Free FE Civil Exam Flashcards

A planar rigid body in equilibrium satisfies ΣFx = 0, ΣFy = 0 and ΣM = 0. Use three independent equations to solve up to three independent reaction unknowns.

For a planar truss, m + r = 2j is a necessary count for static determinacy. Check support arrangement and geometry for stability. The method of joints applies ΣFx = 0 and ΣFy = 0 at each pin.

A composite area has centroid x̄ = Σ(Aᵢx̄ᵢ)/ΣAᵢ. For its area moment about a parallel axis, shift each centroidal value with I = I_c + Ad² before summing.

Convert an observation x to z = (x − μ)/σ. Use the sign and requested tail to select the probability. For a standard normal variable, about 84% of values lie below z = 1.

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.

For constant acceleration, v = v₀ + at, s = s₀ + v₀t + ½at², and v² = v₀² + 2a(s − s₀). With no drag and equal launch and landing heights, projectile range is v₀²sin(2θ)/g.

For a particle, ΣF = ma and net work equals the change in kinetic energy. For planar rigid-body rotation, ΣM about the mass center = Iα.

Compare present worth at the minimum attractive rate of return (MARR), using a common study period. If you use incremental IRR, test whether the extra investment earns at least the MARR.

For a prismatic bar in uniaxial, linear-elastic loading, average axial stress σ = P/A, strain ε = σ/E and axial deformation δ = PL/(AE).

Use σ = My/I for flexure at distance y from the neutral axis and τ = VQ/(Ib) for transverse shear. Q is the first moment of the area beyond the cut and b is the local section width.

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.

With unknown population standard deviation, a normal population or a suitably large sample, and independent observations, use x̄ ± t*·s/√n. The one-sample t critical value uses n − 1 degrees of freedom.

For a downward-positive distributed load w, dV/dx = −w and dM/dx = V. Check interior locations where shear changes sign, concentrated loads and the segment ends for moment extrema.

Specified compressive strength f′c is the design value. Cylinder compressive strength is tested under ASTM C39, normally at 28 days unless the construction documents specify a different age.

For ASTM A992 wide-flange shapes, specified minimum Fy = 50 ksi and minimum Fu = 65 ksi. For standard A36 shapes, minimum Fy = 36 ksi. Structural steel has E ≈ 29,000 ksi (200 GPa).

ASTM C143 measures fresh concrete slump, an indicator of consistency. ASTM C39 tests cylinder compressive strength. ASTM E8/E8M measures metallic tensile properties such as yield and tensile strength.

In water at rest, gauge pressure is p = γh. Fresh water at 5 m gives about 49 kPa. For a submerged plane, compute resultant force using centroidal pressure times area and place the force at the center of pressure.

Slope m = (y₂ − y₁)/(x₂ − x₁). A vertical line has undefined slope. The product of two finite slopes is −1 when their lines are perpendicular.

For steady incompressible flow with no branches, Q = A₁V₁ = A₂V₂. The energy equation balances pressure, velocity and elevation heads, with pump head added and head loss subtracted.

Re = ρVD/μ = VD/ν. For internal pipe flow, values below about 2,000–2,300 are laminar, and above about 4,000 are turbulent. Use the reference’s convention in the transition region.

Manning velocity is V = (k/n)R^(2/3)S_f^(1/2), where R is flow area divided by wetted perimeter and S_f is energy slope. For uniform flow S_f equals the bed slope. Use k = 1 in SI or about 1.49 in U.S. customary units.

Differentiate with respect to the independent variable. If position x(t) = 3t² + 2t, then v(t) = 6t + 2 and acceleration a(t) = 6.

For small catchments, estimate peak runoff as Q ≈ CiA in cfs with i in in/hr and A in acres. In SI with i in mm/hr and A in hectares, Q = CiA/360 in m³/s. Use the intensity for the time of concentration.

If unit price p exceeds variable cost v, break-even quantity is fixed cost divided by (p − v). At that output, revenue equals total cost.

Multiply the distance between sections by the mean of their end areas. With distance in feet and end areas in ft², divide the resulting ft³ by 27 to get yd³.

BOD measures oxygen consumed as microorganisms break down organic matter. Saturated fresh water at 20°C and standard atmospheric pressure holds about 9.1 mg/L of dissolved oxygen.

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.

A conventional treatment train uses coagulation and flocculation to form particles, then sedimentation and filtration to remove them. Disinfection inactivates remaining susceptible pathogens.

Disclose known or potential conflicts to the employer or client when they could affect, or appear to affect, professional judgment or service quality.

When only dead and floor live loads enter this ASCE 7 strength combination, the factored demand is 1.2D + 1.6L. Compare it with design strength φRn. Check other applicable combinations, including 1.4D.

In AISC steel design, ASD compares demand from allowable-strength load combinations with Rn/Ω. LRFD compares factored demand with φRn.

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.

For a singly reinforced rectangular section with yielding tension steel, nominal moment M_n = A_s·f_y·(d − a/2) and equivalent stress-block depth 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.

For a smooth vertical wall and level cohesionless backfill, Rankine gives Ka = tan²(45° − φ′/2) and Kp = tan²(45° + φ′/2). Active pressure develops as the wall moves away, passive as it moves into the soil.

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.

In U.S. customary units, SSD = 1.47·V·t + V²/[30·(a/32.2 + G)], with V in mph, t in seconds, a in ft/s² and G as a signed decimal grade. Use a positive grade uphill and negative downhill.

For a U.S. customary crest vertical curve with S < L and standard stopping-sight-distance heights, L = A·S²/2158. A is the absolute grade difference in percentage points, and S and L are in feet.

Flow q = k·v uses density k and space-mean speed v. In the linear Greenshields model, maximum flow occurs at half the jam density and half the free-flow speed.

Total float = LS − ES = LF − EF. With no imposed finish constraint, activities on the longest path have zero total float. For zero-lag finish-to-start links, free float = earliest successor 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 requires cave-in protection unless the excavation is entirely in stable rock, or it is under 5 ft deep and a competent person finds no indication of a potential cave-in.

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 = √[(ΣLat)² + (ΣDep)²]. Express relative precision as 1:N, with N = total traverse length divided by misclosure. 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.

The NCEES Model Rules place public health, safety and welfare first. Seal only work in your area of competence and under your responsible charge. State boards apply their own laws and rules.