Principles and Practice of Engineering Exam (PE) Civil Engineering (PE Civil) Syllabus

In masonry design, what compressive stress and modulus relationship is commonly used for the modulus of elasticity of clay/concrete masonry?

$E_m = 700 f'_m$ for clay masonry and $E_m = 900 f'_m$ for concrete masonry, where $f'_m$ is the specified masonry compressive strength.

Define void ratio $e$ and porosity $n$ for a soil, and give the relationship between them.

$e = \dfrac{V_v}{V_s}$ (voids/solids), $n = \dfrac{V_v}{V}$ (voids/total). Relationship: $n = \dfrac{e}{1+e}$ and $e = \dfrac{n}{1-n}$.

State the phase relationship linking specific gravity, water content, void ratio, and degree of saturation.

$S e = w G_s$, where $S$ is degree of saturation, $e$ void ratio, $w$ water content, and $G_s$ specific gravity of solids.

What is the formula for the dry unit weight of soil in terms of $G_s$, $\gamma_w$, and void ratio?

$\gamma_d = \dfrac{G_s \gamma_w}{1 + e}$, where $\gamma_w$ is the unit weight of water ($62.4\ \text{lb/ft}^3$ or $9.81\ \text{kN/m}^3$).

In the Unified Soil Classification System (USCS), what coefficients define a well-graded soil and what are the criteria for well-graded gravel?

$C_u = \dfrac{D_{60}}{D_{10}}$ (uniformity) and $C_c = \dfrac{D_{30}^{2}}{D_{10}\,D_{60}}$ (curvature). Well-graded gravel (GW): $C_u \geq 4$ and $1 \leq C_c \leq 3$.

What are the Atterberg limits, and how is the plasticity index defined?

Liquid limit (LL), plastic limit (PL), and shrinkage limit (SL) are water contents at consistency boundaries. Plasticity index $PI = LL - PL$.

On the USCS plasticity (Casagrande) chart, what is the equation of the A-line?

$PI = 0.73(LL - 20)$. Soils above the A-line are clays (CL/CH); below are silts/organics (ML/MH/OL/OH).

What is the standard penetration test (SPT) and what does the N-value represent?

The SPT drives a split-spoon sampler with a $140\ \text{lb}$ hammer falling $30\ \text{in}$. The N-value is the blow count for the last $12\ \text{in}$ (second and third $6\ \text{in}$ increments) of a $18\ \text{in}$ drive.

What is the corrected SPT energy-normalized value $N_{60}$ and the overburden-corrected value $(N_1)_{60}$?

$N_{60} = N \cdot \dfrac{E_m}{60}\,C_B C_S C_R$ (energy/borehole/sampler/rod corrections); $(N_1)_{60} = C_N N_{60}$ with overburden factor $C_N = \sqrt{\dfrac{p_a}{\sigma'_{v0}}}$.

Name the principal in-situ subsurface exploration tests besides the SPT used to characterize soils.

Cone penetration test (CPT), vane shear test (for soft clays), pressuremeter test, dilatometer test (DMT), and geophysical methods (seismic refraction, resistivity).

State Terzaghi's general bearing capacity equation for a shallow strip footing.

$q_{ult} = c N_c + q N_q + \tfrac{1}{2}\gamma B N_\gamma$, where $c$ is cohesion, $q$ surcharge, $\gamma$ unit weight, $B$ footing width, and $N_c, N_q, N_\gamma$ are bearing capacity factors of $\phi$.

How is the allowable bearing capacity obtained from ultimate bearing capacity, and what is the net ultimate?

$q_{all} = \dfrac{q_{ult}}{FS}$ with typical $FS = 3$; net ultimate $q_{net} = q_{ult} - \gamma D_f$ subtracts the overburden at the footing base depth $D_f$.

What is the elastic (immediate) settlement formula for a flexible footing on an elastic half-space?

$S_e = q B \dfrac{(1-\mu^{2})}{E_s} I_f$, where $q$ is contact pressure, $B$ width, $\mu$ Poisson's ratio, $E_s$ soil modulus, and $I_f$ an influence factor.

What is the consolidation settlement equation for a normally consolidated clay layer?

$S_c = \dfrac{C_c H}{1 + e_0}\log_{10}\!\left(\dfrac{\sigma'_0 + \Delta\sigma'}{\sigma'_0}\right)$, where $C_c$ is the compression index, $H$ layer thickness, $e_0$ initial void ratio, $\sigma'_0$ initial effective stress.

What is Terzaghi's time factor relation governing the rate of 1D consolidation?

$T_v = \dfrac{c_v t}{H_{dr}^{2}}$, where $c_v$ is the coefficient of consolidation, $t$ time, and $H_{dr}$ the longest drainage path. For $U \leq 60\%$, $T_v \approx \dfrac{\pi}{4}U^{2}$.

State the Rankine active and passive lateral earth pressure coefficients for a level cohesionless backfill.

$K_a = \tan^{2}\!\left(45^\circ - \tfrac{\phi}{2}\right) = \dfrac{1-\sin\phi}{1+\sin\phi}$ and $K_p = \tan^{2}\!\left(45^\circ + \tfrac{\phi}{2}\right) = \dfrac{1+\sin\phi}{1-\sin\phi}$.

What is the factor of safety for an infinite slope of cohesionless soil (dry) at angle $\beta$?

$FS = \dfrac{\tan\phi}{\tan\beta}$, where $\phi$ is the friction angle and $\beta$ the slope angle. The slope is stable when $\beta < \phi$.

State the Mohr-Coulomb shear strength equation for soil.

$\tau_f = c' + \sigma'\tan\phi'$, where $c'$ is effective cohesion, $\sigma'$ effective normal stress, and $\phi'$ effective friction angle.

What is the continuity equation and the Bernoulli (energy) equation for steady incompressible pipe flow?

Continuity: $Q = A_1 V_1 = A_2 V_2$. Bernoulli/energy: $\dfrac{p_1}{\gamma} + \dfrac{V_1^{2}}{2g} + z_1 = \dfrac{p_2}{\gamma} + \dfrac{V_2^{2}}{2g} + z_2 + h_L$.

State the Darcy-Weisbach equation for head loss in pipe flow.

$h_f = f \dfrac{L}{D}\dfrac{V^{2}}{2g}$, where $f$ is the friction factor, $L$ pipe length, $D$ diameter, $V$ velocity, $g$ gravitational acceleration.

State the Hazen-Williams equation form for head loss (US units) and define $C$.

$V = 1.318\,C R^{0.63} S^{0.54}$ (fps), where $C$ is the Hazen-Williams roughness coefficient, $R$ hydraulic radius, $S$ slope of energy grade line. $C \approx 100$ for old cast iron, $\approx 130\text{--}150$ for new pipe.

State Manning's equation for open-channel flow (US units) and the Froude number for flow regime.

$V = \dfrac{1.49}{n}R^{2/3}S^{1/2}$, with $Q=VA$. Froude number $Fr = \dfrac{V}{\sqrt{g D}}$: $Fr<1$ subcritical, $Fr=1$ critical, $Fr>1$ supercritical.

What is the Rational Method for peak stormwater runoff, and what does each term represent?

$Q = C i A$, where $Q$ is peak discharge (cfs), $C$ the dimensionless runoff coefficient, $i$ rainfall intensity (in/hr), and $A$ drainage area (acres). Valid for small watersheds ($A \lesssim 200$ acres).

Define the time of concentration and its role in the Rational Method.

$t_c$ is the time for runoff to travel from the hydraulically most distant point to the outlet. Rainfall intensity $i$ is read from an IDF curve at duration equal to $t_c$, since that produces the peak flow.

What is the design basis (loading) for sizing an activated-sludge or sedimentation process — give the surface overflow rate definition?

Surface overflow rate $SOR = \dfrac{Q}{A_s}$ (gpd/ft$^2$), the design flow divided by the basin surface area; particles with settling velocity $v_s \geq SOR$ are removed in an ideal settling tank.

What is the relationship for chlorine disinfection contact (CT concept) and BOD removal first-order kinetics?

Disinfection: $CT$ = residual concentration $\times$ contact time governs log-inactivation. First-order BOD: $L_t = L_0 e^{-k t}$, so $BOD_t = L_0(1 - e^{-kt})$ where $L_0$ is ultimate BOD and $k$ the deoxygenation rate.

On a horizontal highway curve, what is the relationship among design speed, radius, superelevation, and side friction?

$e + f = \dfrac{V^{2}}{15 R}$ (US units, $V$ in mph, $R$ in ft), where $e$ is superelevation rate, $f$ the side friction factor, and $R$ the curve radius.

What is the stopping sight distance (SSD) equation on a grade?

$SSD = 1.47 V t + \dfrac{V^{2}}{30\left(\frac{a}{32.2} \pm G\right)}$, with $V$ in mph, $t$ perception-reaction time ($\approx 2.5$ s), $a$ deceleration ($\approx 11.2\ \text{ft/s}^2$), and $G$ grade (decimal, + uphill).

For a crest vertical curve, what is the minimum length based on sight distance when $S < L$?

$L = \dfrac{A S^{2}}{2158}$ (US units, headlight/eye-object heights standard), where $A$ is the algebraic difference in grades (%) and $S$ the sight distance (ft).

State the fundamental relationship of traffic flow among flow, speed, and density.

$q = k v$, where $q$ is flow rate (veh/hr), $k$ density (veh/mi), and $v$ space-mean speed (mi/hr). Maximum flow (capacity) occurs at the critical density.

What is the equation for capacity / saturation flow and the Highway Capacity Manual peak hour factor?

Peak Hour Factor $PHF = \dfrac{V}{4 \times V_{15}}$, the hourly volume divided by four times the peak 15-minute volume; design flow $= \dfrac{V}{PHF}$.

What is the AASHTO flexible pavement structural number relationship?

$SN = a_1 D_1 + a_2 D_2 m_2 + a_3 D_3 m_3$, where $a_i$ are layer coefficients, $D_i$ layer thicknesses, and $m_i$ drainage coefficients for unbound layers.

In pavement and materials, how are equivalent single axle loads (ESALs) used and what defines the standard axle?

Traffic is converted to repetitions of an $18{,}000\ \text{lb}$ (18-kip) single-axle load via load equivalency factors $LEF \approx \left(\dfrac{W}{18}\right)^{4}$; design ESALs accumulate over the analysis period.

What is the productivity / learning-curve and the basic construction productivity rate definition?

Productivity $= \dfrac{\text{output (units)}}{\text{labor-hours}}$. Learning curve: $T_n = T_1 n^{b}$ with $b = \dfrac{\log(\text{learning rate})}{\log 2}$, where $T_n$ is the time for the $n$-th unit.

In CPM scheduling, define total float and how the critical path is identified.

Total float $TF = LS - ES = LF - EF$ (late minus early start/finish). The critical path is the longest path through the network where $TF = 0$; it sets the project duration.

What are the forward-pass and backward-pass rules in CPM activity-on-node scheduling?

Forward pass: $EF = ES + D$, $ES = \max(EF \text{ of predecessors})$. Backward pass: $LS = LF - D$, $LF = \min(LS \text{ of successors})$, where $D$ is activity duration.

In construction safety, what does OSHA require for excavation/trench protective systems and at what depth?

OSHA (29 CFR 1926 Subpart P) requires a protective system (sloping, shoring, or shielding) for trenches $\geq 5\ \text{ft}$ deep (unless in stable rock); a competent person must inspect daily and classify the soil (Type A, B, or C).

What maximum allowable slope does OSHA assign to Type A, B, and C soils for excavations up to 20 ft?

Type A: $\tfrac{3}{4}:1$ ($53^\circ$); Type B: $1:1$ ($45^\circ$); Type C: $1\tfrac{1}{2}:1$ ($34^\circ$), expressed as horizontal:vertical.

In construction contracts, compare lump-sum, unit-price, and cost-plus contract types.

Lump-sum: fixed total price, contractor bears quantity risk. Unit-price: payment per measured unit of work, suits uncertain quantities. Cost-plus: owner reimburses actual costs plus a fee, used when scope is undefined; risk lies with owner.

What is the earned value management formula for cost and schedule variance, and the performance indices?

$CV = EV - AC$, $SV = EV - PV$; $CPI = \dfrac{EV}{AC}$, $SPI = \dfrac{EV}{PV}$. Values $>1$ (or positive variance) indicate under budget / ahead of schedule.