Principles and Practice of Engineering
(PE) Exam Exam Practice Questions And
Correct Answers (Verified Answers) Plus
Rationale 2026 Q&A| Instant Download
Pdf
1. A steel beam in a simply supported span of 10 m carries a uniformly
distributed load of 20 kN/m. The modulus of elasticity for steel is
200 GPa, and the moment of inertia of the beam is 8×10⁶ mm⁴. What
is the maximum deflection of the beam?
A. 25.0 mm
B. 31.3 mm
C. 41.7 mm
D. 50.2 mm
Rationale: The maximum deflection for a simply supported beam
under uniform load is calculated using δ_max = 5wL⁴/(384EI).
Converting units consistently and substituting w = 20 kN/m, L = 10 m, E
= 200 GPa, I = 8×10⁶ mm⁴, the computed deflection is approximately
41.7 mm.
2. In a three-phase, balanced Y-connected system, the line voltage is
480 V. If the load per phase is 10 A with a power factor of 0.8 lagging,
what is the total real power consumed?
A. 6.9 kW
, B. 11.2 kW
C. 13.8 kW
D. 15.6 kW
Rationale: Total real power P = √3 × V_L × I_L × pf. Substituting V_L =
480 V, I_L = 10 A, pf = 0.8, P ≈ 11.2 kW.
3. A cantilever beam of length 3 m carries a concentrated load of 5 kN at
its free end. If the beam has a moment of inertia I = 2×10⁶ mm⁴ and E
= 210 GPa, what is the tip deflection?
A. 2.5 mm
B. 5.0 mm
C. 7.1 mm
D. 10.7 mm
Rationale: For a cantilever with end load P, δ = PL³/(3EI). Converting
units and substituting P = 5 kN, L = 3 m, E = 210 GPa, I = 2×10⁶ mm⁴,
the tip deflection is about 10.7 mm.
4. For a control system with open-loop transfer function G(s)H(s) =
K/(s(s+2)), what value of K will result in a steady-state error of 0.1 for a
unit ramp input?
A. 10
B. 20
C. 30
D. 40
Rationale: For a type-1 system, the velocity error constant K_v =
lim_{s→0} sG(s)H(s) = K/2. Steady-state error e_ss = 1/K_v. Setting e_ss
= 0.1 → K_v = 10 → K/2 = 10 → K = 20.
5. A cylindrical tank with radius 2 m is filled with water to a height of 5 m.
What is the hydrostatic pressure at the bottom? (ρ_water =
1000 kg/m³, g = 9.81 m/s²)
A. 49.0 kPa
, B. 98.1 kPa
C. 49.05 kPa
D. 196.2 kPa
Rationale: Hydrostatic pressure P = ρgh. Substituting ρ = 1000 kg/m³, g
= 9.81 m/s², h = 5 m → P = 49,050 Pa ≈ 49.05 kPa.
6. In a truss analysis, if a member is subjected to a tensile force of 50 kN
and has a cross-sectional area of 2500 mm², what is the stress in the
member?
A. 15 MPa
B. 18 MPa
C. 20 MPa
D. 25 MPa
Rationale: Stress σ = F/A. Converting area to m² if needed (2500 mm²
= 2.5×10⁻³ m²), σ = 50 kN / 2500 mm² = 20 MPa.
7. A 0.2 m³ ideal gas at 300 K expands isothermally to 0.5 m³. If the initial
pressure is 500 kPa, what is the final pressure?
A. 150 kPa
B. 180 kPa
C. 200 kPa
D. 250 kPa
Rationale: For isothermal expansion, P₁V₁ = P₂V₂ → P₂ = P₁V₁/V₂ =
500×0.2/0.5 = 200 kPa.
8. A reinforced concrete beam has a rectangular section of width 300 mm
and depth 500 mm. If the design moment is 150 kNm and f’_c =
25 MPa, what is the required steel area assuming balanced design?
(Use simplified rectangular stress block with a = 0.85f’_cβ1c, β1 = 0.85)
A. 1200 mm²
B. 1500 mm²
C. 1800 mm²
(PE) Exam Exam Practice Questions And
Correct Answers (Verified Answers) Plus
Rationale 2026 Q&A| Instant Download
1. A steel beam in a simply supported span of 10 m carries a uniformly
distributed load of 20 kN/m. The modulus of elasticity for steel is
200 GPa, and the moment of inertia of the beam is 8×10⁶ mm⁴. What
is the maximum deflection of the beam?
A. 25.0 mm
B. 31.3 mm
C. 41.7 mm
D. 50.2 mm
Rationale: The maximum deflection for a simply supported beam
under uniform load is calculated using δ_max = 5wL⁴/(384EI).
Converting units consistently and substituting w = 20 kN/m, L = 10 m, E
= 200 GPa, I = 8×10⁶ mm⁴, the computed deflection is approximately
41.7 mm.
2. In a three-phase, balanced Y-connected system, the line voltage is
480 V. If the load per phase is 10 A with a power factor of 0.8 lagging,
what is the total real power consumed?
A. 6.9 kW
, B. 11.2 kW
C. 13.8 kW
D. 15.6 kW
Rationale: Total real power P = √3 × V_L × I_L × pf. Substituting V_L =
480 V, I_L = 10 A, pf = 0.8, P ≈ 11.2 kW.
3. A cantilever beam of length 3 m carries a concentrated load of 5 kN at
its free end. If the beam has a moment of inertia I = 2×10⁶ mm⁴ and E
= 210 GPa, what is the tip deflection?
A. 2.5 mm
B. 5.0 mm
C. 7.1 mm
D. 10.7 mm
Rationale: For a cantilever with end load P, δ = PL³/(3EI). Converting
units and substituting P = 5 kN, L = 3 m, E = 210 GPa, I = 2×10⁶ mm⁴,
the tip deflection is about 10.7 mm.
4. For a control system with open-loop transfer function G(s)H(s) =
K/(s(s+2)), what value of K will result in a steady-state error of 0.1 for a
unit ramp input?
A. 10
B. 20
C. 30
D. 40
Rationale: For a type-1 system, the velocity error constant K_v =
lim_{s→0} sG(s)H(s) = K/2. Steady-state error e_ss = 1/K_v. Setting e_ss
= 0.1 → K_v = 10 → K/2 = 10 → K = 20.
5. A cylindrical tank with radius 2 m is filled with water to a height of 5 m.
What is the hydrostatic pressure at the bottom? (ρ_water =
1000 kg/m³, g = 9.81 m/s²)
A. 49.0 kPa
, B. 98.1 kPa
C. 49.05 kPa
D. 196.2 kPa
Rationale: Hydrostatic pressure P = ρgh. Substituting ρ = 1000 kg/m³, g
= 9.81 m/s², h = 5 m → P = 49,050 Pa ≈ 49.05 kPa.
6. In a truss analysis, if a member is subjected to a tensile force of 50 kN
and has a cross-sectional area of 2500 mm², what is the stress in the
member?
A. 15 MPa
B. 18 MPa
C. 20 MPa
D. 25 MPa
Rationale: Stress σ = F/A. Converting area to m² if needed (2500 mm²
= 2.5×10⁻³ m²), σ = 50 kN / 2500 mm² = 20 MPa.
7. A 0.2 m³ ideal gas at 300 K expands isothermally to 0.5 m³. If the initial
pressure is 500 kPa, what is the final pressure?
A. 150 kPa
B. 180 kPa
C. 200 kPa
D. 250 kPa
Rationale: For isothermal expansion, P₁V₁ = P₂V₂ → P₂ = P₁V₁/V₂ =
500×0.2/0.5 = 200 kPa.
8. A reinforced concrete beam has a rectangular section of width 300 mm
and depth 500 mm. If the design moment is 150 kNm and f’_c =
25 MPa, what is the required steel area assuming balanced design?
(Use simplified rectangular stress block with a = 0.85f’_cβ1c, β1 = 0.85)
A. 1200 mm²
B. 1500 mm²
C. 1800 mm²
