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Civil Engineering Board Exam Study Notes
Complete Reviewer for the Civil Engineer Licensure Examination
In This Guide
About the CE Board Exam
The Civil Engineer Licensure Examination is administered by the Professional Regulation Commission (PRC) to assess competency in civil engineering practice. It covers major disciplines including structural, geotechnical, hydraulics, and construction management.
Exam Subjects
- • Mathematics & Surveying
- • Hydraulics & Geotechnical
- • Structural Engineering & Construction
Requirements
- • BS Civil Engineering degree
- • Passing score: 70%
- • No subject below 50%
Part 1: Mathematics & Surveying
Engineering Mathematics
Key Formulas
Algebra
- Quadratic: x = (-b ± √(b²-4ac))/2a
- Arithmetic: aₙ = a₁ + (n-1)d
- Geometric: aₙ = a₁ × r^(n-1)
- Sum AP: S = n(a₁ + aₙ)/2
- Sum GP: S = a₁(1 - rⁿ)/(1 - r)
Trigonometry
- sin²θ + cos²θ = 1
- tan θ = sin θ / cos θ
- Law of Sines: a/sinA = b/sinB
- Law of Cosines: c² = a² + b² - 2ab·cosC
Calculus Applications
- Derivatives: Rate of change, slope, optimization
- Integrals: Area under curve, volume, work
- Differential Equations: Modeling physical systems
Surveying
Leveling
- HI (Height of Instrument): HI = Elev + BS
- Elevation: Elev = HI - FS
- Backsight (BS): Reading on known elevation
- Foresight (FS): Reading to determine unknown elevation
- Turning Point (TP): Intermediate point for instrument relocation
Traverse Computation
- Latitude: L = Distance × cos(Bearing)
- Departure: D = Distance × sin(Bearing)
- Error of Closure: √(ΣL² + ΣD²)
- Precision: 1/n where n = Perimeter/Error
Area Calculations
- DMD Method: Area = Σ(DMD × Latitude)/2
- Coordinate Method: 2A = Σ(Xᵢ(Yᵢ₊₁ - Yᵢ₋₁))
- Trapezoidal Rule: A = (d/2)(y₁ + 2y₂ + ... + yₙ)
- Simpson's Rule: A = (d/3)(y₁ + 4y₂ + 2y₃ + ... + yₙ)
Part 2: Structural Engineering
Strength of Materials
Stress & Strain
- Stress (σ): σ = P/A (Force/Area)
- Strain (ε): ε = ΔL/L (Change/Original)
- Young's Modulus: E = σ/ε
- Poisson's Ratio: ν = -ε_lateral/ε_axial
- Shear Stress: τ = V/A
- Shear Modulus: G = τ/γ
- Thermal Stress: σ = EαΔT
- Factor of Safety: FS = Ultimate/Allowable
Beam Analysis
- Bending Stress: σ = Mc/I (where M = moment, c = distance to neutral axis, I = moment of inertia)
- Shear Stress in Beams: τ = VQ/Ib
- Deflection: EIy'' = M(x)
- Section Modulus: S = I/c
Common Beam Formulas
Simply Supported - Center Load
M_max = PL/4
δ_max = PL³/48EI
Simply Supported - Uniform Load
M_max = wL²/8
δ_max = 5wL⁴/384EI
Cantilever - End Load
M_max = PL
δ_max = PL³/3EI
Cantilever - Uniform Load
M_max = wL²/2
δ_max = wL⁴/8EI
Reinforced Concrete Design (NSCP)
USD (Ultimate Strength Design)
- Design Equation: φMₙ ≥ Mᵤ
- Nominal Moment: Mₙ = Asfy(d - a/2)
- Compression Block: a = Asfy/(0.85f'c·b)
- Steel Ratio: ρ = As/bd
- ρ_min = 1.4/fy or √f'c/(4fy)
- ρ_max = 0.75ρ_b
Load Combinations (NSCP)
- U = 1.4D
- U = 1.2D + 1.6L
- U = 1.2D + 1.6L + 0.5(Lr or S or R)
- U = 1.2D + 1.0E + L
- U = 0.9D + 1.0E
Structural Analysis
Methods of Analysis
- Method of Joints: Analyze forces at truss joints (ΣFx = 0, ΣFy = 0)
- Method of Sections: Cut through truss, analyze section (ΣM = 0)
- Moment Distribution: Iterative method for continuous beams
- Slope-Deflection: Relationship between moments and rotations
- Three-Moment Equation: For continuous beams
Part 3: Geotechnical Engineering
Soil Properties
Index Properties
- Void Ratio: e = Vᵥ/Vₛ
- Porosity: n = Vᵥ/V = e/(1+e)
- Degree of Saturation: S = Vw/Vᵥ
- Water Content: w = Ww/Ws
- Unit Weight: γ = W/V
- Specific Gravity: Gs = γs/γw
Atterberg Limits
- Liquid Limit (LL): Water content at which soil flows
- Plastic Limit (PL): Water content at which soil crumbles
- Plasticity Index: PI = LL - PL
- Shrinkage Limit (SL): Minimum water content for saturation
- Liquidity Index: LI = (w - PL)/PI
Soil Classification
USCS Classification
Coarse-Grained
- GW: Well-graded gravel
- GP: Poorly-graded gravel
- SW: Well-graded sand
- SP: Poorly-graded sand
Fine-Grained
- CL: Low plasticity clay
- CH: High plasticity clay
- ML: Low plasticity silt
- MH: High plasticity silt
Bearing Capacity
Terzaghi's Equation
qᵤ = cNc + γDfNq + 0.5γBNγ
- c = cohesion
- γ = unit weight of soil
- Df = depth of foundation
- B = width of foundation
- Nc, Nq, Nγ = bearing capacity factors (function of φ)
Part 4: Hydraulics & Water Resources
Fluid Properties
- Density (ρ): Mass per unit volume (kg/m³)
- Specific Weight (γ): γ = ρg (N/m³); Water: 9.81 kN/m³
- Specific Gravity: SG = ρ/ρwater
- Viscosity (μ): Resistance to flow
- Reynolds Number: Re = ρVD/μ (Laminar < 2000 < Turbulent)
Fluid Statics
Pressure
- Hydrostatic Pressure: P = γh
- Force on Submerged Surface: F = γh̄A
- Center of Pressure: yp = ȳ + Ic/(ȳA)
- Buoyancy: Fb = γVdisplaced
Fluid Dynamics
Fundamental Equations
- Continuity: A₁V₁ = A₂V₂ (Q = AV)
- Bernoulli: P₁/γ + V₁²/2g + z₁ = P₂/γ + V₂²/2g + z₂ + hL
- Energy: Total head = Pressure head + Velocity head + Elevation head
Pipe Flow
- Darcy-Weisbach: hf = f(L/D)(V²/2g)
- Hazen-Williams: V = 0.849CR^0.63S^0.54
- Manning's: V = (1/n)R^(2/3)S^(1/2)
- Hydraulic Radius: R = A/P (Area/Wetted Perimeter)
Open Channel Flow
- Froude Number: Fr = V/√(gD) (Subcritical < 1 < Supercritical)
- Critical Depth: yc = (Q²/gB²)^(1/3)
- Specific Energy: E = y + V²/2g
- Hydraulic Jump: y₂/y₁ = 0.5(√(1 + 8Fr₁²) - 1)
Part 5: Construction Management
Project Scheduling
CPM/PERT
- Critical Path: Longest path through network; determines project duration
- Float/Slack: LS - ES = LF - EF (Total Float)
- ES (Early Start): Earliest time activity can start
- EF (Early Finish): ES + Duration
- LS (Late Start): LF - Duration
- LF (Late Finish): Latest time activity can finish
PERT Time Estimates
- Expected Time: te = (a + 4m + b)/6
- Variance: σ² = ((b - a)/6)²
- a = optimistic, m = most likely, b = pessimistic
Estimating & Quantity Surveying
Common Conversions
- 1 cubic meter concrete ≈ 9.5 bags cement (for 1:2:4 mix)
- 1 bag cement = 40 kg
- Steel bars: #3 = 10mm, #4 = 12mm, #5 = 16mm, #6 = 20mm
- 1 square meter CHB wall (4" thick) ≈ 12.5 pieces
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