Preparing for the PE Civil Exam? Try these Free Sample Problems

At StrataWay, we have study resources designed for those preparing for the PE exam. Here are sample problems for each discipline to help you get ready. Step-by-step solutions are provided below. Be sure to explore our other blogs for more free sample problems.

Geotechnical:

A 5.0-ft-long rock core run was drilled during a subsurface investigation. The following intact core lengths were recovered:

• 3 pieces at 10 in

• 2 pieces at 5 in

• 4 pieces at 3 in

• 3 pieces at 2 in

Using the Rock Quality Designation (RQD) method, determine the rock quality for this core run.

A. Poor

B. Fair

C. Good

D. Excellent

Construction:

A pavement section measuring approximately 100 ft long by 12 ft wide will require undercutting and placement of geotextile fabric directly on top of the subgrade to provide a stable base. Geogrid will then be placed on top of the fabric within half of the undercut area for reinforcement. The cost of geotextile fabric and geogrid is $1.50 and $1.35 per square ft, respectively. Accounting for 10% waste of material during construction, a sales tax of 9.5%, and a mark-up of 15% from the subcontractor, what is most nearly the total cost for the material that the general contractor will incur?

A. $2,500

B. $2,750

C. $3,500

D. $3,750

Transportation:

A vertical curve connects an ascending grade of +3.5% to a descending grade of -1.5%. If the rate of vertical curvature is 150 ft, find the rate of change of grade in percent per 100 feet.

A. 0.67% per 100 ft

B. 1.33% per 100 ft

C. 2.00% per 100 ft

D. 4.00% per 100 ft

Structural:

A newly constructed commercial building includes a reinforced concrete shear wall system designed to resist seismic loads in Seismic Design Category C. During the review of the concrete mix design, the special inspector notes that the concrete will be placed in structural elements designed with a compressive strength f^′_c​ of 5,000 psi.

The inspector receives three test results for one batch of concrete:

• Test 1 = 4,920 psi

• Test 2 = 5,100 psi

• Test 3 = 5,180 psi

Does this batch of concrete meet the required strength criteria for special inspection purposes?

A. Yes, both conditions are met

B. No, the average is below the required strength

C. No, one test falls below the minimum individual limit

D. No, both conditions are violated

Water Resources and Environmental:

A completely turbulent mechanical mixing system is being designed for a wastewater treatment basin using a fan turbine (6 blades at 45°). Assume fully turbulent conditions, and the following parameters apply:

• Impeller diameter, D_i = 1.1 m

• Rotational speed, n = 80 rpm

• Fluid: Water at standard conditions ρ = 1,000 kg/cubic meter

What is most nearly the power required to drive the mixer, in kilowatts?

A. 7.0 kW

B. 4.0 kW

C. 6.0 kW

D. 5.0 kW

Solution - Geotechnical:

RQD is the percentage of the total length of sound core pieces greater than 4 inches over the total length of the core run.

Identify and calculate the total valid core length (pieces greater than 4 inches):

• 3 pieces at 10 in will be included. 3 × 10 = 30 in.

• 2 pieces at 5 in will be included. 2 × 5 = 10 in. 

• 4 pieces at 3 in will not be included.

• 3 pieces at 2 in will not be included.

The sum of the lengths of core pieces greater than 4 inches is 40 in. Total length of core run:

Core run is 30 in + 10 in + 12 in + 6 in = 58 in

Compute RQD:

RQD = (40 in / 58 in) × 100

RQD = 69% (a RQD of 69% reflects a fair rock quality) (Answer is B)

Solution - Construction:

Calculate the cost of fabric:

100 ft × 12 ft = 1,200 ft²

1,200 ft² × 1.1 = 1,320 ft² (to account for waste)

1,320 ft² × $1.50/ft² = $1,980

$1,980 + (0.095 × $1,980) + (0.15 × $1,980) = $2,465.10

Calculate the cost of geogrid:

100 ft × 12 ft × 0.5 = 600 ft²

600 ft² × 1.1 = 660 ft² (to account for waste)

660 ft² × $1.35/ft² = $891

$891 + (0.095 × $891) + (0.15 × $891) = $1,109.30

Calculate the total cost:

$2,465.10 + $1,109.30 = $3,574.40 (Answer is C)

Solution - Transportation:

Find the algebraic difference in grades:

∣g₂−g₁∣ = ∣−1.5%−3.5%∣ = 5.0%

Use the equation to find the length of curve, L:

L = K × ∣g₂−g₁∣

L = 150 ft × 5 = 750 ft

Calculate the rate of change of grade, r:

r = ∣ g₂−g₁∣/L

r = (5.0/750) × 100

r ​= 0.6667% per 100 ft (Answer is A)

Solution - Structural:

Reference the IBC, 2018 edition and ACI 318 Building Code Requirements for Structural Concrete and Commentary, 2014 edition. According to Chapter 17 of the IBC and ACI 318 requirements, the average of three consecutive strength tests must be at least f^′_c​, and no single test shall fall below f^′_c​ − 500 psi.

Step 1: Check the average of three tests:

Average = (4,920 psi + 5,100 psi + 5,1803 psi)/3

Average = 5,066.67 psi

Compare to required average f^′_c​ = 5,000 psi (condition met)

Step 2: Check individual test limit:

Minimum allowed individual strength = f^′_c​ – 500

Minimum allowed individual strength = 5,000−500

Minimum allowed individual strength = 4,500 psi

Lowest test = 4,920 psi > 4,500 psi (condition met)

Both conditions are met. (Answer is A)

Solution - Water Resources and Environmental:

Determine the impeller constant from the provided table (Values of the Impeller Constant) in the NCEES Reference Handbook:

K_T = 1.65 for a fan turbine, 6 blades at 45°.

Convert rotational speed to revolutions per second:

N = 80 rpm/60 = 1.333 rev/s

Apply the equation for turbulent flow impeller mixing power:

P = K_T × (n)³ × (Di)⁵ × ρ_f

P = 1.65 × (1.33 rev/s)³ × (1.1 m)⁵ × 1,000 kg/cubic meters

P = 6,301.2 W

Convert to kilowatts:

P = 6.3 kW (Answer is C)

Final Thoughts:

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