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FE Civil Cheat Sheet

Practice this exam

Math, Ethics, Economics

  • 21-32% of exam
  • Math + Statistics Engineering Sciences Computational Tools Ethics + Practice Engineering Economics

Statics + Mechanics

  • 20-30% of exam
  • Statics Dynamics Mechanics of Materials Materials

Fluids + Water Resources

  • 16-25% of exam
  • Fluid Mechanics Hydraulics + Hydrology Environmental Manning + Rational

Structural + Geotechnical

  • 16-25% of exam
  • Structural Geotechnical Load Combos Bearing Capacity

Transportation + Site

  • 15-22% of exam
  • Transportation Construction Surveying Curves + CPM

Quick Facts

  • Exam FE Civil
  • Questions 110 multiple-choice
  • Time 5h 20m exam
  • Appointment 6 hours CBT
  • Fee $175 NCEES
  • Result Pass/Fail
  • Pass rate ~67% first-time
  • Reference FE Handbook only
  • Provider Pearson VUE

Sample s vs Population σ FO

Sample s

  • n-1 denominator
  • Estimated mean
  • Bessel correction

Population σ

  • n denominator
  • Known mean
  • Full data
  • n-1 vs n

Formula Picker FO

  • Present from future → P/F factor ( P=F/(1+i)ⁿ )
  • Annualize cost → A/P factor ( Capital recovery )
  • Beam max moment → wL²/8 ( Simple span )
  • Bending stress → σ=Mc/I ( Extreme fiber )
  • Shaft shear → τ=Tr/J ( Torsion )
  • Column buckling → Euler P_cr ( π²EI/(KL)² )
  • Open channel V → Manning ( (1/n)R^⅔S^½ )
  • Peak runoff → Rational ( Q=CiA )
  • Effective stress → σ'=σ-u ( Terzaghi )

Math + Statistics FO

  • z-score z=(x-µ)/σ
  • Sample s n-1 denominator
  • Population σ n denominator
  • Linear ODE Integrating factor e^∫P
  • Mean Σx/n
  • Determinant Solve linear systems

Engineering Economics FO

  • 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 ROR ≥ MARR
  • B/C ≥1.0 justifies project
  • SL depr (cost-salvage)/N

Ethics + Practice FO

  • Paramount duty Public safety first
  • Competence Stay in expertise
  • Seal Own responsible charge
  • Conflict Disclose, get consent
  • EI / EIT FE pass designation
  • PE path ~4 yrs + PE exam

Computational Tools FO

  • $A$1 Absolute reference
  • A1 Relative, shifts
  • Newton-Raphson x-f(x)/f'(x)
  • Trapezoidal (h/2)[y₀+2y₁+...+yₙ]
  • Sig figs Match least input
  • Units Carry through always

2-D Equilibrium ME

  • Sum Fx, Sum Fy, Sum M = zero
  • ΣFx=0 ΣFy=0 ΣM=0 3 unknowns max

Shear vs Moment ME

Shear V

  • Slope = load w
  • Sums vertical force
  • Max at supports

Moment M

  • Slope = shear V
  • Max where V=0
  • σ=Mc/I
  • dV/dx=w, dM/dx=V

Method Picker ME

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

Statics ME

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

Beam Diagram Slopes ME

  • Load slopes shear, shear slopes moment
  • dV/dx=w dM/dx=V M peak at V=0

Dynamics ME

  • Velocity v=v₀+at
  • Position s=s₀+v₀t+½at²
  • No-time v²=v₀²+2aΔs
  • Newton 2nd ΣF=ma
  • Rotation ΣM=Iα
  • Work-energy W=ΔKE
  • Impulse FΔt=mΔv
  • Range v₀²sin2θ/g

Mechanics of Materials ME

  • 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

Materials ME

  • f'c test 28-day cylinder C39
  • A992 Fy 50 ksi
  • A36 Fy 36 ksi
  • Steel E 29,000 ksi
  • Concrete Ec 57000√f'c psi
  • Slump ASTM C143 workability
  • Steel Ductile yield plateau
  • Concrete Brittle, weak tension

Water Treatment Train WA

  • Clean Flocs Settle, Filters Disinfect
  • Coagulation Flocculation Sedimentation Filtration Disinfection

Laminar vs Turbulent WA

Laminar

  • Re < 2,100
  • Smooth layers
  • Parabolic profile

Turbulent

  • Re > 4,000
  • Mixing eddies
  • Flat profile
  • Reynolds decides

Fluid Mechanics WA

  • Hydrostatic p=γh
  • Water γ 9.81 kN/m³
  • Water γ (US) 62.4 lb/ft³
  • Continuity Q=A₁V₁=A₂V₂
  • Bernoulli p/γ+V²/2g+z
  • Darcy h_f f(L/D)(V²/2g)
  • Reynolds Re=ρVD/µ
  • Laminar Re < 2,100

NAAQS Pollutants WA

  • Cops Patrol No Ozone, So Particulates
  • CO Pb NO₂ O₃ SO₂ PM

Hydraulics + Hydrology WA

  • Manning SI V=(1/n)R^⅔S^½
  • Manning US Use 1.486 constant
  • Hydraulic R A/P
  • Full pipe R D/4
  • Rational Q=CiA
  • Darcy GW Q=kiA
  • Critical Froude Fr=1
  • Specific energy E=y+V²/2g

Environmental WA

  • BOD Organic pollution load
  • DO sat ≈9 mg/L at 20°C
  • Mass balance Acc=In-Out+Gen
  • Treatment Coag→floc→sed→filt→disinf
  • Coliform MCL Zero detectable
  • NAAQS CO Pb NO₂ O₃ SO₂ PM

USCS Codes CI

  • Good Soils Make Clean Order
  • G=gravel S=sand M=silt C=clay O=organic

Active vs Passive CI

Active

  • Wall moves away
  • Soil pushes
  • Lower coefficient

Passive

  • Wall moves into
  • Soil resists
  • Higher coefficient
  • Ka < K0 < Kp

Design Method Picker CI

  • Factored loads → LRFD ( φRn ≥ Σγ )
  • Service loads → ASD ( Rn/Ω )
  • Gravity floor → 1.2D + 1.6L ( ASCE 7 )
  • RC beam moment → Asfy(d-a/2) ( ACI 318 )
  • Pipe full flow → R=D/4 ( Hydraulic radius )
  • Slope misclosure → √(ΣLat²+ΣDep²) ( Traverse )

Structural CI

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

Total vs Effective Stress CI

Total σ

  • Full overburden
  • Includes water
  • γ·depth

Effective σ'

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

Geotechnical CI

  • 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 cNc+qNq+0.5γBNγ

USCS vs AASHTO CI

USCS

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

AASHTO

  • A-1 to A-8
  • Highway subgrade
  • Group index
  • Building vs road

LRFD vs ASD CI

LRFD

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

ASD

  • Service loads
  • Rn/Ω
  • Safety factor
  • Factored vs service

Transportation SI

  • Min radius R=V²/[15(e+f)]
  • SSD 1.47Vt + brake
  • PRT t = 2.5 s
  • Crest L AS²/2158 (S<L)
  • Greenshields q=kv
  • q_max k_jam/2, v_free/2

Construction SI

  • Total float LS-ES = LF-EF
  • Critical path Zero total float
  • Free float Next ES - EF
  • Cost variance CV=EV-AC
  • Schedule var SV=EV-PV
  • CPI / SPI EV/AC ; EV/PV
  • OSHA Subpart P Protect ≥5 ft

Surveying SI

  • New elev BM + BS - FS
  • HI Benchmark + backsight
  • Misclosure √(ΣLat²+ΣDep²)
  • Departure L·sin(azimuth)
  • Latitude L·cos(azimuth)
  • Curve L L=R·Δ (radians)

Common Traps

Sample vs population stdev

  • Sample uses n-1 ≠ Population uses n

Manning SI vs US

  • SI: V=(1/n)R^⅔S^½ ≠ US: add 1.486

Total vs effective stress

  • σ includes water ≠ σ'=σ-u

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

  • i in in/hr ≠ A in acres → cfs

Pcr K factor

  • Pinned K=1.0 ≠ Fixed-free K=2.0

Last Minute

  • 1. 110 questions, 5h 20m, $175
  • 2. Closed-book: on-screen FE Handbook only
  • 3. Equilibrium: ΣFx=ΣFy=ΣM=0
  • 4. Truss determinate when m+r=2j
  • 5. Bending stress σ=Mc/I
  • 6. Torsion shaft τ=Tr/J
  • 7. Euler buckling P_cr=π²EI/(KL)²
  • 8. Simple beam Mmax=wL²/8
  • 9. Manning SI: V=(1/n)R^⅔S^½
  • 10. Full pipe R=D/4
  • 11. Rational runoff Q=CiA
  • 12. Effective stress σ'=σ-u
  • 13. Terzaghi q_ult=cNc+qNq+0.5γBNγ
  • 14. LRFD factored; ASD service
  • 15. Sample s uses n-1
  • 16. Public safety outranks client/employer