Free FE Civil Exam Flashcards

A planar body is in equilibrium when ΣFx = 0, ΣFy = 0, and ΣM = 0 — three independent equations solving up to three unknown reactions. Statics underpins every structural and geotechnical topic on the FE Civil exam.

A planar truss is statically determinate when members m plus reactions r equal twice the joints (m + r = 2j). The method of joints then writes two equilibrium equations per pin to solve member forces.

x̄ = Σ(Aᵢx̄ᵢ)/ΣAᵢ. Locate the centroid before replacing a distributed load with its resultant. Rectangular section I = bh³/12 about its centroid; circular section I = πd⁴/64.

Moment of inertia about a parallel axis is I = Ī + Ad², where Ī is the centroidal value and d is the offset distance. A recurring FE Reference Handbook lookup for built-up sections.

On the verge of motion, friction equals the maximum static value F = μₛN, not μₖN. Below impending slip, friction is only as large as equilibrium requires.

v = v₀ + at, s = s₀ + v₀t + ½at², and v² = v₀² + 2a(s − s₀). Valid only when acceleration is constant. Projectile range on level ground is R = v₀²sin(2θ)/g, maximized at 45°.

For a particle, ΣF = ma. For rigid-body rotation about the mass center, ΣM = Iα. Draw a dynamic free-body diagram and keep mass units consistent before substituting.

Work-energy: net work equals change in kinetic energy, W = ΔKE = ½m(v₂² − v₁²). Linear impulse-momentum: ΣF·Δt = m(v₂ − v₁); momentum is conserved when no external impulse acts.

Axial normal stress σ = P/A; elastic axial deformation δ = PL/(AE); Hooke's law σ = Eε. These connect external load to stress, strain, and member shortening or elongation.

Bending stress σ = Mc/I, maximum at the extreme fiber. Transverse shear stress τ = VQ/(Ib), where Q is the first moment of the area above the cut. Get a moment diagram before applying either.

τ = Tr/J, with J = πd⁴/32 for a solid circular shaft (πr⁴/2). Applies directly to circular sections only; other cross-sections need the handbook's specific relationships.

Pcr = π²EI/(KL)². Effective-length factor K: 1.0 pinned-pinned, 0.5 fixed-fixed, 2.0 fixed-free. Buckling controls slender compression members and uses the weak-axis I.

The slope of the shear diagram equals the load; the slope of the moment diagram equals the shear (dM/dx = V). Maximum bending moment occurs where shear crosses zero.

Concrete is strong in compression but weak in tension. Design compressive strength f′c is measured on 28-day cylinders per ASTM C39. Concrete behaves brittlely and fails without significant yielding.

ASTM A992 (wide-flange) has Fy = 50 ksi, Fu = 65 ksi; ASTM A36 has Fy = 36 ksi. Steel modulus E ≈ 29,000 ksi (200 GPa). Steel is ductile with a defined yield plateau.

Concrete slump (ASTM C143) measures workability; cylinder compression (ASTM C39) gives f′c; steel tension (ASTM E8) yields Fy and Fu. Knowing the test reference answers many materials items.

p = γh. For fresh water γ = 9.81 kN/m³ (62.4 lb/ft³), so 5 m of water gives ≈ 49 kPa. Resultant force on a submerged surface uses pressure at the centroid acting at the center of pressure.

For incompressible flow, Q = A₁V₁ = A₂V₂. Halving the diameter quarters the area and quadruples the velocity. The starting point for most pipe and channel-flow problems.

p/γ + V²/2g + z + h_pump = (downstream p/γ + V²/2g + z) + h_L. Include pump head and head loss whenever the system has machinery or significant friction.

Re = ρVD/μ = VD/ν. Pipe flow is laminar below Re ≈ 2,100 and turbulent above Re ≈ 4,000. Darcy-Weisbach head loss is h_f = f(L/D)(V²/2g); Hazen-Williams uses empirical coefficient C for water.

V = (1/n)R^(2/3)S^(1/2) in SI; multiply by 1.486 for US customary units. n is the roughness coefficient and S the channel slope — the core open-channel flow tool.

R = A/P, the flow area divided by the wetted perimeter. For a full circular pipe, R = D/4. Used inside Manning's equation and friction-loss calculations.

Q = CiA. In US units Q is in cfs with rainfall intensity i in in/hr and area A in acres; C is the dimensionless runoff coefficient (higher for impervious surfaces).

Q = kiA, where k is hydraulic conductivity, i = dh/dL is the hydraulic gradient, and A is the cross-sectional area of flow. Governs seepage and well-flow problems.

Critical flow occurs at Froude number Fr = 1. Specific energy E = y + V²/2g is minimized at the critical depth, the dividing line between subcritical and supercritical flow.

BOD measures the oxygen consumed by microbes degrading organic pollution; higher BOD means more pollution. Dissolved-oxygen saturation in fresh water is ≈ 9 mg/L at 20°C and pH 7.

Accumulation = Inflow − Outflow + Generation. At steady state with no reaction, mass in equals mass out. The setup behind most dilution and reactor FE Civil problems.

Conventional sequence under the EPA Safe Drinking Water Act: coagulation → flocculation → sedimentation → filtration → disinfection. Each step removes progressively finer particles and pathogens.

The six National Ambient Air Quality Standards pollutants are CO, lead (Pb), NO₂, ozone (O₃), SO₂, and particulate matter (PM₁₀/PM₂.₅).

Basic ASCE 7 Load and Resistance Factor Design combination for typical floor gravity design is 1.2D + 1.6L. LRFD compares factored load to φ·R_n (design strength).

Allowable Strength Design compares service-level demand to nominal strength divided by safety factor Ω. LRFD compares factored loads to φ·R_n. Both target adequate margin against failure by different formats.

For a uniform load w over span L: maximum moment = wL²/8 at midspan and maximum shear = wL/2 at the supports. One of the most-used standard cases on the exam.

When tension steel yields, nominal moment M_n = A_s·f_y·(d − a/2), with depth of the equivalent stress block a = A_s·f_y / (0.85·f′c·b).

Dead loads (permanent self-weight), live loads (occupancy/use), plus environmental wind, snow, and seismic loads. ASCE 7 governs magnitudes and load combinations.

G = gravel, S = sand, M = silt, C = clay, O = organic. Well-graded coarse soils get suffix W, poorly graded get P (e.g., SW, GP). Based on grain size and Atterberg limits.

Void ratio e = V_v/V_s; porosity n = V_v/V_total; degree of saturation S = V_w/V_v. These relate soil volumes of solids, water, and air for weight-volume problems.

σ′ = σ − u, where σ is total stress and u is pore water pressure. Effective stress controls soil strength and consolidation — pore pressure reduces the stress carried by the soil skeleton.

Ultimate bearing capacity of a strip footing: q_ult = c·N_c + q·N_q + 0.5·γ·B·N_γ. The N factors depend on the soil friction angle; the three terms are cohesion, surcharge, and footing-width contributions.

Active and passive earth pressures use coefficients Ka = tan²(45 − φ/2) and Kp = tan²(45 + φ/2). Active pressure acts when a wall moves away from soil; passive when it pushes into it.

R = V² / [15·(e + f)] in US customary units, with V in mph and superelevation e and side-friction factor f as decimals. Sharper curves need more superelevation or lower speed.

SSD = 1.47·V·t + V² / [30·(a/32.2 ± G)], where perception-reaction time t is commonly 2.5 s, a is deceleration, and G the grade. Grade lengthens SSD downhill, shortens it uphill.

For stopping sight distance with sight distance less than curve length, L = A·S² / 2158 (AASHTO design control), where A is the algebraic grade difference in percent.

Flow q = k·v (density times speed). Maximum flow q_max occurs at half the jam density and half the free-flow speed. The fundamental relationship of uninterrupted traffic flow.

Total float = LS − ES = LF − EF. Activities with zero total float lie on the critical path and directly control project duration. Free float = (earliest following ES) − current EF.

Cost Variance CV = EV − AC; Schedule Variance SV = EV − PV; SPI = EV/PV; CPI = EV/AC. Values below 1.0 (or negative variances) indicate over budget or behind schedule.

OSHA 1926 Subpart P requires a protective system — sloping, shoring, or shielding — for excavations 5 ft or deeper unless made entirely in stable rock.

New elevation = known benchmark elevation + backsight (BS) − foresight (FS). The backsight adds to the height of instrument; the foresight subtracts to the new point.

Linear misclosure = √(ΣLat² + ΣDep²). Precision = misclosure / total traverse length, expressed as a ratio (e.g., 1:10,000). Departure = L·sin(azimuth); Latitude = L·cos(azimuth).

Single-payment present worth P = F(P/F, i, n) = F/(1+i)ⁿ; capital recovery A = P(A/P, i, n). Draw the cash-flow diagram first; the interest period must match the cash-flow period.

Under the NCEES Model Rules, engineers must hold the public's safety, health, and welfare above duties to clients, employers, and themselves. Engineers may seal only work in their competence and responsible charge.