φ=friction angle, σ=normal stress on failure plane
Terzaghi Bearing Capacity
qult = c′Nc + qNq + 0.5γBNγ
Strip footing; N-factors depend on φ (from tables/charts)
Consolidation Settlement
Sc = [CcH/(1+e0)]·log(σ′f/σ′0)
Normally consolidated clay, primary consolidation only
Rankine Active/Passive Pressure
Ka = tan²(45−φ/2); Kp = tan²(45+φ/2)
Pa = ½KaγH² acting at H/3 from base
Relative Density
Dr = (emax−e)/(emax−emin) × 100%
Compares in-situ void ratio to loosest/densest states
Factor of Safety (slope)
FS = ΣResisting forces (or moments) / ΣDriving forces (or moments)
FS > 1 = stable; typical design target ≥1.5
Compaction — % Compaction
%Compaction = γd,field / γd,max × 100
Field dry density vs. max dry density from Proctor test
10. Structural EngineeringNCEES Handbook (Ed. 10.6): Civil Eng. — Structural Analysis p.274, Design p.278
RC Beam Nominal Moment
Mn = Asfy(d−a/2)
a = Asfy/(0.85f′cb); φMn ≥ Mu for LRFD design
Steel Plastic Moment
Mp = Fy·Z
Z = plastic section modulus (compact sections)
Shear-Moment Relations
dV/dx = −w(x); dM/dx = V(x)
Slope of shear diagram = −load; slope of moment diagram = shear
Simple Beam — UDL
Mmax = wL²/8; Vmax = wL/2
Simply supported, uniform load w over full span L
Simple Beam — Center Point Load
Mmax = PL/4; Vmax = P/2
Simply supported, point load P at midspan
Cantilever — End Point Load
Mmax = PL (at fixed end); δ = PL³/3EI
Fixed at one end, load P at free end
Simple Beam Deflection — UDL
δmax = 5wL4/384EI
At midspan, simply supported uniform load
Column Slenderness Ratio
λ = KL/r
K: 0.5 fixed-fixed, 0.7 fixed-pinned, 1.0 pinned-pinned, 2.0 fixed-free
Deflection Serviceability Limits
δlive ≤ L/360; δtotal ≤ L/240
Typical common code limits (verify per governing code)
LRFD / ASD Basic Load Combos
LRFD: 1.2D+1.6L; ASD: D+L
D=dead load, L=live load (simplified governing combos)
Reinforcement Ratio
ρ = As/(bd)
Compare to ρmin and ρmax for section adequacy check
Retaining Wall Overturning FS
FSo = ΣMresisting / ΣMoverturning
About the toe; typical target FS ≥ 2.0
11. Transportation EngineeringNCEES Handbook (Ed. 10.6): Civil Engineering — Transportation, p.306
Stopping Sight Distance
SSD = 1.47Vt + V²/(30(f+G))
V=mph, t=reaction time (~2.5s), f=friction, G=grade decimal (+up/−down)
Reaction Distance
dr = 1.47Vt
Distance traveled during perception-reaction time before braking
Superelevation
e + f = V²/(15R) [US, V=mph,R=ft]
SI: e+f = V²/(127R), V=km/h, R=m
Vertical Curve Rate
K = L/A
A=|g2−g1| (% algebraic grade diff); L=K×A for design
Degree of Curve
D = 5729.58/R
Same as surveying — R in ft, D in deg/100ft arc
Flow-Density-Speed
q = k·vs
q=flow (veh/hr), k=density (veh/mi), v_s=space mean speed
Greenshields Model
v = vf(1 − k/kj)
v_f=free-flow speed, k_j=jam density; linear speed-density model
Max Flow (Capacity)
qmax = vfkj/4 (at k=kj/2, v=vf/2)
Peak of the Greenshields flow-density parabola
Pavement Structural Number
SN = ΣaiDimi
a=layer coeff., D=layer thickness (in), m=drainage coeff.
Signal Cycle Length (Webster)
C = (1.5L + 5) / (1 − ΣY)
L=total lost time/cycle, Y=critical flow ratio per phase
12. Construction EngineeringNCEES Handbook (Ed. 10.6): Civil Engineering — Construction, p.316
Average End Area Volume
V = L(A1+A2)/2
Earthwork cut/fill between two stations, distance L apart
Swell Factor
SF = Vloose/Vbank
SF > 1 (soil expands when excavated/loosened)
Shrinkage Factor
Sh = Vcompacted/Vbank
Sh < 1 (soil compacts denser than bank state)
Load Factor
LF = 1/SF = γbank/γloose
Converts loose hauled volume back to bank-equivalent
Production Rate / Duration
Duration = Quantity / Production rate
Basic scheduling estimate for a repetitive task
Number of Hauling Units
N = Cycle time / Load time
Matches truck fleet size to loader production (queueing balance)
Relative Compaction
RC = γd,field/γd,max × 100%
Field density test vs. Proctor max dry density
Equipment Owning + Operating Cost
Total cost/hr = Owning cost/hr + Operating cost/hr
Owning = depreciation+interest+insurance; Operating = fuel+maintenance+labor
Concrete Yield
Yield = Actual volume produced / Design (theoretical) volume
Should be ≈1.0; low yield flags batching/air-content issues
13. Project Planning & ManagementNCEES Handbook (Ed. 10.6): Civil Eng. — Construction, p.316 (nearby)
Activity Float
Float = LS − ES = LF − EF
Zero-float activities lie on the critical path
CPM Forward Pass
EF = ES + Duration; ESnext = max(EF of predecessors)
Determines earliest start/finish, moving left→right
CPM Backward Pass
LS = LF − Duration; LFprev = min(LS of successors)
Determines latest start/finish, moving right→left
PERT Expected Duration
te = (o + 4m + p) / 6
o=optimistic, m=most likely, p=pessimistic time
PERT Variance
σ² = ((p−o)/6)²
Sum variances along critical path for project-duration variance
Cost / Schedule Variance
CV = EV − AC; SV = EV − PV
Negative CV/SV = over budget / behind schedule
Cost / Schedule Performance Index
CPI = EV/AC; SPI = EV/PV
<1.0 = unfavorable (over cost / behind schedule)
Estimate at Completion
EAC = BAC / CPI
Projected total cost assuming current CPI trend continues
Estimate to Complete
ETC = EAC − AC
Remaining budget needed to finish the project
Percent Complete
%Complete = EV / BAC × 100
EV=earned value, BAC=budget at completion
14. Engineering EconomicsNCEES Handbook (Ed. 10.6): Engineering Economics, p.235
Simple Interest
F = P(1 + i·n)
I = P·i·n (interest not compounded)
Compound Interest
F = P(1+i)n
i = interest rate/period, n = number of periods
Effective Annual Rate
ieff = (1 + r/m)m − 1
r = nominal annual rate, m = compounding periods/yr
Continuous Compounding
F = P·ern
m → ∞ limit of compound interest
Straight-Line Depreciation
D = (B−S)/n; BVt = B − t·D
B=initial cost, S=salvage value, n=useful life
Break-Even Quantity
Qbe = FC / (Price − VC)
FC=fixed cost, VC=variable cost/unit
Benefit-Cost Ratio
BCR = PW(benefits) / PW(costs)
Accept project if BCR ≥ 1
Capitalized Cost
P = A / i
Present worth of a perpetual (infinite) uniform series
Rate of Return
Solve: PW(benefits) − PW(costs) = 0 for i*
i* is the project's internal rate of return (IRR)
Inflation-Adjusted (Real) Rate
i′ = (i − f) / (1 + f)
i=market rate, f=inflation rate, i′=real interest rate
Cash Flow Factor Formulas (compute directly — faster than table lookup)
| Factor | Name | Formula |
|---|---|---|
| (F/P, i, n) | Single Payment Compound Amount | F = P(1+i)n |
| (P/F, i, n) | Single Payment Present Worth | P = F / (1+i)n |
| (F/A, i, n) | Uniform Series Compound Amount | F = A·[((1+i)n−1) / i] |
| (A/F, i, n) | Sinking Fund | A = F·[i / ((1+i)n−1)] |
| (P/A, i, n) | Uniform Series Present Worth | P = A·[((1+i)n−1) / (i(1+i)n)] |
| (A/P, i, n) | Capital Recovery | A = P·[i(1+i)n / ((1+i)n−1)] |
15. Ethics & Professional PracticeNCEES Handbook (Ed. 10.6): Ethics and Professional Practice, p.4
Canon 1 — Paramount Duty
Public safety, health, & welfare > all else
Overrides client/employer instructions if they conflict with public safety
Canon 2 — Competence
Only perform work within your area of competence
Decline or bring in a qualified specialist otherwise
Canon 3 — Truthful Public Statements
Objective & truthful only; disclose when speaking on behalf of an interested party
No misleading technical claims in public/media statements
Canon 4 — Faithful Agent / Trustee
Act faithfully for each employer or client; avoid conflicts of interest
Disclose any known conflict to all affected parties before proceeding
Canon 5 — Honest Reputation
No deceptive acts; never misrepresent qualifications or take credit for others' work
Applies to resumes, proposals, and public claims alike
Canon 6 — Lawful, Honorable Conduct
Conduct yourself honorably, responsibly, ethically, and lawfully
Enhances the honor/integrity/usefulness of the profession
Public-Safety Escalation Order
Notify employer → notify client → notify authorities/affected public
Escalate only as far as needed to resolve an unaddressed safety risk
Conflict of Interest Rule
Disclose fully before accepting; don't accept compensation from >1 party for the same service without consent
Includes gifts/contributions that could influence judgment
FE → PE Path
FE exam → E.I./E.I.T. status → work experience → PE exam → licensure
Only a licensed PE may legally "seal" engineering documents
Exam Answer Heuristic
Pick the option that protects public safety & is most transparent
On ethics scenario questions, the "report/disclose it" answer is almost always more correct than "stay quiet" or "handle it informally"
Glossary — Common Symbols & Terms
The same symbol often means different things in different sections — this is what it means in the context each formula appears in, plus which topics you'll see it in most.
| Symbol / term | Meaning | Used in |
|---|---|---|
| σ (sigma) | Normal stress — force per unit area, perpendicular to a surface | Mechanics of Materials, Structural, Geotechnical |
| τ (tau) | Shear stress — force per unit area, parallel to a surface | Mechanics of Materials, Statics, Geotechnical |
| γ (gamma) | Unit weight (weight per unit volume); occasionally shear strain | Geotechnical, Fluid Mechanics, Materials |
| φ (phi) | Angle of internal friction (soil); sometimes a diameter symbol | Geotechnical |
| θ (theta) | Generic angle | Statics, Dynamics, Surveying, Transportation |
| ρ (rho) | Mass density | Fluid Mechanics, Dynamics |
| μ (mu) | Coefficient of friction (Statics) or dynamic viscosity (Fluids) — context decides which | Statics, Fluid Mechanics |
| ν (nu) | Poisson's ratio — lateral strain divided by axial strain | Mechanics of Materials |
| δ (delta) | Deflection or displacement | Mechanics of Materials, Structural |
| Δ (capital delta) | "Change in" a quantity (final minus initial) | Used across nearly every section |
| ε (epsilon) | Normal strain — deformation per unit length | Mechanics of Materials |
| Σ (capital sigma) | Summation symbol | Statics equilibrium equations, Statistics |
| ω (omega) | Angular velocity | Dynamics |
| α (alpha) | Angular acceleration (Dynamics) or significance level (Statistics) | Dynamics, Math & Statistics |
| Hydraulic radius (R) | Cross-sectional flow area divided by wetted perimeter (A/P) — governs flow efficiency | Fluid Mechanics |
| Void ratio (e) | Volume of voids divided by volume of solids in a soil sample | Geotechnical |
| Factor of safety (FS) | Capacity divided by demand — FS > 1 means adequate/stable | Geotechnical, Structural, Mechanics of Materials |
| Critical path | Longest sequence of dependent activities in a schedule — sets the minimum project duration | Construction, Project Mgmt |
| Yield strength | Stress at which a material begins to deform permanently (plastically) | Materials, Mechanics of Materials |
| Modulus of elasticity (E) | Ratio of stress to strain in the elastic region — a material's stiffness | Mechanics of Materials, Materials |
| Present worth (P) | Equivalent value of a future cash flow, discounted to today at a given interest rate | Eng. Economics |
| Degree of saturation (S) | Percent of a soil's void space that's filled with water | Geotechnical |
| Level of service (LOS) | Letter grade (A–F) describing traffic flow quality / congestion | Transportation |
| Determinacy | Whether equilibrium equations alone solve a structure (determinate) or extra compatibility equations are needed (indeterminate) | Structural |
| BOD | Biochemical oxygen demand — oxygen microorganisms need to break down organic matter in water; higher BOD = more pollution | Environmental |
| Superelevation (e) | Banking/tilt of a roadway on a horizontal curve, counteracting lateral acceleration | Transportation |
| Bearing capacity | Maximum pressure a soil can support without shear failure | Geotechnical |
| Datum | Fixed reference elevation (commonly mean sea level) all other elevations are measured from | Surveying |