BEAM ANALYSIS
BEAM CONFIGURATION
SUPPORTS (CLICK TO PLACE)
LOADS
CROSS SECTION PROPERTIES
PRESETS
DRAW CUSTOM SECTION
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SECTION PROPERTIES
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MATERIALS DATABASE
| NAME | E (GPa) | Sy (MPa) | Su (MPa) | DENSITY | POISSON |
|---|
STRESS ANALYSIS
STRESS STATE
RESULTS
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MOHR'S CIRCLE
BOLT ANALYSIS
BOLT CONFIGURATION
JOINT RESULTS
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BOLT REFERENCE TABLES
GRADES
| GRADE | Sp (MPa) | Sy (MPa) | Su (MPa) |
|---|
SIZES
| SIZE | NOM (mm) | PITCH | At (mm²) |
|---|
SPRING DESIGN
SPRING PARAMETERS
SPRING RESULTS
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SEAL / O-RING ANALYSIS
GLAND CONFIGURATION
COMPRESSION ANIMATION
SEAL RESULTS
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FORCE-DEFLECTION CURVE
STRESS-STRAIN CURVE
MATERIAL PROPERTIES
FINISHES & COATINGS GLOSSARY
RECOMMENDATION ENGINE
SET IMPORTANCE OF EACH PROPERTY (0 = IGNORE, 10 = CRITICAL). HIGHER RATING = BETTER PERFORMANCE.
MATH SOLVERS
SOLVER TYPE
ALGEBRAIC SOLVER
EQUATIONS REFERENCE
BEAM EQUATIONS
| Bending Stress | σ = M·y / I |
| Shear Stress (Beam) | τ = V·Q / (I·b) |
| Deflection (SS, center pt) | δ = P·L³ / (48·E·I) |
| Deflection (Cantilever, end) | δ = P·L³ / (3·E·I) |
| Moment of Inertia (Rect) | I = b·h³ / 12 |
| Section Modulus | S = I / c |
| Radius of Gyration | r = √(I / A) |
STRESS / FAILURE
| Von Mises | σ_vm = √(σ₁²−σ₁σ₂+σ₂²+3τ²) |
| Tresca | τ_max = (σ₁−σ₃) / 2 |
| Principal Stress | σ₁,₂ = (σx+σy)/2 ± √[((σx−σy)/2)²+τxy²] |
| Mohr's Circle Center | C = (σx+σy) / 2 |
| Mohr's Circle Radius | R = √[((σx−σy)/2)²+τxy²] |
| Factor of Safety | FoS = S_y / σ_applied |
BOLT / FASTENER
| Bolt Load (w/ preload) | F_b = F_i + C·F_ext |
| Joint Load | F_j = F_i − (1−C)·F_ext |
| Torque (K-factor) | T = K·F_i·d |
| Tensile Stress | σ = F / A_t |
| Interaction Ratio | IR = (σ/S_p)² + (τ/0.577·S_p)² |
| Proof Load | F_proof = S_p · A_t |
SPRING
| Spring Rate | k = G·d⁴ / (8·D³·N_a) |
| Shear Stress | τ = 8·F·D / (π·d³) |
| Wahl Factor | K_w = (4C−1)/(4C−4) + 0.615/C |
| Deflection | δ = F / k |
| Solid Length | L_s = N_t · d |
| Natural Frequency | f_n = (1/2)·√(k/m) |
SEAL / O-RING
| Squeeze % | S = (d − G_d − gap) / d × 100 |
| Mooney-Rivlin Stress | σ = 2(C₁₀+C₀₁/λ)(λ−1/λ²) |
| Hardness → Modulus | E = 0.0981(56+7.62S)/(0.138(254−2.54S)) |
| Contact Width | w = 2√(d·δ) |
| Shape Factor (Face) | SF = (w·d) / (π·d·w) |
| Volume Fill | V_fill = (π·r²) / (G_d·G_w) × 100 |
MATERIALS / PROPERTIES
| Hooke's Law | σ = E·ε |
| Shear Modulus | G = E / (2(1+ν)) |
| Thermal Strain | ε_T = α·ΔT |
| Poisson's Ratio | ν = −ε_lateral / ε_axial |
| Bulk Modulus | K = E / (3(1−2ν)) |
UNIT CONVERSION CONSTANTS
| 1 inch | = 25.4 mm |
| 1 foot | = 304.8 mm |
| 1 lbf | = 4.44822 N |
| 1 ksi | = 6.89476 MPa |
| 1 psi | = 6894.76 Pa |
| 1 in⁴ | = 416,231 mm⁴ |
| 1 ft·lbf | = 1.35582 N·m |
UNIT CONVERTER
QUICK REFERENCE
| FROM | TO | FACTOR |
|---|
FATIGUE (STRESS-LIFE)
LOAD / MATERIAL
SAFETY FACTORS
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GOODMAN / SODERBERG DIAGRAM
HEAT TRANSFER
CONDUCTION (PLANE WALL)
CONVECTION
RADIATION
FIN (ADIABATIC TIP)
RESULTS
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VISUALIZATION
ELECTROCHEMISTRY
NERNST EQUATION
TAFEL
BUTLER-VOLMER
CORROSION RATE (NACE)
FARADAY (ELECTROPLATING)
RESULTS
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TAFEL / B-V CURVE
BATTERY PACK
PACK SIZING
RUNTIME
PEUKERT
SOC & COULOMBIC EFF.
RESULTS
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DISCHARGE CURVE
FLUID MECHANICS
MOODY / PIPE FLOW
BERNOULLI
REYNOLDS
RESULTS
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MOODY CHART (f vs Re)
HEAT EXCHANGER
LMTD
NTU / ε
RESULTS
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ε vs NTU
PRESSURE VESSEL
THIN-WALL (HOOP / AXIAL)
LAMÉ (THICK-WALL)
ASME VIII-1 THICKNESS
RESULTS
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σ(r) PROFILE
THERMODYNAMIC CYCLES
CARNOT
OTTO (SI ENGINE)
DIESEL
BRAYTON
REFRIGERATION COP
RESULTS
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CYCLE SCHEMATIC
HVAC & PSYCHROMETRICS
PSYCHROMETRIC
COOLING LOAD
DUCT SIZING (EQ.)
RESULTS
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PSYCHROMETRIC LITE
ELECTRICAL
OHM'S LAW
AC POWER TRIANGLE
3-PHASE POWER
WIRE DROP
RC / RL TIME CONST.
RESULTS
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POWER TRIANGLE
VIBRATION
NATURAL FREQUENCY (SDOF)
ISOLATOR (TRANSMISSIBILITY)
RESONANCE AMP.
RESULTS
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TR vs ω/ω_n
GEARS
SPUR GEAR GEOMETRY
GEAR RATIO & SPEED
LEWIS BENDING STRESS
RESULTS
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FORMULAS
d = m·N | d_a = d + 2m | d_b = d·cosφ
p = π·m | GR = N_g/N_p
n_out = n_in/GR | T_out = T_in·GR·η
σ_b = W_t / (F·m·Y) (Lewis)
COLUMNS (BUCKLING)
EULER / JOHNSON
RESULTS
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σ_cr vs SLENDERNESS
SHAFTS
TORSION
CRITICAL SPEED (SDOF)
KEY SIZING (ASME)
RESULTS
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TORSION STRESS DISTRIBUTION
WELDS (FILLET)
FILLET WELD
WELD GROUP (POLAR)
RESULTS
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WELD SECTION
BEARINGS (L10 LIFE)
L10 / LIFE HOURS (ISO 281)
RESULTS
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L vs LOAD (C/P)^p
PUMPS
HYDRAULIC POWER
NPSH AVAILABLE
AFFINITY LAWS
SPECIFIC SPEED
RESULTS
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SYSTEM CURVE (H vs Q)
COMBUSTION
STOICHIOMETRIC AFR (C_xH_y)
ADIABATIC FLAME (SIMPLE)
LHV ↔ HHV
RESULTS
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λ SWEEP
MOTORS
SYNCHRONOUS / SLIP
TORQUE FROM POWER
FULL-LOAD CURRENT (3φ)
NEMA SERVICE FACTOR
RESULTS
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T-N CURVE (SIMPLIFIED)
NEC WIRE / BREAKER SIZING
WIRE SIZING (NEC 310.16, 75°C Cu)
VOLTAGE DROP (NEC 3% rec.)
RESULTS
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AMPACITY TABLE (75°C, Cu)
14 AWG → 20 A (breaker 15) | 12 → 25 (20) | 10 → 35 (30)
8 → 50 | 6 → 65 | 4 → 85 | 3 → 100
2 → 115 | 1 → 130 | 1/0 → 150 | 2/0 → 175
3/0 → 200 | 4/0 → 230 | 250 kcmil → 255 | 350 → 310
REFERENCES & STANDARDS
Complete index of formulas, theory, and standards referenced across all Amni-Calc modules. Each module tab filters this to its own card; this tab shows the full list.
Theory, Formulas & Standards Referenced
Amni-Calc implements classical closed-form engineering methods and selected code-based checks for preliminary sizing and conceptual analysis. Results are always first-principles approximations — final designs must be validated against current editions of the governing codes and by a licensed professional engineer.
Beam Bending
Euler-Bernoulli theory: EI y″″ = w(x). Superposition of point, distributed, and moment loads via influence functions. Deflection at load δ = PL³/48EI for simply supported mid-span.
Combined Stress & Mohr's Circle
Principal stresses from 2D state: σ1,2 = (σx+σy)/2 ± √[((σx-σy)/2)² + τxy²]. Von Mises equivalent stress gates yield.
Section Properties
Area, centroid, second moment of area I, section modulus S = I/c, radius of gyration r = √(I/A) for I-beams, HSS, channels, custom shapes via parallel-axis theorem.
Bolt Preload & Torque
T = K · d · Fi with nut factor K = 0.15-0.20. Recommended preload for static Fi = 0.75 Fp, reusable joints 0.75·Sp·At.
Helical Springs
Shear stress τ = Kw · 8FD/(πd³), rate k = Gd⁴/(8D³Na). Bergsträsser/Wahl factor corrects curvature. Belleville disc via Almen-Laszlo.
O-Ring & Elastomer Seals
Squeeze 15-30% typical for static radial; 10-20% face. Compression-set and swell bound service envelope. Internal node FEA approximates contact region and peak stress.
Column Buckling
Transition slenderness Cc = √(2π²E/Sy). Euler for long columns: σcr = π²E/(KL/r)². Johnson parabolic for intermediate: σcr = Sy[1 - Sy(KL/r)²/(4π²E)].
Shaft Torsion & Critical Speed
Polar moment J = π(Do⁴-Di⁴)/32; max shear τ = Tr/J; twist θ = TL/GJ. Dunkerley ωn = √(g/δ) for first whirl.
Fillet Welds (AWS)
Throat t = 0.707 a for equal-leg fillet. Allowable shear on throat = 0.30 FEXX. Weld-group polar moment Jg = Ix + Iy for eccentrically loaded groups.
Bearing Life
Basic rating life L10 = a1 (C/P)p, with p = 3 for ball, 10/3 for roller bearings. Reliability factor a1 for L5, L1 adjustments.
Fatigue (High-Cycle)
Four failure criteria on the Goodman diagram: Goodman, Soderberg, Gerber (parabolic), ASME-Elliptic. Marin factors modify endurance limit Se = kakbkckdkekf Se'.
Vibration & Isolation
Natural frequency fn = (1/2π)√(k/m). Transmissibility TR = √(1+(2ζr)²)/√((1-r²)²+(2ζr)²) where r = f/fn.
Gears (Lewis Bending)
Tooth bending stress σ = WtPd/(FY). Geometry: module m, pressure angle 20°/25°, addendum a = m, dedendum b = 1.25m.
Fluid Flow (Moody)
Darcy-Weisbach Δp = f (L/D)(ρV²/2). Friction factor f from Moody chart — Colebrook-White implicit or Swamee-Jain explicit. Reynolds Re = ρVD/μ.
Pumps & NPSH
NPSHa = (Patm-Pvap)/(ρg) - Hs - HL. Affinity laws: Q∝N, H∝N², P∝N³. Specific speed Ns = N√Q/H3/4.
Heat Transfer
Conduction q = -kA(dT/dx), convection q = hAΔT, radiation q = εσA(Ts⁴-T∞⁴). Fin efficiency η = tanh(mL)/(mL).
Heat Exchangers
LMTD ΔTlm = (ΔT1-ΔT2)/ln(ΔT1/ΔT2). NTU-effectiveness for unknown outlet temps. Correction factor F for shell-and-tube.
Pressure Vessels
Thin-wall circumferential σh = PD/2t, longitudinal σl = PD/4t. Thick-wall Lamé stress distribution. Code-based minimum thickness per ASME VIII-1 UG-27.
Thermodynamic Cycles
Carnot η = 1 - TL/TH. Otto η = 1 - 1/rk-1. Diesel, Brayton, Rankine efficiencies. Refrigeration COPR = QL/Wnet.
HVAC & Psychrometrics
Humidity ratio W = 0.622 Pw/(P-Pw), enthalpy h = 1.006T + W(2501+1.86T), dew point from water-vapor saturation.
Electrical & Power
Ohm V = IR, AC active P = VI cosφ, reactive Q = VI sinφ. 3-phase line-to-line P = √3 VLL I cosφ. RC/RL time constants τ = RC, τ = L/R.
Motors (3-Phase)
Synchronous speed Ns = 120f/P, slip s = (Ns-N)/Ns. Shaft torque T = 9549 PkW/Nrpm. FLA I = P/(√3 V · pf · η).
NEC Wire Sizing
75°C Cu ampacity per NEC Table 310.16. 125% continuous-load multiplier, ambient temperature and conductor-count derating per 310.15. Voltage drop Vd = 2I · RΩ/ft · L.
Electrochemistry
Nernst E = E° - (RT/nF) ln Q. Tafel η = a + b log|i|. Butler-Volmer for electrode kinetics. Faraday m = ItM/(nF) for deposition.
Battery Sizing
Peukert runtime t = C/Ik where k ≈ 1.1-1.3 for Li-ion. Pack voltage = Vcell · S-count, capacity = Ccell · P-count, with thermal derating.
Combustion
Stoichiometric AFR for CxHy: AFRs = (x+y/4) · 4.76 · 28.97 /(12x+y). Lambda λ = AFR/AFRs. Adiabatic flame Tad = Ti + LHV/((AFR+1)cp).
Unit Conversion & Constants
SI / Imperial conversion for length, force, pressure, energy, power, temperature, torque, viscosity, density. Engineering constants (g, R, σSB, NA) to 6 significant figures.
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