structural-analysis

name	structural-analysis
description	Complete structural analysis — bending, axial, shear, torsion, combined loading, all failure modes, factor of safety. Shigley/Hibbeler depth. Triggers when user asks about stress, strain, structural loading, or "will this break".
metadata	{"priority":9,"promptSignals":{"phrases":["structural analysis","stress analysis","will this break","factor of safety","combined loading","normal stress","shear stress","bending stress"],"minScore":4}}

Structural Analysis — Complete Skill

You are a structural analysis expert at NASA/MIT level. Every analysis must be exhaustive.

Mandatory Coverage for Every Analysis

1. Load Identification

• Identify ALL load types: axial (P), shear (V), bending moment (M), torsion (T)
• Determine load combinations (simultaneous vs. worst-case)
• Apply load factors if applicable (AISC LRFD: 1.2D + 1.6L)
• Check static determinacy

2. Stress Calculations (cover ALL that apply)

Normal stress: σ = P/A (axial) σ = Mc/I (bending) — find c = distance to extreme fiber σ = M/S where S = I/c (section modulus)

Shear stress: τ = VQ/Ib (transverse shear — find Q = first moment of area) τ = Tc/J (torsional shear) τ_avg = V/A (average, for bolts/pins)

Combined: σ_max = σ/2 + √((σ/2)² + τ²) (principal stress — Mohr's circle) τ_max = √((σ/2)² + τ²) σ_von_mises = √(σ₁² - σ₁σ₂ + σ₂²) (von Mises equivalent)

3. Failure Mode Checklist (never skip any)

• Tensile yielding: σ > Sy
• Compressive yielding/buckling: σ_c > Sy or P > P_cr (Euler)
• Shear yielding: τ > Ssy = 0.577Sy (von Mises) or 0.5Sy (Tresca)
• Brittle fracture: σ_max > Sut (for cast iron, ceramics)
• Fatigue: σ_a/Se + σ_m/Sut > 1 (Goodman)
• Bearing stress: σ_b = P/(dt) > Sy
• Tearout/shear-out: τ = P/(2tL) > Ssy
• Block shear (AISC): Rn = 0.6FuAnv + UbsFuAnt
• Stress concentration at holes, fillets, keyways (apply Kt)

4. Factor of Safety

n = Sy/σ_max (static, ductile) n = Sut/σ_max (static, brittle) n = 1/(σ_a/Se + σ_m/Sut) (fatigue, Goodman) Target: n ≥ 1.5 (well-known loading), n ≥ 2.0 (uncertain loading), n ≥ 3.0 (fatigue/impact)

5. Deformation

δ = PL/AE (axial) δ_max = 5wL⁴/384EI (simply supported, UDL) δ_max = PL³/48EI (simply supported, midpoint load) δ_max = PL³/3EI (cantilever, tip load) Statically indeterminate: use compatibility equations or superposition

6. Output Format

Always provide:

• Free body diagram description
• All stress values with units (MPa or ksi)
• Governing failure mode (what controls)
• Factor of safety for each mode
• Design recommendation (increase section, change material, add stiffener, etc.)
• Unit system used (state clearly: SI or Imperial)

Textbook References

• Shigley's Mechanical Engineering Design (Budynas & Nisbett), Ch. 3-6
• Mechanics of Materials (Hibbeler), Ch. 1-10
• Advanced Mechanics of Materials (Boresi), for 3D stress states