#MoonSteel - Steel Structure Design Calculation Library

#Features

#Core Structural Calculations

• Axial Tension Members: Strength verification for tension-loaded members (σ = N/A ≤ f)
• Axial Compression Members: Strength and stability verification for compression-loaded members
• Bending Members: Stress verification for beams under bending moments (σ = M/W ≤ f)
• Beam-Columns: Combined axial and bending load analysis
• Stability Analysis: Overall and local stability checks for structural members

#Connection Design

• Welded Connections: Butt weld and fillet weld strength calculations
• Bolted Connections: Ordinary and high-strength bolt capacity calculations
• Connection Verification: Stress checks for various connection types

#Material Properties and Constants

• Steel Material Properties: Elastic modulus (E), shear modulus (G), Poisson's ratio (ν), density (ρ)
• Steel Grades: Q235, Q345, Q390, Q420 design strength values
• Weld Strength: Weld metal strength design values for different steel grades
• Bolt Strength: Ordinary and high-strength bolt strength design values

#Auxiliary Functions

• Load Combinations: Basic and standard load combinations per building codes
• Section Classification: Steel section classification based on width-thickness ratios
• Fatigue Analysis: Fatigue strength verification and allowable stress ranges
• Fire Protection: Fire resistance calculations and protection layer thickness
• Geometric Verification: Minimum thickness, bolt spacing, and edge distance checks

#Usage

#Basic Axial Member Calculations

test "axial member design" {
  // Axial tension member: N=1000kN, A=0.01m², Q235 steel
  // σ = N/A = 1000×10³/0.01 = 100MPa < 215MPa (Q235 design strength)
  let sigma = axial_tension_strength(1000.0 * KN_TO_N, 0.01, F_Q235 * MPA_TO_PA)
  assert_eq(approx_equal(sigma / MPA_TO_PA, 100.0, 1.0), true)

  // Check if design is satisfied
  let check = axial_tension_check(1000.0 * KN_TO_N, 0.01, F_Q235 * MPA_TO_PA)
  assert_eq(check, true)

  // Axial compression with stability: N=2000kN, A=0.02m², φ=0.8, Q235
  let sigma_comp = axial_compression_stability(
    2000.0 * KN_TO_N, 0.8, 0.02, F_Q235 * MPA_TO_PA
  )
  assert_eq(approx_equal(sigma_comp / MPA_TO_PA, 125.0, 1.0), true)
}

#Beam Design and Analysis

test "beam design" {
  // Bending stress: M=500kN·m, W=0.005m³, Q235 steel
  // σ = M/W = 500×10³/0.005 = 100MPa < 215MPa
  let sigma = bending_stress(500.0 * KN_TO_N, 0.005, F_Q235 * MPA_TO_PA)
  assert_eq(approx_equal(sigma / MPA_TO_PA, 100.0, 1.0), true)

  // Check bending stress
  let check = bending_stress_check(500.0 * KN_TO_N, 0.005, F_Q235 * MPA_TO_PA)
  assert_eq(check, true)

  // Shear stress in beam: V=300kN, S=0.001m³, I=0.0001m⁴, t_w=0.01m
  let tau = shear_stress_beam(
    300.0 * KN_TO_N, 0.001, 0.0001, 0.01, FV_Q235 * MPA_TO_PA
  )
  assert_eq(tau > 0.0, true)
}

#Beam-Column Analysis

test "beam column analysis" {
  // Beam-column: N=1000kN, A=0.01m², M=200kN·m, W=0.002m³, Q235
  // σ = N/A + M/W = 100 + 100 = 200MPa < 215MPa
  let sigma = beam_column_strength(
    1000.0 * KN_TO_N, 0.01, 200.0 * KN_TO_N, 0.002, F_Q235 * MPA_TO_PA
  )
  assert_eq(approx_equal(sigma / MPA_TO_PA, 200.0, 5.0), true)

  // In-plane stability check
  let stability_check = beam_column_in_plane_stability_check(
    1000.0 * KN_TO_N, 0.9, 0.01, 200.0 * KN_TO_N, 0.85, 0.002, F_Q235 * MPA_TO_PA
  )
  assert_eq(stability_check, false)
}

#Connection Design

test "connection design" {
  // Butt weld tension: N=500kN, l_w=0.5m, t=0.01m, Q235 weld
  let sigma_weld = butt_weld_tension(
    500.0 * KN_TO_N, 0.5, 0.01, FTW_Q235 * MPA_TO_PA
  )
  assert_eq(approx_equal(sigma_weld / MPA_TO_PA, 100.0, 1.0), true)

  // Fillet weld strength: σ_f=50MPa, τ_f=50MPa, Q235 weld
  // √(50² + 50²) = 70.7MPa < 160MPa (Q235 fillet weld strength)
  let weld_stress = fillet_weld_strength(
    50.0 * MPA_TO_PA, 50.0 * MPA_TO_PA, FFW_Q235 * MPA_TO_PA
  )
  assert_eq(approx_equal(weld_stress / MPA_TO_PA, 70.7, 1.0), true)

  // Effective fillet weld thickness: h_f=0.01m, h_e=0.7×h_f=0.007m
  let he = fillet_weld_effective_thickness(0.01)
  assert_eq(approx_equal(he, 0.007, 0.0001), true)
}

#Bolted Connections

test "bolted connections" {
  // Ordinary bolt shear capacity: n_v=2, d=0.02m, f_v^b=140MPa (4.6级)
  let n_v_bolt = bolt_shear_capacity(2, 0.02, FVB_46 * MPA_TO_PA)
  assert_eq(n_v_bolt > 0.0, true)

  // Ordinary bolt bearing capacity: d=0.02m, Σt=0.04m, f_c^b=305MPa
  let n_c_bolt = bolt_bearing_capacity(0.02, 0.04, FCB_46 * MPA_TO_PA)
  assert_eq(n_c_bolt > 0.0, true)

  // High-strength bolt friction capacity: n_f=2, μ=0.4, P=100kN
  let n_hsb = hsb_friction_shear_capacity(2, 0.4, 100.0 * KN_TO_N)
  assert_eq(n_hsb > 0.0, true)

  // High-strength bolt preload: A_s=π×d²/4, f_u=400MPa
  let area_s = PI * 0.02 * 0.02 / 4.0  // 螺纹有效面积
  let preload = hsb_preload(area_s, FTB_88 * MPA_TO_PA)
  assert_eq(preload > 0.0, true)
}

#Parameter Ranges

#Valid Input Ranges

• Forces: 0–10,000 kN (axial forces, shear forces, bending moments)
• Areas: 10⁻⁴–10 m² (cross-sectional areas)
• Lengths: 10⁻³–100 m (dimensions, weld lengths)
• Thicknesses: 10⁻³–0.1 m (plate thicknesses, weld sizes)
• Material Strengths: 100–500 MPa (steel design strengths)
• Stability Factors: 0.1–1.0 (φ coefficients)
• Load Factors: 1.0–2.0 (γ_G, γ_Q factors)

#Typical Steel Design Values

• Q235 Steel: f = 215 MPa, f_v = 125 MPa
• Q345 Steel: f = 310 MPa, f_v = 180 MPa
• Q390 Steel: f = 350 MPa, f_v = 205 MPa
• Q420 Steel: f = 380 MPa, f_v = 220 MPa
• Steel Density: ρ = 7,850 kg/m³
• Elastic Modulus: E = 206 GPa

#Testing

moon test

#Test Coverage

• Mathematical utility functions and constants
• Axial member strength and stability calculations
• Beam bending and shear stress analysis
• Beam-column combined loading scenarios
• Welded and bolted connection design
• Geometric and construction requirements
• Boundary conditions and edge cases
• Load combination calculations
• Fatigue and fire protection analysis

#Technical Details

#Standards Implemented

• GB 50017-2017: Code for Design of Steel Structures
• GB 50018-2017: Code for Design of Steel-Concrete Composite Structures
• JGJ 82-2011: Technical Specification for High Strength Bolt Connections
• GB/T 19879-2005: Stainless Steel Wires for Welding

#Mathematical Methods

• Structural Analysis: Force equilibrium, stress-strain relationships
• Stability Theory: Euler buckling, effective length method
• Connection Mechanics: Elastic method for fastener groups
• Fatigue Analysis: S-N curves, Miner’s rule (simplified)
• Load Combinations: Linear superposition of load effects

#Unit System

• Length: meters (m)
• Force: newtons (N)
• Stress: pascals (Pa)
• Mass: kilograms (kg)
• Time: seconds (s)

#Notes

1. Design Standards: Calculations follow Chinese steel structure design codes
2. Safety Factors: All calculations include appropriate safety factors as per codes
3. Material Properties: Default values for common structural steels (Q235, Q345, etc.)
4. Geometric Requirements: Functions check minimum thickness and spacing requirements
5. Load Factors: Default load factors (γ_G=1.35, γ_Q=1.5) can be modified for specific projects
6. Temperature Effects: Standard calculations assume normal temperature conditions
7. Dynamic Loads: Library focuses on static load analysis; dynamic analysis requires additional considerations
8. Software Validation: Results should be verified against commercial structural analysis software

#Application Scenarios

• Structural Engineering: Steel frame buildings, bridges, industrial structures
• Civil Engineering Design: Building design offices, structural consulting firms
• Construction Quality Control: Construction supervision and inspection
• Educational Use: Structural engineering education and training
• Research Applications: Structural analysis research and development
• Preliminary Design: Conceptual design and feasibility studies
• Code Compliance: Verification of design code requirements
• Construction Documentation: Calculation reports and design documentation

#Version Information

• Axial member analysis (tension, compression with stability)
• Beam analysis (bending, shear, deflection)
• Beam-column analysis (combined axial and bending)
• Connection design (welding, bolting)
• Material properties and design constants
• Geometric verification functions
• Load combination calculations