PE Civil cheat sheet

Water-cement ratio by weight controls concrete compressive strength: lowering w/c from about 0.60 to 0.40 raises 28-day strength and durability but reduces workability.

Slump test (ASTM C143) measures concrete consistency; acceptance uses the specified slump plus ACI 301 tolerances, not a single target value.

Standard concrete acceptance specimens are 6 x 12 in. cylinders moist-cured and tested in compression per ASTM C39; the 28-day result is compared to design f'c.

OSHA 29 CFR 1926 Subpart P requires a protective system (sloping, benching, shoring, or shield) for trenches 5 ft deep or more, and a ladder, ramp, or stair within 25 ft of lateral travel.

Crane lifting capacity decreases as load radius and boom length increase; capacity must be read from the manufacturer's load chart at the actual radius and configuration.

The critical path is the longest-duration path through a CPM network; its activities have zero total float and its length sets the project completion date.

Earned value indices: CPI = EV/AC (below 1.0 means over budget) and SPI = EV/PV (below 1.0 means behind schedule).

Standard Proctor (ASTM D698) uses a 5.5-lb hammer, 12-in. drop, 3 layers and 25 blows; Modified Proctor (ASTM D1557) uses a 10-lb hammer, 18-in. drop, 5 layers and 25 blows, giving a higher maximum dry density.

Wellpoint systems draw down groundwater roughly 15 to 20 ft per stage; deeper dewatering requires multistage wellpoints, deep wells, or ejectors.

Effective stress is sigma-prime = total stress minus pore pressure (sigma' = sigma - u); consolidation, shear strength, and lateral earth pressure all depend on effective rather than total stress.

Terzaghi ultimate bearing capacity for a strip footing: qu = cNc + qNq + 0.5gammaB*Ngamma, where q is the surcharge at footing base and N factors depend on the friction angle.

Rankine active coefficient Ka = tan^2(45 deg - phi/2) = (1 - sin phi)/(1 + sin phi); the passive coefficient Kp = 1/Ka = tan^2(45 deg + phi/2).

One-dimensional primary consolidation settlement: Sc = [Cc*H/(1 + e0)] * log10[(sigma'0 + delta-sigma)/sigma'0], where Cc is the compression index from the e-log p curve.

Plasticity index PI = LL - PL; PI of 30 or more together with LL of 50 or more identifies a high-plasticity clay (CH) per USCS.

Standard Penetration Test: a 2-in. split spoon is driven 18 in. with a 140-lb hammer on a 30-in. drop; N is the blow count over the final 12 in., and N above 50 is commonly treated as refusal.

Liquefaction is most likely in saturated, loose to medium-dense clean sands with low corrected (N1)60, a shallow water table, and strong cyclic seismic loading.

Axial pile capacity is Qult = Qpoint + Qshaft; in saturated clay, unit shaft resistance is typically taken as alpha*su with alpha near 1.0 for soft clays and lower for stiff clays.

Pile group efficiency is generally less than 1.0 for spacings below about 3 diameters; common design spacings are 2.5 to 3 diameters.

ACI 318 strength reduction factors: phi = 0.90 for tension-controlled flexure, 0.75 for shear and torsion, and 0.65 for tied compression-controlled columns (0.75 spiral).

Nominal moment for a singly reinforced rectangular section: Mn = Asfy(d - a/2), where a = Asfy/(0.85f'c*b).

Minimum beam reinforcement: As,min = max(3*sqrt(f'c)/fy, 200/fy) * bw * d, with f'c and fy in psi.

A section is tension-controlled when net tensile strain in the extreme steel layer at nominal strength is at least 0.005; compression-controlled corresponds to strain of 0.002 or less.

Basic LRFD combination is 1.2D + 1.6L (plus other applicable cases); design requires phi*Rn >= Ru. ASD compares service loads to allowable stress.

Concrete shear strength for nonprestressed members without axial load: Vc = 2*sqrt(f'c)bwd in psi units; excess shear requires stirrups or shear reinforcement.

ACI minimum thickness for one-way slabs (fy = 60 ksi, normal-weight concrete): l/20 simply supported, l/24 one end continuous, l/28 both ends continuous, l/10 cantilever.

IBC/ASCE 7 deflection limits: L/360 for floors under live load and L/240 for roof members under live load (L/180 for plaster ceilings).

Nominal shear strength of a bolt is Rn = Fnv*Ab, where Ab is the unthreaded body area; threads in the shear plane reduce the effective area and strength.

AASHTO stopping sight distance: SSD = 1.47Vt + V^2/[30*(f +/- G)], with V in mph, t in seconds (typically 2.5 s), f the side friction factor, and G the grade in decimal form.

Superelevation balance: e + f = V^2/(15*R), with V in mph and R in feet; e is the superelevation rate and f the side friction factor.

Arc-definition degree of curve: R = 5729.58/D in U.S. customary units, so a 1-degree curve has a radius of about 5,730 ft.

Horizontal curve geometry: tangent T = Rtan(delta/2) and length L = 100delta/D (delta in degrees), or L = R*delta when delta is in radians.

Vertical curve length: L = K*A, where A is the algebraic difference in grades in percent and K is the rate of vertical curvature (ft per percent).

Peak hour factor: PHF = peak-hour volume divided by four times the peak 15-minute volume; values approach 1.0 for uniformly distributed flow.

AASHTO flexible pavement structural number: SN = a1D1 + a2D2m2 + a3D3*m3, with layer coefficients a and drainage coefficients m.

Level of service grades run A through F: A is free flow with low density, E is at or near capacity, and F is breakdown or forced flow.

The AASHTO side friction factor f decreases as design speed increases, so higher-speed curves require larger radius or more superelevation.

Manning equation in U.S. customary units: Q = (1.486/n)AR^(2/3)*S^(1/2), where R = A/P is the hydraulic radius and S is the channel slope; the SI constant is 1.0.

Rational method peak runoff: Q = CiA, giving cfs when i is rainfall intensity in in/hr and A is drainage area in acres; use the time of concentration to select i from the IDF curve.

Froude number Fr = V/sqrt(g*D) with D the hydraulic depth; Fr < 1 is subcritical, Fr = 1 critical, and Fr > 1 supercritical flow.

Detention time = volume/flow; keep units consistent and note that short-circuiting makes actual detention time shorter than the theoretical value.

BOD exertion follows first-order kinetics: BODt = L0*(1 - e^(-k*t)), with L0 the ultimate carbonaceous demand and k the reaction rate constant in 1/day.

Chlorine demand equals the applied dose minus the residual chlorine remaining after the contact period; breakpoint chlorination occurs where residual rises sharply.

Darcy's law for groundwater flow: Q = KiA, and aquifer transmissivity T = K*b, where b is saturated thickness.

Sharp-crested weir discharge: Q = 3.33LH^1.5 in U.S. customary units, with L the crest length and H the head above the crest.

NRCS (SCS) curve number runoff: Q = (P - 0.2S)^2/(P + 0.8S) and S = 1000/CN - 10, all in inches, with CN ranging from about 30 to 100.

water cement ratio

slump test

critical path method

OSHA trench protective system