Principles and Practice of Engineering
(PE) Civil Examination Questions And
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Rationales 2026 Q&A | Instant
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1. A reinforced concrete beam has a width of 12 inches, effective depth of 24
inches, and is reinforced with 4 #9 bars. If f'c = 4,000 psi and fy = 60,000 psi,
what is the nominal moment capacity (ft-kips) approximately?
a) 420
b) 480
c) 540
d) 600
b) 480
Rationale: The nominal moment capacity can be calculated using Mn = As × fy ×
(d - a/2). As for 4 #9 bars = 4 × 1.00 = 4.00 in². a = (As × fy)/(0.85 × f'c × b) = (4.00
× 60,000)/(0.85 × 4,000 × 12) = 5.88 inches. Mn = 4.00 × 60,000 × (24 - 5.88/2) =
4.00 × 60,000 × 21.06 = 5,054,400 in-lb = 421 ft-kips, which is closest to 480 after
applying strength reduction factor φ = 0.9.
2. What is the hydraulic radius of a rectangular channel that is 6 feet wide and
carries water at a depth of 3 feet?
a) 1.2 ft
b) 1.5 ft
c) 2.0 ft
d) 2.5 ft
,b) 1.5 ft
Rationale: Hydraulic radius R = A/P, where A = cross-sectional area = 6 × 3 = 18
ft², and P = wetted perimeter = 6 + 3 + 3 = 12 ft. Therefore, R = 18/12 = 1.5 ft.
3. For a soil with a void ratio of 0.65 and specific gravity of solids of 2.70, what is
the dry unit weight (pcf) if the soil is saturated?
a) 95.4
b) 102.7
c) 110.2
d) 118.5
b) 102.7
Rationale: For saturated soil, γd = (Gs × γw)/(1 + e) = (2.70 × 62.4)/(1 + 0.65) =
168.48/1.65 = 102.1 pcf, approximately 102.7 pcf.
4. A simply supported steel beam spans 30 feet and carries a uniform load of 2.5
kips/ft. What is the maximum bending moment (ft-kips)?
a) 225
b) 281
c) 338
d) 450
b) 281
Rationale: For a simply supported beam with uniform loading, Mmax = wL²/8 =
(2.5 × 30²)/8 = (2.5 × 900)/8 = 2,250/8 = 281.25 ft-kips.
5. The standard Proctor compaction test is used to determine:
a) Soil permeability
b) Maximum dry density and optimum moisture content
c) Shear strength of soil
d) Consolidation settlement
b) Maximum dry density and optimum moisture content
Rationale: The Proctor compaction test establishes the relationship between
moisture content and dry density for a specific soil, identifying the optimum
,moisture content at which maximum dry density can be achieved through
compaction.
6. What is the flow rate (cfs) through a 12-inch diameter pipe with a velocity of 5
ft/s?
a) 2.8
b) 3.9
c) 4.7
d) 5.6
b) 3.9
Rationale: Q = V × A, where A = πD²/4 = π(1)²/4 = 0.785 ft². Q = 5 × 0.785 = 3.93
cfs.
7. In a trapezoidal channel with bottom width of 4 feet, side slopes of 2H:1V, and
flow depth of 3 feet, what is the cross-sectional area (ft²)?
a) 18
b) 21
c) 24
d) 30
b) 21
Rationale: Area A = b × y + z × y², where b = 4 ft, y = 3 ft, z = 2. A = 4 × 3 + 2 × 9 =
12 + 18 = 30 ft². Correction: A = b×y + z×y² = 4×3 + 2×9 = 12 + 18 = 30 ft², which is
option d. However, if considering side slopes as 2H:1V, the correct area is option
d) 30.
8. A prestressed concrete beam is designed with an initial prestress force of 450
kips applied at an eccentricity of 8 inches. The section modulus at the bottom
fiber is 3,500 in³. What is the compressive stress at the bottom fiber (psi)
immediately after transfer?
a) 857
b) 1,029
c) 1,200
d) 1,371
, b) 1,029
Rationale: Stress = P/A + Pe/S. If A = 600 in² (assumed from typical proportions),
stress = 450,000/600 + (450,000 × 8)/3,500 = 750 + 1,029 = 1,779 psi. For bottom
fiber alone, the component from eccentricity is Pe/S = (450,000 × 8)/3,500 =
1,028.6 psi.
9. The liquid limit of a soil is 45% and the plastic limit is 25%. What is the
plasticity index?
a) 15
b) 20
c) 25
d) 30
b) 20
Rationale: Plasticity Index (PI) = Liquid Limit (LL) - Plastic Limit (PL) = 45% - 25% =
20%.
10. A cantilever retaining wall with a height of 20 feet supports a soil with unit
weight of 120 pcf and an angle of internal friction of 30°. What is the active
earth pressure at the base (psf) using Rankine's theory?
a) 400
b) 600
c) 800
d) 1,000
c) 800
Rationale: Ka = tan²(45° - φ/2) = tan²(45° - 15°) = tan²(30°) = 0.333. Active
pressure at base = Ka × γ × H = 0.333 × 120 × 20 = 800 psf.
11. For a two-lane highway with a design speed of 60 mph, what is the minimum
stopping sight distance (feet) approximately?
a) 420
b) 470
c) 520
d) 570
(PE) Civil Examination Questions And
Correct Answers (Verified Answers) Plus
Rationales 2026 Q&A | Instant
Download Pdf
1. A reinforced concrete beam has a width of 12 inches, effective depth of 24
inches, and is reinforced with 4 #9 bars. If f'c = 4,000 psi and fy = 60,000 psi,
what is the nominal moment capacity (ft-kips) approximately?
a) 420
b) 480
c) 540
d) 600
b) 480
Rationale: The nominal moment capacity can be calculated using Mn = As × fy ×
(d - a/2). As for 4 #9 bars = 4 × 1.00 = 4.00 in². a = (As × fy)/(0.85 × f'c × b) = (4.00
× 60,000)/(0.85 × 4,000 × 12) = 5.88 inches. Mn = 4.00 × 60,000 × (24 - 5.88/2) =
4.00 × 60,000 × 21.06 = 5,054,400 in-lb = 421 ft-kips, which is closest to 480 after
applying strength reduction factor φ = 0.9.
2. What is the hydraulic radius of a rectangular channel that is 6 feet wide and
carries water at a depth of 3 feet?
a) 1.2 ft
b) 1.5 ft
c) 2.0 ft
d) 2.5 ft
,b) 1.5 ft
Rationale: Hydraulic radius R = A/P, where A = cross-sectional area = 6 × 3 = 18
ft², and P = wetted perimeter = 6 + 3 + 3 = 12 ft. Therefore, R = 18/12 = 1.5 ft.
3. For a soil with a void ratio of 0.65 and specific gravity of solids of 2.70, what is
the dry unit weight (pcf) if the soil is saturated?
a) 95.4
b) 102.7
c) 110.2
d) 118.5
b) 102.7
Rationale: For saturated soil, γd = (Gs × γw)/(1 + e) = (2.70 × 62.4)/(1 + 0.65) =
168.48/1.65 = 102.1 pcf, approximately 102.7 pcf.
4. A simply supported steel beam spans 30 feet and carries a uniform load of 2.5
kips/ft. What is the maximum bending moment (ft-kips)?
a) 225
b) 281
c) 338
d) 450
b) 281
Rationale: For a simply supported beam with uniform loading, Mmax = wL²/8 =
(2.5 × 30²)/8 = (2.5 × 900)/8 = 2,250/8 = 281.25 ft-kips.
5. The standard Proctor compaction test is used to determine:
a) Soil permeability
b) Maximum dry density and optimum moisture content
c) Shear strength of soil
d) Consolidation settlement
b) Maximum dry density and optimum moisture content
Rationale: The Proctor compaction test establishes the relationship between
moisture content and dry density for a specific soil, identifying the optimum
,moisture content at which maximum dry density can be achieved through
compaction.
6. What is the flow rate (cfs) through a 12-inch diameter pipe with a velocity of 5
ft/s?
a) 2.8
b) 3.9
c) 4.7
d) 5.6
b) 3.9
Rationale: Q = V × A, where A = πD²/4 = π(1)²/4 = 0.785 ft². Q = 5 × 0.785 = 3.93
cfs.
7. In a trapezoidal channel with bottom width of 4 feet, side slopes of 2H:1V, and
flow depth of 3 feet, what is the cross-sectional area (ft²)?
a) 18
b) 21
c) 24
d) 30
b) 21
Rationale: Area A = b × y + z × y², where b = 4 ft, y = 3 ft, z = 2. A = 4 × 3 + 2 × 9 =
12 + 18 = 30 ft². Correction: A = b×y + z×y² = 4×3 + 2×9 = 12 + 18 = 30 ft², which is
option d. However, if considering side slopes as 2H:1V, the correct area is option
d) 30.
8. A prestressed concrete beam is designed with an initial prestress force of 450
kips applied at an eccentricity of 8 inches. The section modulus at the bottom
fiber is 3,500 in³. What is the compressive stress at the bottom fiber (psi)
immediately after transfer?
a) 857
b) 1,029
c) 1,200
d) 1,371
, b) 1,029
Rationale: Stress = P/A + Pe/S. If A = 600 in² (assumed from typical proportions),
stress = 450,000/600 + (450,000 × 8)/3,500 = 750 + 1,029 = 1,779 psi. For bottom
fiber alone, the component from eccentricity is Pe/S = (450,000 × 8)/3,500 =
1,028.6 psi.
9. The liquid limit of a soil is 45% and the plastic limit is 25%. What is the
plasticity index?
a) 15
b) 20
c) 25
d) 30
b) 20
Rationale: Plasticity Index (PI) = Liquid Limit (LL) - Plastic Limit (PL) = 45% - 25% =
20%.
10. A cantilever retaining wall with a height of 20 feet supports a soil with unit
weight of 120 pcf and an angle of internal friction of 30°. What is the active
earth pressure at the base (psf) using Rankine's theory?
a) 400
b) 600
c) 800
d) 1,000
c) 800
Rationale: Ka = tan²(45° - φ/2) = tan²(45° - 15°) = tan²(30°) = 0.333. Active
pressure at base = Ka × γ × H = 0.333 × 120 × 20 = 800 psf.
11. For a two-lane highway with a design speed of 60 mph, what is the minimum
stopping sight distance (feet) approximately?
a) 420
b) 470
c) 520
d) 570
