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FE Civil Cheat Sheet

Practice QuestionsStudy Guide

Mathematics and Statistics

7.3-10.9%of exam

8–12 questionsMath + StatisticsAnalytic geometryCalculus

Ethics and Professional Practice

3.6-5.5%of exam

4–6 questionsEthics + PracticePublic safetyResponsible charge

Engineering Economics

4.5-7.3%of exam

5–8 questionsEngineering EconomicsPresent worthRate of return

Statics

7.3-10.9%of exam

8–12 questionsStaticsEquilibriumTrusses

Dynamics

3.6-5.5%of exam

4–6 questionsDynamicsKinematicsWork and energy

Mechanics of Materials

6.4-10.0%of exam

7–11 questionsMechanics of MaterialsShear vs MomentTorsion

Materials

4.5-7.3%of exam

5–8 questionsMaterialsConcreteStructural steel

Fluid Mechanics

5.5-8.2%of exam

6–9 questionsFluid MechanicsLaminar vs TurbulentBernoulli

Surveying

5.5-8.2%of exam

6–9 questionsSurveyingLevelingTraverse closure

Water Resources and Environmental Engineering

9.1-13.6%of exam

10–15 questionsHydraulics + HydrologyEnvironmentalWater Treatment Train

Structural Engineering

9.1-13.6%of exam

10–15 questionsStructuralLRFD vs ASDLoad combinations

Geotechnical Engineering

9.1-13.6%of exam

10–15 questionsGeotechnicalActive vs PassiveTotal vs Effective Stress

Transportation Engineering

8.2-12.7%of exam

9–14 questionsTransportationStopping sight distanceVertical curves

Construction Engineering

7.3-10.9%of exam

8–12 questionsConstructionCritical pathEarned value

Quick Facts

Exam
FE Civil
Questions
110, including alternative items
Time
5h 20m exam
Appointment
5h 55m CBT
Fee
$225 NCEES
Result
Pass/Fail
Pass rate
66% first-time cohort (July 2026)
Reference
FE Handbook only
Provider
NCEES via Pearson

Sample s vs Population σ

Sample s

  • n-1 denominator
  • Estimated mean
  • Bessel correction

Population σ

  • n denominator
  • Known mean
  • Full data

n-1 vs n

Math + Statistics

z-score
z=(x-µ)/σ
Sample s
n-1 denominator
Population σ
n denominator
Slope
Δy/Δx; instantaneous dy/dx
Mean
Σx/n
One-sample t interval
x̄ ± t*·s/√n

Ethics + Practice

Paramount duty
Public safety first
Competence
Stay in expertise
Seal
Own responsible charge
Conflict
Disclose to employer or client
EI / EIT
Certification is board-specific
PE path
Board sets education, experience, exams

Formula Picker

  1. Present from future→P/F factor(P=F/(1+i)ⁿ)
  2. Annualize cost→A/P factor(Capital recovery)
  3. Beam max moment→wL²/8(Simple span, full uniform load)
  4. Bending stress→σ=Mc/I(Extreme fiber)
  5. Shaft shear→τ=Tr/J(Torsion)
  6. Column buckling→Euler P_cr(π²EI/(KL)²)
  7. Open channel V→Manning(Uniform SI: (1/n)R^⅔S_f^½)
  8. Peak runoff→Rational(Q≈CiA (in/hr, acres, cfs))
  9. Effective stress→σ'=σ-u(Terzaghi)

Engineering Economics

P/F
P=F/(1+i)ⁿ
P/A
Uniform series PW
A/P
Capital recovery
A/F
Sinking fund
ROR
NPW=0, solve i
Accept
Conventional IRR ≥ MARR
B/C
Independent project: ≥1.0
SL depr
(cost-salvage)/N

2-D Equilibrium

Sum Fx, Sum Fy, Sum M = zero

ΣFx=0ΣFy=0ΣM=03 unknowns max

Method Picker

  1. All truss forces→Method of joints(2 eqs/pin)
  2. One member force→Method of sections(Cut + ΣM)
  3. Speed, no time→v²=v₀²+2aΔs(Kinematics)
  4. Impact velocity→Work-energy(W=ΔKE)
  5. Collision→Impulse-momentum(∫ΣF dt = mΔv)
  6. Bearing capacity→Terzaghi(Strip footing)
  7. Soil ID code→USCS(G S M C O)

Statics

Equilibrium
ΣFx=ΣFy=ΣM=0
Planar truss count
m+r=2j; verify stability
Centroid
x̄=Σ(Aᵢx̄ᵢ)/ΣA
Parallel axis
I=Ī+Ad²
Rect I
bh³/12
Circle I
πd⁴/64
Friction
F=µₛN impending

Dynamics

Velocity
v=v₀+at
Position
s=s₀+v₀t+½at²
No-time
v²=v₀²+2aΔs
Newton 2nd
ΣF=ma
Rotation
ΣM about mass center = Iα
Work-energy
W=ΔKE
Impulse
∫ΣF dt = mΔv
Range
v₀²sin(2θ)/g, level, no drag

Beam Diagram Slopes

Downward load lowers shear; shear sets moment slope

dV/dx=−wdM/dx=VCheck V sign changes

Shear vs Moment

Shear V

  • Slope = −w
  • Jumps at point loads
  • Units of force

Moment M

  • Slope = V
  • Check extrema and ends
  • Units of force × length

w down: V′=−w, M′=V

Mechanics of Materials

Axial stress
σ=P/A
Axial δ
PL/AE
Hooke
σ=Eε
Bending
σ=Mc/I
Shear stress
τ=VQ/Ib
Torsion
τ=Tr/J
Solid J
πd⁴/32
Euler P_cr
π²EI/(KL)², elastic buckling

Materials

Cylinder strength
ASTM C39, usually 28 days
A992 Fy
50 ksi specified minimum
A36 Fy
36 ksi for typical shapes
Steel E
29,000 ksi
Concrete Ec
Normalweight: 57,000√f'c (psi)
Slump
ASTM C143 consistency
Steel
Ductile in typical tension tests
Concrete
Brittle, weak tension

Laminar vs Turbulent

Laminar

  • Re below ~2,000–2,300
  • Smooth layers
  • Parabolic profile

Turbulent

  • Re > 4,000
  • Mixing eddies
  • Fuller velocity profile

Approximate pipe-flow transition range

Fluid Mechanics

Hydrostatic
p=γh
Water γ
9.81 kN/m³
Water γ (US)
62.4 lbf/ft³
Continuity
Q=A₁V₁=A₂V₂
Bernoulli
p/γ+V²/(2g)+z = constant
Darcy h_f
f(L/D)(V²/2g)
Reynolds
Re=ρVD/µ
Laminar
Pipe Re below ~2,000–2,300

Surveying

New elev
BM + BS - FS
HI
Benchmark + backsight
Misclosure
√[(ΣLat)²+(ΣDep)²]
Departure
L·sin(azimuth)
Latitude
L·cos(azimuth)
Curve L
L=R·Δ (radians)

Water Treatment Train

Clean Flocs Settle, Filters Disinfect

CoagulationFlocculationSedimentationFiltrationDisinfection

Hydraulics + Hydrology

Manning SI
V=(1/n)R^⅔S_f^½
Manning US
Multiply SI form by ~1.49
Hydraulic R
A/P
Full pipe R
D/4
Rational
Q≈CiA (in/hr, acres, cfs)
Darcy GW
|Q|=kiA (gradient magnitude)
Critical
Froude Fr=1
Specific energy
E=y+V²/2g

NAAQS Pollutants

Cops Patrol No Ozone, So Particulates

COPbNO₂O₃SO₂PM

Environmental

BOD
Biochemical oxygen demand
Freshwater DO sat
≈9.1 mg/L (20°C, 1 atm)
Mass balance
Acc=In-Out+Gen
Treatment
Coag→floc→sed→filt→disinf
Revised Total Coliform Rule
E. coli MCL; coliform triggers
NAAQS
CO Pb NO₂ O₃ SO₂ PM

LRFD vs ASD

LRFD

  • Factored loads
  • φ·Rn
  • 1.2D+1.6L

ASD

  • ASD load combinations
  • Rn/Ω
  • Safety factor

LRFD φRn / ASD Rn/Ω

Design Method Picker

  1. Factored loads→LRFD(Factored demand ≤ φRn)
  2. ASD load combination→ASD(Demand ≤ Rn/Ω)
  3. Gravity floor→1.2D + 1.6L(Dead and floor live load case)
  4. RC beam moment→Asfy(d-a/2)(Rectangular section, tension steel yields)
  5. Pipe full flow→R=D/4(Hydraulic radius)
  6. Traverse misclosure→√[(ΣLat)²+(ΣDep)²](Sum signed components first)

Structural

LRFD combo
1.2D + 1.6L for D/L case
ASD
Demand ≤ Rn/Ω
LRFD
Factored ≤ φRn
Max moment
wL²/8 simple beam
Max shear
wL/2 simple beam
ACI Mn
Aₛfᵧ(d−a/2), yielded steel
Whitney a
Asfy/(0.85f'c b)

USCS Codes

Good Soils Make Clean Order

G=gravelS=sandM=siltC=clayO=organic

Active vs Passive

Active

  • Wall moves away
  • Soil pushes
  • Lower coefficient

Passive

  • Wall moves into
  • Soil resists
  • Higher coefficient

Ka < K0 < Kp

Geotechnical

USCS
G S M C O codes
W / P
Well / poorly graded
Void ratio
e=Vv/Vs
Porosity
n=Vv/Vtotal
Saturation
S=Vw/Vv
Effective stress
σ'=σ-u
Terzaghi
Strip: cNc+qNq+0.5γBNγ

Total vs Effective Stress

Total σ

  • Full overburden
  • Uses bulk unit weights
  • Σγᵢhᵢ for layers

Effective σ'

  • σ' = σ - u
  • Grain contact
  • Controls strength

Strength uses σ'

USCS vs AASHTO

USCS

  • G S M C O
  • Lab/structural use
  • Group symbol

AASHTO

  • A-1 through A-7
  • Highway subgrade
  • Group index

USCS symbol / AASHTO group index

Transportation

Min radius (mph → ft)
V²/[15·(e+f)]
SSD
1.47Vt + brake
PRT
t = 2.5 s
Crest L
AS²/2158 (S<L; ft; A%)
Greenshields
q=kv, v=v_free(1−k/k_jam)
q_max
At k_jam/2, v_free/2

Construction

Total float
LS-ES = LF-EF
Critical path
Longest duration path
Free float
Earliest successor ES−EF, zero lag
Cost variance
CV=EV-AC
Schedule var
SV=EV-PV
CPI / SPI
EV/AC ; EV/PV
OSHA Subpart P
Protect ≥5 ft unless stable rock

Common Traps

Sample vs population stdev

Sample uses n-1 ≠ Population uses n

Manning SI vs US

SI coefficient: 1 ≠ U.S. customary coefficient: ~1.49

Total vs effective stress

σ: total stress ≠ σ′: total minus pore pressure

Static vs kinetic friction

Impending: F=µₛN ≠ Sliding: F=µₖN

ASD vs LRFD

ASD: Rn/Ω ≠ LRFD: φRn

Hydraulic radius vs diameter

Full pipe R=D/4 ≠ Not R=D

Rational units

US: Q≈CiA (in/h, acres, cfs) ≠ SI: 1/360 (mm/h, ha)

Pcr K factor

Pinned K=1.0 ≠ Fixed-free K=2.0

Last Minute

  1. 1.110 questions, 5h 20m, $225 NCEES
  2. 2.Closed-book: on-screen FE Handbook only
  3. 3.Equilibrium: ΣFx=ΣFy=ΣM=0
  4. 4.Truss m+r=2j; verify stability
  5. 5.Bending stress σ=Mc/I
  6. 6.Torsion shaft τ=Tr/J
  7. 7.Euler buckling P_cr=π²EI/(KL)²
  8. 8.Simple beam UDL: Mmax=wL²/8
  9. 9.Manning SI: V=(1/n)R^⅔S_f^½
  10. 10.Full pipe R=D/4
  11. 11.Rational: Q≈CiA (in/h, acres, cfs)
  12. 12.Effective stress σ'=σ-u
  13. 13.Strip footing: cNc+qNq+0.5γBNγ
  14. 14.LRFD: φRn; ASD: Rn/Ω
  15. 15.Sample s uses n-1
  16. 16.Public safety outranks client/employer

FE Civil

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