Math, Ethics, Economics
21-32%of exam
Statics + Mechanics
20-30%of exam
Fluids + Water Resources
16-25%of exam
Structural + Geotechnical
16-25%of exam
Transportation + Site
15-22%of exam
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
Sample s
- n-1 denominator
- Estimated mean
- Bessel correction
Population σ
- n denominator
- Known mean
- Full data
n-1 vs n
Formula Picker
- 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
- 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
- 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
- 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
- $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
Sum Fx, Sum Fy, Sum M = zero
ΣFx=0ΣFy=0ΣM=03 unknowns max
Shear vs Moment
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
- 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
- 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
Load slopes shear, shear slopes moment
dV/dx=wdM/dx=VM peak at V=0
Dynamics
- 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
- 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
- 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
Clean Flocs Settle, Filters Disinfect
CoagulationFlocculationSedimentationFiltrationDisinfection
Laminar vs Turbulent
Laminar
- Re < 2,100
- Smooth layers
- Parabolic profile
Turbulent
- Re > 4,000
- Mixing eddies
- Flat profile
Reynolds decides
Fluid Mechanics
- 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
Cops Patrol No Ozone, So Particulates
COPbNO₂O₃SO₂PM
Hydraulics + Hydrology
- 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
- 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
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
Design Method Picker
- 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
- 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
Total σ
- Full overburden
- Includes water
- γ·depth
Effective σ'
- σ' = σ - u
- Grain contact
- Controls strength
Strength uses σ'
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
- cNc+qNq+0.5γBNγ
USCS vs AASHTO
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
LRFD
- Factored loads
- φ·Rn
- 1.2D+1.6L
ASD
- Service loads
- Rn/Ω
- Safety factor
Factored vs service
Transportation
- 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
- 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
- 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
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