Free FE Civil practice questions.

Step 1: Apply equilibrium

A simply supported beam with a single point load P at midspan is symmetric, so each reaction carries half the load.

Step 2: Calculate

R_A = R_B = P / 2 = 10 kN / 2 = 5 kN

Reference: FE Reference Handbook — Statics, Equilibrium of Rigid Bodies.

Step 1: Recall Reynolds number thresholds for pipe flow

Re < 2,100 → Laminar flow

2,100 < Re < 4,000 → Transitional flow

Re > 4,000 → Turbulent flow

Step 2: Classify

Re = 1,800 < 2,100 → Laminar flow (Answer B)

Note: "Supercritical flow" is an open-channel concept (Froude number), not a pipe flow regime.

Step 1: Check Liquid Limit

LL = 45 < 50 → Soil is "low plasticity" (L designation).

Step 2: Plot on the Casagrande plasticity chart

The A-line equation is: PI = 0.73 × (LL − 20) = 0.73 × 25 = 18.25

Given PI = 22 > 18.25 → the soil plots above the A-line → Clay (C).

Step 3: Classify

Low-plasticity clay = CL — Lean Clay

Reference: USCS Classification per ASTM D2487.

Step 1: Recall the SSD formula

SSD = Reaction Distance + Braking Distance

SSD = V × t + V² / (2 × a)

Step 2: Identify the variables

V = design speed, t = perception-reaction time (assumed 2.5 s per AASHTO), a = deceleration rate (11.2 ft/s²).

Step 3: Determine the controlling factors

Both terms depend on design speed. The reaction distance also depends on driver reaction time. Lane width, pavement type, and traffic volume do not directly factor into SSD.

Reference: AASHTO Green Book, Stopping Sight Distance section.

Step 1: Identify the formula

For a cantilever beam with a point load P at the free end, the fixed-end moment is:

M_A = P × L

Step 2: Substitute values

M_A = 20 kN × 3 m = 60 kN·m

Step 3: Determine direction

The 20 kN load creates a clockwise moment about A. The reaction moment at the fixed support must be counterclockwise to maintain equilibrium.

Reference: FE Reference Handbook — Beam Formulas, Cantilever Beams.

Step 1: Identify the formula

Hydrostatic pressure: P = γ × h

Step 2: Substitute values

P = 9.81 kN/m³ × 5 m = 49.05 kPa

Hydrostatic pressure increases linearly with depth in a fluid of constant density.

Reference: FE Reference Handbook — Fluid Mechanics, Hydrostatic Pressure.

Step 1: Identify given values

σ_x = 80 MPa, σ_y = 40 MPa, τ_xy = 30 MPa

Step 2: Apply the maximum in-plane shear stress formula

τ_max = √[((σ_x − σ_y) / 2)² + τ_xy²]

Step 3: Substitute and compute

τ_max = √[((80 − 40) / 2)² + 30²]

τ_max = √[(20)² + (30)²] = √[400 + 900] = √1300 ≈ 36.1 MPa

Reference: FE Reference Handbook — Mechanics of Materials, Mohr's Circle.

Step 1: Identify the formula

For a simply supported beam with a uniformly distributed load (UDL):

M_max = wL² / 8

Step 2: Substitute values

M_max = (6 kN/m)(8 m)² / 8 = (6 × 64) / 8 = 384 / 8 = 48 kN·m

The maximum moment occurs at midspan.

Reference: FE Reference Handbook — Beam Formulas, Simply Supported Beams.

Step 1: Find support reactions

By symmetry (load at midpoint B): A_y = C_y = 10 / 2 = 5 kN (upward)

Step 2: Analyze joint C (method of joints)

Members at C: BC (horizontal) and DC (diagonal at 45°). Roller at C provides vertical reaction = 5 kN ↑.

ΣF_y = 0: F_DC sin(45°) + 5 = 0 → F_DC = −5 / sin(45°) = −7.07 kN (compression)

ΣF_x = 0: F_BC + F_DC cos(45°) = 0 → F_BC = −(−7.07)(0.707) = 5.0 kN (tension)

Reference: FE Reference Handbook — Statics, Truss Analysis.

Step 1: Recall Terzaghi's bearing capacity equation (strip footing)

q_ult = c × N_c + q × N_q + 0.5 × γ × B × N_γ

Step 2: Identify given values

c = 80 kPa, φ = 0°, N_c = 5.7, N_q = 1.0, N_γ = 0. Surface footing → q (surcharge) = 0.

Step 3: Substitute and compute

q_ult = (80)(5.7) + (0)(1.0) + 0.5(γ)(1.5)(0) = 456 + 0 + 0 = 456 kPa

Reference: FE Reference Handbook — Geotechnical, Shallow Foundation Bearing Capacity.

Step 1: Recall LOS criteria for basic freeway segments

Per the Highway Capacity Manual (HCM), LOS is determined by density (pc/mi/ln):

LOS A: ≤ 11 | LOS B: > 11–18 | LOS C: > 18–26 | LOS D: > 26–35 | LOS E: > 35–45 | LOS F: > 45

Step 2: Classify

Density = 35 pc/mi/ln falls within the range > 26–35 → LOS D

Reference: HCM Chapter 12 — Basic Freeway Segments.

Step 1: Recall the deflection formula

For a simply supported beam with UDL: δ_max = 5wL⁴ / (384EI)

Step 2: Identify the variables in the formula

• w (load intensity) — ✅ appears in the formula

• L (span length) — ✅ appears in the formula (to the 4th power)

• E (modulus of elasticity) — ✅ appears in the denominator

• I (moment of inertia) — ✅ appears in the denominator

• ν (Poisson's ratio) — ❌ does NOT appear in the beam deflection formula

Correct answers: A, B, C, E. Poisson's ratio (D) does not affect transverse beam deflection.

Step 1: Calculate unit discharge

q = Q / b = 12 m³/s / 4 m = 3 m²/s

Step 2: Apply the critical depth formula for rectangular channels

y_c = (q² / g)^(1/3)

Step 3: Substitute and compute

y_c = (3² / 9.81)^(1/3) = (9 / 9.81)^(1/3) = (0.9174)^(1/3) ≈ 0.97 m

Reference: FE Reference Handbook — Fluid Mechanics, Open Channel Flow.

Step 1: Identify the Euler buckling formula

P_cr = π²EI / (KL)²

Step 2: Determine effective length

Both ends pinned → K = 1.0. L = 20 ft = 240 in. KL = 1.0 × 240 = 240 in.

Step 3: Substitute values

P_cr = π²(29,000 ksi)(272 in⁴) / (240 in)²

P_cr = (9.8696)(29,000)(272) / 57,600

P_cr = 77,851,000 / 57,600 ≈ 1,352 kips ≈ 1,355 kips

Note: Always use the minimum moment of inertia (weak axis) for buckling unless the column is braced about that axis. This problem specifies I = 272 in⁴.

Reference: FE Reference Handbook — Mechanics of Materials, Column Buckling.

Standard Proctor Test → Determines the maximum dry density (γ_d,max) and optimum moisture content (OMC) for soil compaction.

Atterberg Limits Test → Measures plasticity characteristics: Liquid Limit (LL), Plastic Limit (PL), and Plasticity Index (PI = LL − PL).

Consolidation Test → Determines compressibility parameters: compression index (C_c), coefficient of consolidation (C_v), and preconsolidation pressure.

Direct Shear Test → Measures shear strength parameters: cohesion (c) and friction angle (φ) using the Mohr-Coulomb failure criterion.