Structural Safety & Reliability Engineering · SPAN-SAFETY-01 · Version 1.0.0 · May 2026

LOAD-SPAN

Dynamic Load Redistribution Analysis and Long-Span Structural Stability Assessment
with AI-Assisted Analytical Support
Structural Mechanics · Reliability Engineering · Dynamic Loading · AI-Augmented Monitoring Support

"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."

↗ View on GitHub 📦 PyPI Package 🔬 Zenodo DOI 🦊 GitLab Mirror

Real-Time Safety Governance

Four-Level LSII Signal Classification

Every long-span structure evaluated by LOAD-SPAN receives a continuous safety signal with full redistribution, stability, and fatigue diagnostics.

LSII ≥ 0.90

🟢 STEADY STATE

All redistribution, stability, and fatigue constraints satisfied. Normal operation active — continuous monitoring.

0.75 ≤ LSII < 0.90

🟠 MONITORING PHASE 1

Load redistribution detected or fatigue accumulation. Enhanced monitoring frequency — targeted inspection at flagged details.

0.65 ≤ LSII < 0.75

🟠 MITIGATION PHASE 2

Operational load restriction required. Immediate structural review — buckling verification and hot-spot inspection.

LSII < 0.65

🔴 CRITICAL BREACH

Safety threshold breach. Immediate closure. Exclusion zone enforcement. Full diagnostic: DLRM redistribution map, FARM damage, LSSAM stability report.

Governance Architecture

Four Modules · One Structural State · Continuous Assessment

Fully coupled dynamic load redistribution assessment augmented by real-time sensor fusion and AI-assisted support.

MODULE 01

DLRM — Dynamic Load Redistribution Module

R_struct ≥ 0.70 · DCR ≤ 2.0

Direct stiffness method with influence matrix S_inf(i,j) = ∂F_i/∂k_j. Tracks internal force redistribution after member stiffness changes.

K·u = f → ΔF_member = K_m·Δu_m
S_inf = ∂F_i/∂k_j

MODULE 02

LSSAM — Long-Span Stability Assessment Module

λ_cr ≥ 2.00 · β ≥ 3.50

Euler critical load with dynamic buckling threshold. Euler-Riks arc-length method for post-buckling behavior.

P_cr = π²·E·I/(K·L)²
P_cr,pred = P_cr,euler·[1 - γ·(a_max/g)·sin(Ωt)]

MODULE 03

FARM — Fatigue Accumulation & Reliability Module

D_fatigue < 0.80

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)
β = (μ_R - μ_S)/√(σ_R² + σ_S²)

MODULE 04

AISL — AI-Assisted Support Layer

A_index ≥ 0.15 · 48h Forecast

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

A_index(x,t) = |σ_meas - σ_theo|/σ_theo
ε_AI ≤ 0.05·ΔR_max

LSII

Long-Span Structural Integrity Index

LSII ≥ 0.90

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

LSII = 0.35·(β/β_t) + 0.30·(1-D_fatigue)
+ 0.20·R_struct + 0.15·(λ_cr/λ_t)

SENSOR FUSION

Multi-Sensor Integration

200Hz · 1.8GB/day

Accelerometers, strain gauges, load cells, displacement sensors. Operational modal analysis with EFDD. Real-time data fusion and QC.

SSI-COV: Y = [y|ŷ]·SVD·modal extraction
K_F = P·Hᵀ·[H·P·Hᵀ + R]⁻¹

Experimental Validation

Three Canonical Benchmark Scenarios

Validated against cable-stayed bridge, truss viaduct forensic, and scale model under storm, fatigue, and progressive loading conditions.

Case	Structure Type	LSII Accuracy	Anomaly Detection	Fatigue MAE	β Accuracy	Status
V1	Cable-stayed bridge — storm + strand fracture	±2.9%	93.8%	2.8%	±4.2%	✅ PASS
V2	Truss viaduct — fatigue collapse forensic	±3.1%	91.2%	3.4%	±3.8%	✅ PASS
V3	Scale model — progressive cable removal	±2.6%	95.1%	2.1%	±3.1%	✅ PASS
MEAN	—	±2.87%	93.4%	2.77%	±3.7%	🏆 CERTIFIED

LSII certification threshold = 0.90 · β target = 3.8 · Damage limit = 0.80 · λ_cr target = 2.0

Mathematical Foundation

Governing Equations & Safety Bounds

K·u = f → ΔF_member = K_m·Δu_m
P_cr = π²·E·I/(K·L)²
D_fatigue(t) = Σ n_i/N_i(Δσ_i)
β = (μ_R - μ_S)/√(σ_R² + σ_S²)
LSII = 0.35·(β/β_t) + 0.30·(1-D_fatigue) + 0.20·R_struct + 0.15·(λ_cr/λ_t)

LSII ≥ 0.90

Long-Span Structural Integrity Index

β ≥ 3.50

Reliability index (target 3.8)

λ_cr ≥ 2.00

Buckling critical load factor

D_fatigue < 0.80

Fatigue damage warning threshold

R_struct ≥ 0.70

Structural redundancy index

Quick Start

Deploy Safety Governance in 60 Seconds

pip install load-span-engine

from load_span import LoadSpanAssessor

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

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

from load_span.fatigue import RainflowCounter, PalmgrenMiner
from load_span.fatigue.sn_curves import SNCurve
import numpy as np

# Load strain time series
strain_ts = np.random.randn(10000) * 50

# ASTM E1049-85 rainflow cycle counting
counter = RainflowCounter()
cycles = counter.count(strain_ts)

# Eurocode FAT90 S-N curve
sn = SNCurve(fat_class="FAT90")

# Palmgren-Miner damage accumulation
miner = PalmgrenMiner(sn_curve=sn)
damage = miner.accumulate(cycles)

print(f"Fatigue damage: {damage:.4f} (limit: 0.80, failure: 1.00)")

from load_span.modules.lssam import LongSpanStabilityModule

stab = LongSpanStabilityModule()
stab.configure(lambda_cr_min=2.0, beta_min=3.5)

result = stab.assess()

print(f"λ_cr: {result['lambda_cr']:.3f} (target: 2.0)")
print(f"β: {result['beta']:.3f} (target: 3.8)")
print(f"P_cr: {result['p_cr_euler']/1e6:.2f} MN")

# Launch real-time Streamlit LSII governance dashboard
$ streamlit run examples/streamlit_dashboard.py

# Dashboard at: http://localhost:8501
# Panels: LSII composite gauge · Load redistribution trend · Fatigue damage map · Reliability index β · 24-48h forecast

# Or open web dashboard:
# https://load-span.netlify.app/dashboard

Citation

Cite LOAD-SPAN in Your Research

If LOAD-SPAN contributes to your research, please use one of the citation formats below.

@software{baladi2026loadspan_pypi,
  author    = {Baladi, Samir},
  title     = {{LOAD-SPAN}: Dynamic Load Redistribution Analysis and
               Long-Span Structural Stability Assessment with
               AI-Assisted Analytical Support},
  year      = {2026},
  version   = {1.0.0},
  publisher = {Python Package Index},
  url       = {https://pypi.org/project/load-span-engine},
  note      = {Python package, MIT License, Series SPAN-SAFETY-01}
}

@dataset{baladi2026loadspan_zenodo,
  author    = {Baladi, Samir},
  title     = {{LOAD-SPAN}: Dynamic Load Redistribution Analysis and
               Long-Span Structural Stability Assessment with
               AI-Assisted Analytical Support —
               Research Paper and Simulation Data},
  year      = {2026},
  publisher = {Zenodo},
  version   = {1.0.0},
  doi       = {10.5281/zenodo.20422430},
  url       = {https://doi.org/10.5281/zenodo.20422430},
  note      = {Structural Safety & Reliability Engineering · SPAN-SAFETY-01}
}

@misc{baladi2026loadspan_osf,
  author    = {Baladi, Samir},
  title     = {{LOAD-SPAN} Framework: Pre-registered Study Protocol for
               Dynamic Load Redistribution Analysis and Structural
               Stability Assessment in Long-Span Systems},
  year      = {2026},
  publisher = {Open Science Framework},
  doi       = {10.17605/OSF.IO/H35FU},
  url       = {https://doi.org/10.17605/OSF.IO/H35FU},
  note      = {OSF Preregistration}
}

Baladi, S. (2026). LOAD-SPAN: Dynamic Load Redistribution Analysis
and Long-Span Structural Stability Assessment with AI-Assisted
Analytical Support (Version 1.0.0, Series SPAN-SAFETY-01). Zenodo.
https://doi.org/10.5281/zenodo.20422430