| name | equipment-foundation |
| description | Equipment foundation design — dynamic loads, natural frequency, ACI 351.3R, frequency ratio, vibration isolation, soil-structure interaction, resonance margin, rigid vs. flexible block, rotating machinery mounts. |
| metadata | {"priority":7,"promptSignals":{"phrases":["equipment foundation","machine foundation","dynamic foundation","ACI 351","foundation vibration","rotating machine foundation"],"minScore":3}} |
Equipment Foundation Design — Complete Skill
Foundation Types
Rigid (block) foundation: heavy concrete block; mass > 3–5× machine mass; natural frequency well below operating speed
Flexible (spring-isolated) foundation: machine on springs; natural frequency below operating speed; high isolation
Inertia block: intermediate mass on anti-vibration mounts; common for small compressors, pumps
Elevated frame (tabletop): for large turbine-generator sets; columns + top slab; allows underfloor piping access
Design Criteria (ACI 351.3R)
Frequency separation criteria:
Natural frequency of foundation must be separated from operating speed by ≥ 20% (minimum) to ≥ 30% (recommended)
Frequency ratio: r = f_operating / f_n (foundation)
RIGID design: r >> 1 (f_n << f_operating); foundation too stiff to respond dynamically
Achieve by: heavy concrete mass; rigid soil contact
Isolation design: r << 1 (f_n << f_operating): foundation below resonance
Achieve by: soft springs; flexible mounts
Recommended frequency ratio:
r < 0.6 (below resonance, rigid foundation): foundation natural frequency < 0.6 × f_operating
r > 1.4 (above resonance, soft isolators): foundation natural frequency > 1.4 × f_operating
Avoid r = 0.6–1.4 (resonance zone)
Natural Frequency of Foundation
Translational (vertical) natural frequency:
f_n,v = (1/2π) × √(K_v / m_total) [Hz; K_v = vertical soil spring stiffness; m_total = machine + foundation mass]
Soil stiffness (rigid circular footing on elastic half-space — Lysmer analog):
K_v = 4Gr / (1-ν) [N/m; G = soil shear modulus; r = equivalent radius of footing; ν = Poisson's ratio]
K_h = 32(1-ν)Gr / (7-8ν) [horizontal stiffness; smaller than K_v]
Equivalent radius:
r = √(A / π) [A = footing area]
Soil shear modulus G:
G = ρ_soil × V_s² [Pa; V_s = shear wave velocity; ρ_soil = density]
Typical V_s: soft clay: 80–150 m/s; medium soil: 150–300 m/s; rock: 600–1500 m/s
G range: 10–50 MPa (soft soil); 100–500 MPa (stiff soil/rock)
Foundation natural frequency (all DOF):
6 DOF: vertical, lateral-x, lateral-y, rocking-x, rocking-y, torsional
Rocking stiffness: K_r = 8Gr³ / (3(1-ν)) [N·m/rad; r = equivalent rocking radius]
f_r = (1/2π) × √(K_r / I_rocking) [I_rocking = mass moment of inertia of combined system]
Dynamic Loads
Rotating machinery (unbalanced force):
F_dynamic = m_unbalance × r × ω² [N; m_unbalance = unbalanced mass; r = eccentricity; ω = angular speed [rad/s]]
Grade G2.5 ISO 1940: m × r ≤ 2.5 / (ω / 1000) [g·mm; residual unbalance spec]
Reciprocating machinery:
Primary: F₁ = m_recip × r × ω² × cos θ [first-order; θ = crank angle]
Secondary: F₂ = m_recip × r × λ × ω² × cos 2θ [λ = r/L_conrod]
Multi-cylinder: vector sum of all cylinders; many configurations partially cancel
Allowable vibration amplitude (ACI 351.3R):
| Frequency [Hz] | Allowable displacement amplitude [μm] |
|---|
| < 5 | 500 |
| 5–15 | 250–50 |
| 15–40 | 50–12 |
| > 40 | 12 |
ISO 10816-1 vibration severity (velocity RMS):
Class I (small): 0.28–2.8 mm/s (good-alarm range); Class III (large, rigid): 0.71–7.1 mm/s
Mass Ratio Requirement
ACI 351.3R mass guideline:
For rotating machinery: foundation mass ≥ 3–5× machine mass
For reciprocating: foundation mass ≥ 3–10× machine mass (higher for large horizontal shakers)
Reason: large mass reduces dynamic amplitude proportionally for given unbalanced force
Dynamic amplitude (steady-state forced vibration):
X = F_dyn / (K_soil × √((1-r²)² + (2ζr)²)) [m; r = f_excitation/f_n; ζ = damping ratio]
For r << 1 (rigid foundation): X ≈ F_dyn / K_soil = (m_unbal × r_ecc × ω²) / K_soil
For r >> 1 (isolation): X ≈ F_dyn / (K_springs × r²) → high isolation when r >> 1
Anti-Vibration Mounts
Mount types:
Steel coil springs: k = 10⁻³–10⁷ N/mm; low ζ ≈ 0.03–0.05; durable
Elastomeric mounts (rubber): k = 10–10,000 N/mm; higher ζ ≈ 0.05–0.20; frequency-dependent
Air springs: very low k; for sensitive equipment; lowest natural frequency
Combined steel + rubber: spring for low f_n + rubber for damping
Required spring stiffness (per mount):
K_mount = (2π × f_n)² × m_total / N_mounts [N/m; f_n = target isolation frequency; N_mounts = number]
Static deflection:
δ_static = m × g / (N_mounts × K_mount) = g / (2π × f_n)² [m]
For f_n = 2 Hz: δ = 9.81 / (2π×2)² = 9.81/157.9 = 0.062 m = 62 mm
Damping ratio for spring-mounted equipment:
ζ_soil = 0.05–0.20 (for soil contact); ζ_spring = 0.03–0.05 (coil springs); 0.05–0.15 (rubber)
Foundation Concrete Design
Allowable bearing pressure:
q_allow = q_ultimate / SF [kPa; SF = 3.0 for dynamic; more conservative than static]
Check: total weight (static + dynamic) / base area ≤ q_allow
Concrete requirements (ACI 318):
f'c ≥ 28 MPa (4000 psi) for equipment foundations; ≥ 35 MPa for vibrating equipment
Reinforcement: ACI 318 temperature/shrinkage minimum 0.0018 × b × h; additional for dynamic loads
Anchor bolts:
Tension = dynamic uplift force / N_anchors; shear = horizontal dynamic force / N_anchors
Design per ACI 318 Chapter 17 (anchors); consider prying, concrete breakout, steel rupture
Standards
| Standard | Scope |
|---|
| ACI 351.3R | Foundations for dynamic equipment |
| ISO 10816-1 | Vibration evaluation of machine foundations |
| ISO 1940-1 | Rotor balancing grade specification |
| DIN 4024 | Machine foundations — design guideline |
| ASCE 7 | Minimum design loads (seismic for foundation) |
Output
Provide: machine type and operating speed [RPM], unbalanced force F_dyn [kN], foundation type (rigid/isolated/tabletop), foundation dimensions [m] and mass [kg], mass ratio (foundation/machine), soil shear modulus G [MPa], soil stiffness K_v [MN/m], natural frequency f_n [Hz] (all modes), frequency ratio r = f_op/f_n, dynamic amplitude X [μm] vs. allowable, frequency separation margin [%] vs. 20% minimum, anti-vibration mount stiffness K [N/mm] and static deflection δ [mm], damping ζ, ISO 10816 vibration class, anchor bolt design (size, grade, tension/shear capacity [kN]), and applicable standard (ACI 351.3R, ISO 10816-1, ISO 1940-1).
