Engineer Civil Engineering cheat sheet

Concrete mix design by absolute volume: Vpaste = cement/GSg + water + air; target w/c from strength and durability tables, then adjust for aggregate moisture before batching.

Slump test (ASTM C143) measures workability; nominal max aggregate size limits slump range and requires +25 mm tolerance for aggregates over 40 mm.

Curing: moist cure at least 7 days for Type I cement, 3 days for Type III; cold-weather protection required when ambient falls below 5 °C and falling.

Formwork removal: sides of beams at 24 h if undisturbed; soffits of slabs/beams require 7 days (props retained) and 14–21 days for full removal depending on span and cement type.

Critical path method: float = LS − ES = LF − EF; total float shared by a path, free float is float before successor's early start. Crashing selects lowest cost-per-day slope on the critical path.

Compaction: standard Proctor (ASTM D698) vs modified Proctor (ASTM D1557, 4.5× energy); field density by sand cone or nuclear gauge must reach 95–98% of max dry density per spec.

Asphalt paving: compaction must occur between breakdown and finish rolling while mix temperature exceeds 85 °C (viscosity-based); density target typically 92% of theoretical maximum (Rice) or 96% of lab density.

Earned value: CV = EV − AC, SV = EV − PV, CPI = EV/AC, SPI = EV/PV; over budget when CPI < 1 and behind schedule when SPI < 1.

Effective stress: σ' = σ − u; total stress from overburden, pore pressure from phreatic surface. Consolidation settlement uses σ' changes and Cc or Cr from e–log σ' curve.

Terzaghi bearing capacity (strip): q_ult = cNc + q̄Nq + 0.5γBNγ; Nc, Nq, Nγ depend on φ. For square footing multiply cNc term by 1.3 and γBNγ term by 0.4.

Allowable bearing pressure = q_ult / FS (typically 3 for dead + live, 2 for transient) and must also satisfy settlement limits (often 25 mm).

Rankine active pressure: Ka = tan²(45 − φ/2); passive: Kp = tan²(45 + φ/2). Active pressure acts at H/3 above base for triangular distribution.

Slope stability factor of safety = resisting moment / driving moment; FS ≥ 1.5 for permanent slopes, 1.3 for temporary. Bishop simplified method is standard for circular failures.

Liquefaction screening: saturated, loose, uniform fine sands with (N1)60 < 15 and groundwater within ~10 m; evaluate with CSR/CRR.

Atterberg limits: LL, PL, PI = LL − PL; PI > 30 and LL > 50 indicate high plasticity / expansive clay (CH). A-line: PI = 0.73(LL − 20).

Consolidation time factor: Tv = cv·t/Hdr²; Tv = 0.197 at U = 50%, Tv ≈ 0.848 at U = 90%. Double drainage gives Hdr = H/2.

Flexural design (ACI 318): φMn ≥ Mu; φ = 0.90 for tension-controlled sections (εt ≥ 0.005), 0.65 for compression-controlled (εt ≤ 0.002), linear transition between.

Balanced/steel ratio limits: ρmax corresponds to εt = 0.004 for beams with factored axial load < 0.10f'cAg; ρmin = 3√f'c / fy ≥ 200/fy (psi).

Whitney stress block: a = β1c, β1 = 0.85 for f'c ≤ 28 MPa, reduced by 0.05 per 7 MPa above, minimum 0.65. Nominal moment Mn = As fy (d − a/2).

Shear: φVn ≥ Vu; Vc = 0.17λ√f'c bw d (MPa) for members without axial force; minimum shear reinforcement required when Vu > 0.5φVc.

Development length: ld = (fy ψt ψe ψs)/(1.1 λ √f'c) · db / (cb + Ktr)/db, capped by (cb+Ktr)/db ≤ 2.5; tension lap splices are 1.3 ld.

Serviceability: deflection limits L/360 for floors under live load, L/240 for total load; ACI minimum thickness for non-prestressed beams is L/16 (simply supported, normal weight).

Steel design (AISC): LRFD φbMn = φb Fy Zx for compact sections, φb = 0.90; ASD Ω = 1.67. Slenderness λp, λr distinguish compact, noncompact, slender elements.

Euler buckling: Pcr = π²EI/(KL)²; K = 1.0 pinned–pinned, 0.5 fixed–fixed, 0.7 fixed–pinned, 2.0 fixed–free. Slenderness ratio KL/r governs.

Sight distance: SSD = 0.278 V t + V²/(254(f ± G)) in metric (V km/h, t reaction s); used for stopping, decision, passing, and intersection sight distances.

Horizontal curve: R = 5729.58/D (US customary, D in degrees); superelevation e + f = V²/(127R) in metric; minimum radius from limiting e_max and side friction.

Vertical curves: L = A·K, where A = |g2 − g1| in percent and K is the rate of vertical curvature; K = L/A. Crest K limited by SSD; sag K by headlight sight distance.

Traffic flow: q = k·v (flow = density × speed); Greenshields linear model gives capacity at half free-flow speed and half jam density.

Level of service for basic freeway segments per HCM: LOS A–F based on density (pc/km/ln); LOS D is often the design threshold for urban freeways.

Pavement design: AASHTO flexible equation uses structural number SN = a1D1 + a2D2m2 + a3D3m3; ESALs from axle load equivalency factors (fourth power law).

Asphalt mix: Superpave gyratory compaction Ndesign depends on ESALs and climate; VMA and VFA criteria must be met at 4% air voids.

Highway capacity: lane capacity ~2,200 pc/h/ln under ideal conditions; adjust for heavy vehicles with passenger car equivalent (PCE) factors.

Rational method: Q = CiA (US customary, Q in cfs when i in in/h and A in acres); use for drainage areas under ~80 ha; time of concentration sets i duration.

Manning's equation: Q = (1/n) A R^(2/3) S^(1/2) in metric; n ≈ 0.013 for concrete pipe, 0.024 for earth channels.

NRCS curve number: Q = (P − 0.2S)²/(P + 0.8S), S = 25400/CN − 254 (mm); CN from land use and hydrologic soil group.

Water demand: average day, max day (typically 1.5–2.0× average), peak hour (2.5–4× average) drive storage and distribution sizing.

Secondary treatment: BOD5 and TSS limits commonly 30 mg/L each (30/30 standard); activated sludge F/M 0.2–0.4 d⁻¹, SRT 5–15 d for nitrification.

Chlorine disinfection: CT = concentration × contact time; required CT increases with pH and decreases with temperature; maintain free chlorine residual 0.2–0.5 mg/L in distribution.

Hardness = 2.5[Ca²⁺] + 4.1[Mg²⁺] as CaCO3 (mg/L when ions in mg/L); alkalinity titration to pH 4.5 measures total alkalinity.

Open channel flow: Froude number Fr = V/√(gD); Fr < 1 subcritical, Fr = 1 critical, Fr > 1 supercritical. Hydraulic jump sequesters energy below spillways.