PEC EPE Civil cheat sheet

Flexural design of a singly reinforced rectangular section: nominal moment Mn = As·fy·(d − a/2), where a = As·fy/(0.85·f'c·b); the tension-controlled limit is tensile strain εt ≥ 0.005 at nominal strength.

Balanced/ductility check: reinforcement ratio ρ = As/(b·d) must stay below ρmax tied to εt = 0.005; a section with εt < εt,compression-controlled limits requires either larger section or compression steel.

One-way shear: Vc for non-prestressed members (SI, ACI 318-19) is based on 0.17·λ·√f'c·bw·d for members without axial load and Av ≥ Av,min; otherwise use the size-effect-modified expression with factor λs.

Deflection control: immediate deflection by elastic methods using effective moment of inertia Ie = Ig when service moment Ma ≤ (2/3)Mcr, otherwise Ie interpolates between Mcr and cracking; long-term multiplier applies to sustained load deflection.

Slenderness of columns: for nonsway frames, effects of slenderness may be neglected if klu/r ≤ 34 − 12(M1/M2) and ≤ 40; M1/M2 is positive for single curvature, negative for double curvature.

Steel tension members: nominal strength is the lesser of yielding on gross area (Fy·Ag) and fracture on net effective area (Fu·Ae, Ae = U·An); block shear combines a rupture plane and a yield plane.

Bolted connections: nominal shear strength per bolt depends on whether threads are excluded (0.62·Fub·A) or included (0.45·Fub·A) from the shear plane; bearing and tear-out are checked separately.

Concrete mix and curing: water-cementitious ratio governs strength and durability; 28-day compressive strength is the design basis, and curing moisture retention matters more than total water added for hydration.

Construction sequencing and formwork: form removal depends on in-place strength (e.g., percent of design strength for slabs and beams), not elapsed time alone; reshoring loads must be tracked through the pour sequence.

Effective stress: σ' = σ − u; in a capillary zone above the water table, pore pressure is negative, so effective stress exceeds total stress and apparent cohesion can develop in silty sands.

Terzaghi bearing capacity for a strip footing: qu = c·Nc + q·Nq + 0.5·γ·B·Nγ; N-factors depend on friction angle, and the 0.5·γ·B term vanishes for a footing on the ground surface with no surcharge.

Consolidation: primary settlement Sc = Cc·H/(1+e0)·log10((σ'0 + Δσ)/σ'0) for normally consolidated clay; overconsolidated clay uses Cr until the preconsolidation pressure is reached.

Slope stability and earth pressure: the factor of safety is resisting moment over driving moment for a circular slip surface; Rankine active pressure coefficient Ka = tan²(45° − φ/2).

Darcy's law and flow nets: q = k·i·A; in an isotropic flow net, discharge per unit width = k·H·(Nf/Nd), where Nf is flow channels and Nd is equipotential drops; uplift at a point is total head minus elevation head times unit weight of water.

Open channel flow: Manning's equation Q = (1/n)·A·R^(2/3)·S^(1/2); hydraulic radius R = A/P, and critical flow occurs at Froude number Fr = V/√(g·D) = 1.

Rational method for peak runoff: Q = C·i·A with consistent units; the time of concentration sets the design rainfall intensity, and the runoff coefficient rises with imperviousness and antecedent moisture.

Pavement and traffic loading: ESALs convert mixed traffic to 18-kip equivalent single-axle loads using axle-load equivalency factors; structural number SN = a1·D1 + a2·D2·m2 + a3·D3·m3.

Horizontal curve geometry: degree of curve and radius relate by R = 5729.58/D (US customary, arc definition); superelevation and side friction together supply the centripetal demand, e + f = V²/(15R) with V in mph and R in feet.