LOAD-SPAN Documentation

📖 Overview

"Structural integrity in a long-span system is not a property frozen at commissioning — it is a continuously evolving state of internal force redistribution requiring continuous quantitative assessment."

LOAD-SPAN is a fully coupled, AI-augmented continuum mechanics framework that treats long-span structural safety as a continuously governed dynamic invariant — not a static design property frozen at the completion of a finite element run.

A long-span structure under operational and environmental loading is not in static equilibrium. It is a dynamically evolving system continuously redistributing internal forces, accumulating fatigue damage at connections, and progressing toward or receding from its reliability index threshold in real time. LOAD-SPAN quantifies these changes continuously and governs the safety margin accordingly.

🏗️ 4-Module + AI Architecture

Module 01 — DLRM (Dynamic Load Redistribution Module)

Direct stiffness method with influence matrix S_inf(i,j) = ∂F_i/∂k_j. Tracks internal force redistribution after member stiffness changes. Evaluates progressive collapse via alternate load path (ALP) method.

K·u = f → ΔF_member = K_member·Δu_member
S_inf(i,j) = ∂F_i/∂k_j
DCR = F_redistributed / F_capacity

Module 02 — LSSAM (Long-Span Stability Assessment Module)

Euler critical load with dynamic buckling threshold. Euler-Riks arc-length method for post-buckling behavior. Cornell-Hasofer-Lind reliability index (β).

P_cr = π²·E·I/(K·L)²
P_cr,pred = P_cr,euler·[1 - γ·(a_max/g)·sin(Ωt)]
β = (μ_R - μ_S)/√(σ_R² + σ_S²) → P_f = Φ(−β)

Module 03 — FARM (Fatigue Accumulation and Reliability Module)

ASTM E1049-85 rainflow cycle counting. Palmgren-Miner linear damage accumulation. Eurocode FAT class S-N curves. IIW hot-spot stress extrapolation.

D_fatigue(t) = Σ n_i/N_i(Δσ_i)
σ_a,eq = σ_a / (1 - σ_m/σ_u)
β_augmented = (μ_R - μ_S)/√(σ_R² + σ_S² + σ_AI²)

Module 04 — AISL (AI-Assisted Support Layer)

XGBoost anomaly detection in stress wave fields. LSTM 24-48h LSII trajectory forecast. Physics-constrained with γ_max = 0.15 bound. ε_AI ≤ 0.05·ΔR_max.

A_index(x,t) = |σ_meas - σ_theo|/σ_theo ≥ α_threshold
ε_AI(t) ≤ 0.05·ΔR_max
γ_ML ≤ 0.15 (EN 1090-2 bound)

LSII — Long-Span Structural Integrity Index

Weighted composite of reliability index, fatigue damage, structural redundancy, and buckling factor. Continuous real-time safety certification with 24-48h forecast.

LSII = 0.35·(β/β_t) + 0.30·(1-D_fatigue) + 0.20·R_struct + 0.15·(λ_cr/λ_t) ≥ 0.90
β_t = 3.8, λ_t = 2.0, D_limit = 0.80

📐 Core Equations

⚙️ LSII Governance Protocol

📦 Installation

pip install load-span-engine

# From source
git clone https://github.com/gitdeeper12/LOAD-SPAN.git
cd LOAD-SPAN
pip install -e .

# Quick test
python -c "from load_span import LoadSpanAssessor; print('LOAD-SPAN ready')"

🔧 API Reference

from load_span import LoadSpanAssessor

# Initialize with span configuration
assessor = LoadSpanAssessor(
    span_config="configs/cable_stayed_bridge.yaml",
    sensor_stream="live"
)

# Run full LOAD-SPAN pipeline
result = assessor.evaluate()

print(result.lsii_result.lsii)        # LSII ∈ [0, 1]
print(result.lsii_result.signal.value) # STEADY_STATE | MONITORING_PHASE_1 | MITIGATION_PHASE_2 | CRITICAL_BREACH
print(result.lsii_result.beta)        # Reliability index β
print(result.lsii_result.d_fatigue_max) # Palmgren-Miner damage
print(result.lsii_result.lambda_cr)   # Buckling critical load factor
print(result.lsii_result.r_struct)     # Structural redundancy index

📊 Validation Summary

👤 Author

📝 Citation

"Structural integrity in a long-span system is not a property frozen at commissioning — it is a continuously evolving state of internal force redistribution requiring continuous quantitative assessment." — LOAD-SPAN v1.0.0