PE Civil (NCEES Principles and Practice of Engineering) — All Questions
30 questions
A simply supported beam of span 8 m carries a uniformly distributed load of 4 kN/m over its full length. What is the vertical reaction at each support?
- a.16 kN✓
- b.32 kN
- c.64 kN
- d.8 kN
The total load is w·L = 4 x 8 = 32 kN. By symmetry each support carries half: 32/2 = 16 kN, which also equals w·L/2. Symmetric loading always splits equally between the two supports.
For that same simply supported beam (span 8 m, uniform load 4 kN/m), what is the maximum bending moment?
- a.32 kN·m✓
- b.16 kN·m
- c.256 kN·m
- d.64 kN·m
The maximum moment for a simply supported beam under a uniform load occurs at midspan and equals w·L^2/8 = 4 x 8^2 / 8 = 4 x 64 / 8 = 32 kN·m. The moment diagram is parabolic, peaking at the center.
What is the moment of inertia about the centroidal axis of a rectangular cross-section 200 mm wide and 300 mm deep (bending about the strong axis)?
- a.9.0x10^8 mm^4
- b.2.25x10^8 mm^4
- c.1.8x10^9 mm^4
- d.4.5x10^8 mm^4✓
For a rectangle, I = b·h^3/12 where h is the dimension parallel to the load. I = 200 x 300^3 / 12 = 200 x 2.7x10^7 / 12 = 4.5x10^8 mm^4. Depth is cubed, so orienting the section deep-side up sharply increases stiffness.
What is the section modulus of a rectangular cross-section 200 mm wide and 300 mm deep about its strong axis?
- a.9.0x10^6 mm^3
- b.3.0x10^6 mm^3✓
- c.6.0x10^6 mm^3
- d.1.5x10^6 mm^3
Section modulus S = b·h^2/6 = 200 x 300^2 / 6 = 200 x 90,000 / 6 = 3.0x10^6 mm^3. Bending stress is M/S, so a larger section modulus lowers the stress for a given moment.
What is the specified minimum yield strength, Fy, of ASTM A36 structural steel?
- a.60 ksi
- b.29,000 ksi
- c.50 ksi
- d.36 ksi✓
A36 steel has a minimum yield strength of 36 ksi (about 250 MPa), the value in its designation. A992 steel is 50 ksi and Grade 60 rebar is 60 ksi; 29,000 ksi is steel's modulus of elasticity, not a strength.
In LRFD design, which load combination correctly factors dead load (D) and live load (L) for a basic gravity case?
- a.1.2D + 1.6L✓
- b.0.9D + 1.6L
- c.1.4D + 1.7L
- d.1.0D + 1.0L
The governing ASCE 7 strength combination for dead plus live load is 1.2D + 1.6L. The higher factor on live load reflects its greater uncertainty. The 1.4D + 1.7L form is the older ACI ultimate-strength combination, not current LRFD.
A simply supported beam of span 6 m carries a single concentrated load of 20 kN at midspan. What is the maximum bending moment?
- a.60 kN·m
- b.15 kN·m
- c.120 kN·m
- d.30 kN·m✓
For a central point load on a simply supported beam, the maximum moment is P·L/4 = 20 x 6 / 4 = 30 kN·m. The moment diagram is triangular, peaking under the load.
What is the total vertical stress at a depth of 5 m in a soil with unit weight 18 kN/m^3 (water table well below)?
- a.18 kPa
- b.23 kPa
- c.45 kPa
- d.90 kPa✓
Total vertical stress is the weight of overlying soil: sigma = gamma·h = 18 x 5 = 90 kPa. Stress accumulates linearly with depth, analogous to hydrostatic pressure in a fluid.
At a point 4 m below the water table, the saturated unit weight is 20 kN/m^3 and water unit weight is 10 kN/m^3. What is the effective vertical stress?
- a.120 kPa
- b.40 kPa✓
- c.80 kPa
- d.0 kPa
Total stress sigma = 20 x 4 = 80 kPa; pore pressure u = 10 x 4 = 40 kPa. Terzaghi's principle gives effective stress sigma' = sigma - u = 80 - 40 = 40 kPa. Effective stress, not total stress, controls soil strength and settlement.
Using Rankine theory, what is the active earth pressure coefficient Ka for a cohesionless soil with friction angle 30 degrees?
- a.0.5
- b.0.33✓
- c.3.0
- d.1.0
Ka = tan^2(45 - phi/2) = tan^2(45 - 15) = tan^2(30) = (0.577)^2 = 0.333. The active case (wall moving away from the soil) gives the minimum lateral pressure; the passive coefficient would be its reciprocal, 3.0.
What is the at-rest earth pressure coefficient K0 for a normally consolidated sand with friction angle 30 degrees (Jaky's equation)?
- a.0.87
- b.1.0
- c.0.5✓
- d.0.33
Jaky's equation gives K0 = 1 - sin(phi) = 1 - sin(30) = 1 - 0.5 = 0.5. The at-rest condition applies when the wall does not move, so K0 falls between the active and passive coefficients.
A water table that was at the ground surface is lowered by dewatering. What happens to the effective stress at a point that remains below the new water table?
- a.It is unchanged
- b.It increases✓
- c.It decreases
- d.It becomes zero
Lowering the water table reduces pore water pressure while total stress changes little, so effective stress sigma' = sigma - u increases. This rise in effective stress is what drives consolidation settlement when sites are dewatered.
A soil sample has a total (moist) unit weight of 20 kN/m^3 at a water content of 25%. What is its dry unit weight?
- a.16 kN/m^3✓
- b.20 kN/m^3
- c.25 kN/m^3
- d.15 kN/m^3
Dry unit weight gamma_d = gamma / (1 + w), where w is the decimal water content. gamma_d = 20 / (1 + 0.25) = 20 / 1.25 = 16 kN/m^3. The dry unit weight removes the weight of pore water and is used to assess compaction.
Using the Rational Method, what is the peak runoff for a 20-acre watershed with runoff coefficient C = 0.5 and rainfall intensity i = 3 in/hr?
- a.3 cfs
- b.60 cfs
- c.30 cfs✓
- d.10 cfs
The Rational Method is Q = C·i·A, where in U.S. units i is in in/hr and A in acres, giving Q directly in cfs (the unit conversion factor is approximately 1). Q = 0.5 x 3 x 20 = 30 cfs. The method suits small urban drainage areas.
Water flows at 2 m/s through a channel with cross-sectional flow area 0.5 m^2. What is the discharge?
- a.0.5 m^3/s
- b.2 m^3/s
- c.1 m^3/s✓
- d.4 m^3/s
The continuity equation gives discharge Q = V·A = 2 x 0.5 = 1 m^3/s. For steady incompressible flow, discharge is constant along the channel even as area and velocity vary.
By Manning's equation, if the channel slope is doubled (all else equal), the flow velocity increases by approximately what factor?
- a.4
- b.1.41✓
- c.1
- d.2
Manning's velocity is V = (1/n)·R^(2/3)·S^(1/2), so velocity is proportional to the square root of slope. Doubling S multiplies velocity by sqrt(2) = 1.41. Slope has a weaker-than-linear effect on velocity.
The resultant hydrostatic force on a vertical rectangular gate holding back water acts at what location, measured from the bottom of the gate?
- a.H/3 above the bottom✓
- b.2H/3 above the bottom
- c.H/4 above the bottom
- d.H/2 (the centroid)
Because hydrostatic pressure increases linearly with depth, the pressure distribution is triangular and its resultant acts at the centroid of that triangle, which is H/3 above the bottom (or 2H/3 below the surface). This is the center of pressure.
In the Rational Method, the design storm duration is typically taken equal to what quantity so that the entire watershed contributes to peak flow?
- a.The return period
- b.The storm frequency
- c.The time of concentration✓
- d.One hour
Peak runoff occurs when the storm duration equals the time of concentration, the time for runoff to travel from the hydraulically most distant point to the outlet. At that duration the whole watershed contributes simultaneously, maximizing the peak.
What is the degree of curve (arc definition) for a horizontal curve with radius 1,000 ft?
- a.5.73 degrees✓
- b.11.46 degrees
- c.1.0 degrees
- d.2.86 degrees
By the arc definition, D = 5,729.58 / R = 5,729.58 / 1,000 = 5.73 degrees. The degree of curve is the central angle subtending a 100-ft arc; a larger radius gives a flatter (smaller-degree) curve.
Stopping sight distance (SSD) is defined as the sum of the brake-reaction distance and which other component?
- a.The roadway grade
- b.The horizontal curve length
- c.The braking (deceleration) distance✓
- d.The superelevation runoff
SSD = brake-reaction distance (driver perception-reaction time times speed) + braking distance (distance to decelerate to a stop). Both components grow with speed, so SSD increases sharply at higher design speeds.
Using the fundamental traffic-flow relationship, what is the flow rate for a density of 40 veh/mi and a space-mean speed of 60 mph?
- a.100 veh/hr
- b.1.5 veh/hr
- c.2,400 veh/hr✓
- d.240 veh/hr
The fundamental relationship is flow = density x speed: q = k·v = 40 x 60 = 2,400 veh/hr. This links the three primary traffic-stream variables and defines capacity at the flow's peak.
On a horizontal curve, superelevation (banking of the roadway) is provided primarily to counteract what?
- a.The vertical grade
- b.The lateral (centripetal) demand of vehicles rounding the curve✓
- c.The pavement thickness requirement
- d.The stopping sight distance
Superelevation tilts the roadway inward so that a component of the vehicle's weight, together with side friction, supplies the centripetal force needed to turn. This reduces reliance on tire friction and improves safety and comfort on curves.
A crest vertical curve is 200 ft long and connects grades that differ by an algebraic total of 4%. What is the rate of vertical curvature, K?
- a.50✓
- b.800
- c.4
- d.0.02
K = L / A, where L is the curve length in feet and A is the algebraic difference in grades in percent. K = 200 / 4 = 50 ft per percent. K expresses the horizontal distance needed to change the grade by 1% and is checked against sight-distance minimums.
A task has an earned value (EV) of $8,000 and an actual cost (AC) of $10,000. What is the Cost Performance Index (CPI)?
- a.1.0
- b.0.8✓
- c.0.2
- d.1.25
CPI = EV / AC = 8,000 / 10,000 = 0.8. A CPI below 1.0 means the work is over budget (you earned less value than you spent). CPI is a core earned-value metric for project cost control.
In CPM scheduling, the total float of an activity is correctly computed as:
- a.Late finish minus late start
- b.Early finish minus early start
- c.The activity duration
- d.Late finish minus early finish✓
Total float = Late Finish - Early Finish (equivalently Late Start - Early Start). It is the time an activity can slip without delaying project completion. Activities on the critical path have zero total float.
A soil has a bank (in-place) volume of 100 cubic yards and a swell of 25%. What is the loose (excavated) volume?
- a.125 cubic yards✓
- b.75 cubic yards
- c.80 cubic yards
- d.100 cubic yards
Loose volume = bank volume x (1 + swell) = 100 x 1.25 = 125 cubic yards. Excavating loosens soil so it occupies more volume; swell governs hauling quantities, while shrinkage governs compacted fill.
A concrete slab measures 20 ft by 20 ft by 0.5 ft thick. What volume of concrete is required, in cubic yards?
- a.27 cubic yards
- b.3.7 cubic yards
- c.200 cubic yards
- d.7.4 cubic yards✓
Volume = 20 x 20 x 0.5 = 200 cubic feet. Converting to cubic yards, divide by 27: 200 / 27 = 7.4 cubic yards. Ordering concrete requires this conversion because ready-mix is sold by the cubic yard.
For a given set of materials, reducing the water-cement ratio of a concrete mix generally does what to compressive strength?
- a.Decreases it
- b.Has no effect on it
- c.Makes it unpredictable
- d.Increases it✓
By Abrams' law, lower water-cement ratio yields higher compressive strength (down to the point where the mix becomes unworkable). Excess water creates capillary voids that weaken the hardened paste. Admixtures maintain workability at low water-cement ratios.
What is the nominal diameter of a #8 reinforcing bar (U.S. customary sizes)?
- a.0.5 in
- b.1.0 in✓
- c.0.375 in
- d.0.75 in
U.S. rebar bar numbers give the diameter in eighths of an inch: #8 = 8/8 = 1.0 in. Thus a #4 bar is 0.5 in and a #3 bar is 0.375 in. This rule lets you size reinforcement quickly from the bar number.
The slump test on fresh concrete is primarily a measure of what property?
- a.Air content
- b.Compressive strength
- c.Workability (consistency)✓
- d.Water-cement ratio
The slump test measures the consistency and workability of fresh concrete, that is, how easily it flows and can be placed. It does not directly measure strength; separate cylinder tests determine compressive strength, and other tests measure air content.