Gfrp Structural Design

Document Structure

This skill provides access to comprehensive GFRP design documentation:

1. ASCE/SEI 74-23 Specification (Chapters 1-9)

Location: data/specification/*.md (5 part files covering 125 pages)

Purpose: What you must follow - formulas, requirements, limits, design criteria using LRFD method

Chapters:

• Chapter 1: General Provisions (scope, materials, LRFD basics, load combinations)
• Chapter 2: Design Requirements (resistance factors φ, time effect λ, environmental factors C_M/C_T/C_CH, second-order analysis, deflection, fatigue)
• Chapter 3: Tension Members (gross section, net section, pin-connected, threaded rods)
• Chapter 4: Compression Members (flexural buckling, local flange/web buckling, torsional buckling, effective length)
• Chapter 5: Flexural Members & Shear (material rupture, lateral-torsional buckling, web shear, shear buckling, concentrated loads)
• Chapter 6: Combined Forces (beam-columns, torsion, interaction equations)
• Chapter 7: Plates and Built-Up Members (in-plane loading, open-hole strength, pull-through, two-way bending)
• Chapter 8: Bolted Connections (6+ failure modes: bearing, net tension, shear-out, block shear, pull-through, bolt shear)
• Chapter 9: Seismic Design (R factors, braced frames, cooling towers)

Appendices:

• Appendix A: Symbols and Notations (complete variable definitions)
• Appendix B: Glossary (technical terms)
• Appendix C8.3.2: Multi-row bolted connection full formul as

2. Commentary (Chapters C1-C9)

Location: Integrated within the 5 part files

Purpose: Understand why - background, research basis, design philosophy

Contents: Detailed commentary for each chapter with:

• Historical development and research citations
• Design examples and comparisons
• Limit state explanations
• Special considerations for GFRP orthotropic behavior
• Reliability basis for resistance factors

3. Reference Files

Location: references/ directory (8 comprehensive guides)

This skill includes essential reference materials:

• symbols.md: Complete symbols table (150+ variables with units, sections)
• glossary.md: Technical terms and definitions (50+ terms)
• abbreviations.md: ASTM standards, acronyms, units, conversions
• chapter-structure.md: Complete chapter mapping and navigation guide
• material-properties-guide.md: Typical GFRP properties, testing requirements, statistical basis
• environmental-factors.md: C_M, C_T, C_CH adjustment factors with tables
• resistance-factors.md: φ values by failure mode (0.50-0.85) with rationale
• time-effect-factors.md: λ values by load duration (0.60-1.00) with examples

Automation Scripts

Python scripts available in scripts/ directory:

• smart_search.py: Category-aware keyword search (maps keywords to chapters)
• formula_finder.py: Extract formulas with context (±5 lines)
• material_lookup.py: Property lookup with typical ranges
• environmental_adjustment.py: Calculate adjusted strengths (F_adjusted = F × C_M × C_T × C_CH)
• connection_checker.py: Multi-mode connection design helper (6+ failure modes)

Workflow by Query Type

1. Formula Query (공식 질의)

User Intent: Find specific formula or equation from ASCE/SEI 74-23 Specification.

Example Queries:

• "What is the formula for lateral-torsional buckling of GFRP beams?"
• "Show me the compression buckling equation"
• "GFRP 보의 전단좌굴 공식을 알려줘"

Quick Process:

1. Identify topic (flexure → Chapter 5, compression → Chapter 4, connections → Chapter 8, etc.)
2. Grep relevant chapter file in data/specification/
3. Extract formula with variable definitions from references/symbols.md
4. Note orthotropic dependency: Check if formula uses E_L, E_T, G_LT (direction-dependent)
5. Note environmental factors: Remind user to apply C_M, C_T, C_CH adjustments
6. Present with ASCE citation (e.g., "ASCE/SEI 74-23 Section 5.2.2")

GFRP-Specific Considerations:

• Formulas often include √(E_L × E_T) for orthotropic effects
• Multiple buckling modes must be checked (flexural, local flange, local web, torsional)
• Environmental factors must be applied to all material properties
• Time effect factor λ must be considered for load duration

Keywords: formula, equation, 공식, 계산식, buckling, strength

2. Material Properties Query (물성값 질의 - GFRP-SPECIFIC)

User Intent: Find typical GFRP material properties or understand testing requirements.

Example Queries:

• "What is typical longitudinal modulus for pultruded GFRP?"
• "What's the difference between E_L and E_T?"
• "GFRP의 전형적인 인장강도는 얼마야?"
• "How do I determine characteristic values?"

Quick Process:

1. Check references/material-properties-guide.md for quick reference
2. Identify property type (elastic moduli, strengths, thermal)
3. Return typical ranges with caveats:
   • E_L: 2,000-4,000 ksi (14-28 GPa)
   • E_T: 800-1,500 ksi (40-50% of E_L)
   • G_LT: 300-600 ksi (~15% of E_L)
   • F_L^t: 30-50 ksi (210-345 MPa)
   • F_L^c: 20-40 ksi (60-80% of F_L^t)
4. Emphasize testing requirement: All properties must be determined per ASTM D6121 or D7290
5. Explain statistical basis (75% confidence, 20% exclusion limit)
6. Note orthotropic behavior (L vs T direction differences)

Typical GFRP Properties Table:

Testing Standards Reference:

• ASTM D3039: Tensile properties
• ASTM D3410/D695: Compressive properties
• ASTM D5379: Shear properties (V-notched beam)
• ASTM D6121: Characteristic values determination
• ASTM D7290: Filled-hole properties
• ASTM E1640: Glass transition temperature

Keywords: properties, modulus, strength, E_L, E_T, testing, characteristic value, 물성, 탄성계수, 강도

3. Environmental Adjustment Query (환경보정 질의 - GFRP-SPECIFIC)

User Intent: Apply environmental factors to adjust material properties for end-use conditions.

Example Queries:

• "How does moisture affect GFRP strength?"
• "What C_M factor should I use for wet service?"
• "Calculate adjusted strength for hot, wet, chemical exposure"
• "습윤환경에서 GFRP 강도감소는?"

Quick Process:

1. Identify exposure conditions (moisture, temperature, chemicals)
2. Check references/environmental-factors.md for factor values
3. Determine appropriate factors:
   • C_M (moisture): 0.70-1.00 (dry=1.00, wet=0.75-0.85, immersed=0.70-0.80)
   • C_T (temperature): 0.75-1.00 (< 100°F=1.00, check T vs T_g)
   • C_CH (chemical): 0.50-1.00 (varies by chemical type and pH)
   • C_CA (composite action): 0.60-1.00 (for built-up members)
   • C_LS (load sharing): 1.00-1.15 (for multiple parallel members)
4. Apply adjustment formula: F_adjusted = F_reference × C_M × C_T × C_CH × C_CA × C_LS
5. Use scripts/environmental_adjustment.py for automated calculation
6. Warning: Combined effects can reduce capacity 30-50%!

Environmental Factors Quick Table:

Critical Reminders:

• Apply factors to ALL material properties (E_L, E_T, F_L^t, F_L^c, F_LT^s, etc.)
• Test in actual service environment when critical
• Combined hot + wet is worse than sum of individual effects
• Glass transition temperature T_g is absolute limit (typically 180-250°F)

Keywords: environmental, moisture, temperature, chemical, C_M, C_T, C_CH, adjustment, wet, 환경, 습기, 온도, 화학

4. Time Effect Factor Query (시간효과계수 질의 - GFRP-SPECIFIC)

User Intent: Apply time effect factor for load duration effects (creep rupture).

Example Queries:

• "What λ factor for dead load?"
• "Time effect factor for snow load combination"
• "Why does GFRP have time-dependent strength?"
• "지속하중에 대한 강도감소는?"

Quick Process:

1. Identify load duration from load combination
2. Check references/time-effect-factors.md for λ values
3. Return appropriate factor:
   • Permanent (50+ years): λ = 0.60 (dead load only)
   • 10 years: λ = 0.70 (D + L combinations)
   • 2 months: λ = 0.80 (D + S combinations)
   • 7 days: λ = 0.90 (D + L_r combinations)
   • 10 minutes: λ = 1.00 (D + W, D + E combinations)
4. Use shortest significant duration in load combination
5. Explain creep rupture mechanism (matrix creep, stress concentrations over time)

Time Effect Factors Table (ASCE/SEI 74-23 Table 2-1):

Load Combination Examples:

• 1.4D → λ = 0.60 (dead only)
• 1.2D + 1.6L → λ = 0.70 (live controls)
• 1.2D + 1.6S → λ = 0.80 (snow controls)
• 1.2D + 1.0W → λ = 1.00 (wind controls)
• 1.2D + 1.0E → λ = 1.00 (seismic controls)

Design Equation: $$R_u \leq \phi \lambda R_n$$

Combined with φ example:

• Flexure: φ = 0.75, λ = 0.70 (D+L case)
• Design strength = 0.75 × 0.70 × M_n = 0.525 M_n (~50% of nominal!)

Keywords: time effect, duration, creep, λ, lambda, sustained load, permanent, 시간효과, 지속하중, 크리프

5. Calculation Query (계산 질의)

User Intent: Perform structural calculations using ASCE/SEI 74-23 formulas with GFRP-specific considerations.

Example Queries:

• "Calculate lateral-torsional buckling: GFRP I-beam, L_b=10ft, wet service"
• "Determine compression capacity: GFRP tube 6x6x0.375, KL=12ft, hot environment"
• "GFRP 보의 휨강도를 계산해줘: W12x6, 습윤환경, 설하중 조합"

Quick Process:

1. Identify all input parameters:
   • Section properties (shape, dimensions)
   • Material properties (E_L, E_T, G_LT, F_L^t, F_L^c, F_LT^s)
   • Environmental conditions (wet/dry, temperature, chemicals)
   • Load duration (permanent, 10-year, snow, wind, seismic)
   • Unbraced lengths, boundary conditions
2. Apply environmental adjustments:
   • Determine C_M, C_T, C_CH factors
   • Adjust ALL material properties: F_adjusted = F_ref × C_M × C_T × C_CH
3. Find relevant formula from Specification (use Formula Query workflow)
4. Check MULTIPLE limit states (GFRP often has 3-4 competing modes):
   • Flexure: Material rupture, LTB, local flange buckling, local web buckling
   • Compression: Flexural buckling, local flange, local web, torsional, flexural-torsional
   • Connections: Bearing, net tension, shear-out, block shear, pull-through, bolt shear
5. Apply resistance factor φ (varies by failure mode: 0.50-0.85)
6. Apply time effect factor λ (varies by load duration: 0.60-1.00)
7. Generate Python code following ASCE examples
8. Execute and validate

GFRP-Specific Checks (CRITICAL):

• ✅ Orthotropic properties specified (E_L, E_T, G_LT all required)
• ✅ Environmental factors applied (C_M, C_T, C_CH)
• ✅ Time effect factor applied (λ)
• ✅ Glass transition temperature verified (T_service < T_g - 20°F)
• ✅ Multiple buckling modes checked
• ✅ Direction of loading identified (longitudinal vs transverse)
• ✅ Serviceability checked (deflection often controls due to low E)

Example Calculation Framework:

# GFRP Beam Flexural Strength Calculation
# ASCE/SEI 74-23 Section 5.2

# 1. Material Properties (from testing per ASTM D6121)
E_L = 3000  # ksi, longitudinal modulus
E_T = 1200  # ksi, transverse modulus
G_LT = 450  # ksi, shear modulus
F_Lc = 35  # ksi, longitudinal compressive strength (reference)
F_Lt = 40  # ksi, longitudinal tensile strength (reference)
nu_LT = 0.30  # Poisson's ratio

# 2. Environmental Adjustment Factors (Section 2.4)
C_M = 0.85  # Wet service
C_T = 0.90  # Sustained 130°F
C_CH = 1.00  # No chemicals
# Adjusted strengths
F_Lc_adj = F_Lc * C_M * C_T * C_CH  # = 35 * 0.85 * 0.90 = 26.8 ksi
F_Lt_adj = F_Lt * C_M * C_T * C_CH  # = 40 * 0.85 * 0.90 = 30.6 ksi

# 3. Section Properties
S_x = 15.0  # in^3, section modulus
I_y = 5.0  # in^4, weak axis moment of inertia
J = 0.5  # in^4, torsion constant
L_b = 120  # in, unbraced length

# 4. Check Limit States
# (a) Material Rupture (Section 5.2.1)
M_n_rupture = S_x * F_Lc_adj  # = 15.0 * 26.8 = 402 kip-in

# (b) Lateral-Torsional Buckling (Section 5.2.2)
import math
C_b = 1.0  # Conservative (uniform moment)
M_n_LTB = C_b * math.sqrt(E_L * I_y * G_LT * J)  # Equation 5-7
# = 1.0 * sqrt(3000 * 5.0 * 450 * 0.5) = 1.0 * sqrt(3,375,000) = 1,837 kip-in

# (c) Local Buckling: Check flange and web per Section 5.2.3, 5.2.4
# (Not shown for brevity, but must be checked)

# 5. Controlling Limit State
M_n = min(M_n_rupture, M_n_LTB)  # = min(402, 1837) = 402 kip-in
controlling_mode = "Material Rupture"

# 6. Apply Resistance Factor (Section 2.3.2)
phi = 0.75  # Flexure resistance factor

# 7. Apply Time Effect Factor (Section 2.3.3)
lambda_factor = 0.80  # Snow load (2-month duration)

# 8. Design Strength
M_design = phi * lambda_factor * M_n
# = 0.75 * 0.80 * 402 = 241 kip-in

print(f"Nominal Strength: {M_n:.1f} kip-in ({controlling_mode})")
print(f"Design Strength: {M_design:.1f} kip-in")
print(f"Reduction Factors: φ={phi}, λ={lambda_factor}")

Keywords: calculate, compute, determine, design, capacity, strength, 계산, 산정, 설계, 강도

6. Connection Design Query (연결부 설계 - GFRP-SPECIFIC)

User Intent: Design bolted connections considering multiple failure modes.

Example Queries:

• "Design GFRP bolted connection: 3/4" bolt, e1=3", e2=2", t=0.5""
• "Check all failure modes for multi-row connection"
• "볼트연결부 설계: 볼트 4개, FRP-to-steel"

Quick Process:

1. Identify connection geometry:
   • Bolt diameter d_b, hole diameter d_h
   • End distance e_1, edge distance e_2
   • Pitch spacing s, gage g
   • Plate thickness t, number of bolts n, number of rows n_r
   • Materials connected (FRP-FRP vs FRP-steel)
   • Angle θ (connection force vs pultrusion direction)
2. Check minimum geometry requirements (Table 8-1):
   • e_1 ≥ 3d_h
   • e_2 ≥ 2d_h
   • s ≥ 3d_h
   • g ≥ 3d_h
3. Check ALL 6+ failure modes (Chapter 8.3): a. Bolt shear/tension (φ=0.75): Per AISC for steel bolt b. Bearing (φ=0.65): R_bf = C_b × ζ × F_br × d_b × t c. Net tension (φ=0.50): R_nt = K_nt × F_L^t × (w - d_h) × t d. Shear-out (φ=0.50): R_so = (e_2 + s/2) × t × F_LT^s e. Block shear (φ=0.65): Combined shear + tension tearing f. Pull-through (φ=0.50): R_pt = bearing pressure × washer area
4. Multi-row load distribution (if n_r > 1):
   • FRP-steel, 2 rows: 100% / 0%
   • FRP-steel, 3 rows: 60% / 40% / 0%
   • FRP-FRP, 2 rows: 60% / 40%
   • FRP-FRP, 3 rows: 60% / 30% / 20%
5. Use scripts/connection_checker.py for automated multi-mode checking
6. Controlling mode: Minimum of all 6+ capacities

Connection Failure Modes Table:

Why Connection φ is Low?:

• Stress concentrations at holes (brittle)
• Geometric variability (hole tolerance)
• Orthotropic bearing behavior
• No ductility warning before failure
• Net tension φ=0.50 is lowest in standard!

Multi-Row Example:

# 3-row FRP-to-FRP connection design
n_r = 3  # number of rows
# Load distribution factors (Table C8-1)
f_u1 = 0.60  # 1st row (furthest from free end)
f_u2 = 0.30  # 2nd row
f_u3 = 0.20  # 3rd row (nearest to free end)

# Check each row
R_nt1 = f_u1 * (net tension capacity at row 1)
R_nt2 = f_u2 * (net tension capacity at row 2)
R_nt3 = f_u3 * (net tension capacity at row 3)

# Connection capacity = min of all modes

Use scripts/connection_checker.py:

python3 connection_checker.py \
  --d_b 0.75 --e_1 3.0 --e_2 2.0 --t 0.5 \
  --F_br 40 --F_Lt 35 --F_LTs 7 \
  --n 2 --n_r 2 --material FRP-FRP

Keywords: connection, bolt, bolted, bearing, net tension, shear-out, block shear, pull-through, 연결부, 볼트, 지압, 순인장

7. Terminology Query (용어 설명)

User Intent: Understand meaning and context of GFRP design terminology.

Example Queries:

• "What is orthotropic behavior?"
• "Explain time effect factor"
• "What's the difference between characteristic value and nominal value?"
• "펄트루전이 뭐야?"

Quick Process:

1. Check references/glossary.md first
2. If not found, search "Glossary" sections in Specification (Appendix B)
3. Present definition with ASCE citation
4. Provide usage examples from Specification chapters
5. For GFRP-specific terms: Explain material science background

GFRP-Specific Terminology:

Orthotropic: Material having different properties in three mutually perpendicular directions (L, T, through-thickness). GFRP is orthotropic because continuous fibers run in longitudinal direction.

• E_L ≠ E_T ≠ E_through-thickness
• F_L^t >> F_T^t (typically 5:1 to 8:1 ratio)
• Unlike steel/aluminum which are isotropic (same in all directions)

Pultruded/Pultrusion: Manufacturing process where continuous fibers are pulled through resin bath and heated die, creating constant cross-section shapes. Like "extrusion" but pulling instead of pushing.

Characteristic Value: Statistically determined minimum property value with 75% confidence that at least 80% of population exceeds this value. Per ASTM D6121:

• NOT the average value
• NOT the minimum test value
• Statistical lower bound: F_char = mean - k×std_dev

Time Effect Factor (λ): Reduction factor for sustained loads due to creep rupture. GFRP strength decreases over time under constant stress:

• Short-term (10 min): λ = 1.00 (full strength)
• Long-term (50 years): λ = 0.60 (60% strength)
• Unique to GFRP and wood (metals don't have this)

Glass Transition Temperature (T_g): Critical temperature above which polymer matrix becomes rubbery and loses strength/stiffness. Typically 180-250°F for polyester/vinyl ester systems. Absolute design limit.

Bearing Strength (F_br): Compressive strength of GFRP under localized bolt bearing. Must be determined by testing (ASTM D7290), not calculated from material properties. Varies with:

• Load angle θ relative to pultrusion direction
• Bolt diameter to thickness ratio (d/t)
• Edge distance to diameter ratio (e/d)

Keywords: what is, explain, definition, meaning, 뭐야, 설명, 의미, 정의

8. Symbol/Notation Query (기호 질의)

User Intent: Understand what a mathematical symbol represents.

Example Queries:

• "What does E_L mean?"
• "Define C_M moisture factor"
• "λ 기호는 무엇을 의미하나요?"

Quick Process:

1. Check references/symbols.md
2. Return: Symbol | Definition | Units | Section Reference
3. Example: E_L = Longitudinal elastic modulus | ksi (MPa) | Sections 1.4, 2.3, 4.2, 5.2
4. For GFRP-specific symbols: Explain orthotropic context

Common GFRP Symbols:

Material Properties:

• E_L: Longitudinal elastic modulus (parallel to fibers) = 2,000-4,000 ksi
• E_T: Transverse elastic modulus (perpendicular to fibers) = 800-1,500 ksi (~40% of E_L)
• G_LT: In-plane shear modulus = 300-600 ksi (~15% of E_L)
• ν_LT: Poisson's ratio = 0.25-0.35 (typically 0.3)
• T_g: Glass transition temperature = 180-250°F (critical threshold)

Strengths (with superscripts):

• F_L^t: Longitudinal tensile strength = 30-50 ksi
• F_T^t: Transverse tensile strength = 5-10 ksi (much lower!)
• F_L^c: Longitudinal compressive strength = 20-40 ksi (60-80% of F_L^t)
• F_LT^s: Longitudinal-transverse shear strength = 4-10 ksi

Adjustment Factors:

• C_M: Moisture factor (0.70-1.00) - reduces strength for wet service
• C_T: Temperature factor (0.75-1.00) - reduces strength for elevated temperature
• C_CH: Chemical factor (0.50-1.00) - reduces strength for aggressive chemicals
• φ: Resistance factor (0.50-0.85) - accounts for variability, varies by failure mode
• λ: Time effect factor (0.60-1.00) - accounts for load duration (creep rupture)

Superscripts:

• ^t = tension
• ^c = compression
• ^f = flexure
• ^s = shear

Subscripts:

• _L = longitudinal direction (0°, direction of pultrusion)
• _T = transverse direction (90°, perpendicular to pultrusion)
• _LT = longitudinal-transverse (in-plane shear)
• _w = web
• _f = flange

Keywords: symbol, notation, variable, 기호, 표기, 변수

9. Comparison Query (비교 질의)

User Intent: Compare GFRP with steel/aluminum, or compare different GFRP configurations.

Example Queries:

• "GFRP vs steel structural design differences"
• "Compare E_L and E_T for GFRP"
• "GFRP와 철골 설계의 차이는?"
• "Why is GFRP deflection often critical?"

Quick Process:

1. Identify items to compare
2. For GFRP vs metals:
   • Material properties (E, density, strength)
   • Design philosophy (LRFD, factors, time effects)
   • Behavior (ductile vs brittle, isotropic vs orthotropic)
   • Environmental sensitivity
3. For GFRP directional comparison (L vs T):
   • Property ratios (E_L/E_T, F_L^t/F_T^t)
   • Orthotropic effects in design
4. Present in comparison table format

GFRP vs Steel Comprehensive Comparison:

GFRP Longitudinal vs Transverse Comparison:

Critical Design Philosophy Differences:

Steel:

• Yielding provides ductility and warning
• Properties uniform in all directions
• No time or environmental effects
• Deflection rarely controls
• φ factors higher (0.90 typical)

GFRP:

• No yielding - brittle failure without warning
• Orthotropic - must consider L vs T directions
• Time-dependent - λ factor for creep rupture
• Environmentally sensitive - C_M, C_T, C_CH factors
• Deflection often controls - E is 1/12 of steel
• φ factors lower - especially connections (0.50)
• Multiple buckling modes - flexural, local flange, local web, torsional

When GFRP is Advantageous:

1. Corrosion resistance: Chemical plants, marine, wastewater treatment
2. Lightweight: Roof structures, pedestrian bridges, temporary structures
3. EMI transparency: Near radar, MRI facilities
4. Thermal insulation: Cold storage, process equipment
5. Ease of installation: No welding, lighter crane requirements

When Steel is Better:

1. Stiffness-critical: Long spans with tight deflection limits
2. High temperature: Above 200°F sustained
3. Ductility required: Seismic zones needing R > 3
4. Fire resistance: Occupied buildings without fireproofing
5. Cost: Simple structural framing where corrosion not issue

Keywords: compare, difference, vs, 차이, 비교, steel, aluminum, metal, orthotropic, isotropic

10. Serviceability Query (사용성 질의)

User Intent: Check deflection, drift, or vibration criteria.

Example Queries:

• "What deflection limit for GFRP beams?"
• "Calculate GFRP beam deflection under service loads"
• "Why does deflection control GFRP design?"
• "GFRP 처짐 제한은?"

Quick Process:

1. Identify serviceability criterion (deflection, drift, vibration)
2. Note: No φ or λ factors for serviceability!
3. Use service load combinations (unfactored per ASCE 7)
4. Use mean modulus values (not characteristic reduced values)
5. For deflection:
   • Instantaneous: Standard elastic equation
   • Long-term creep: Δ_total = Δ_instant × (1 + ψ_creep)
   • Creep multiplier ψ typically 1.5-3.0 for sustained loads
6. Compare to limits (Section 2.6):
   • Floors: L/360 (or L/240 for special cases)
   • Roofs: L/240 or L/180
   • Cantilevers: More stringent
7. Deflection often governs GFRP design!

Why Deflection Controls GFRP:

• E_GFRP ≈ E_steel / 12 (much more flexible)
• Deflection ∝ 1/E (inversely proportional)
• Same load, same span → GFRP deflects 12× more than steel
• L/360 limit often exceeded unless section is large

Deflection Calculation Example:

# GFRP Simple Beam Deflection
# No φ, no λ for serviceability!

# Service loads (unfactored)
w_D = 50  # plf, dead load
w_L = 100  # plf, live load
L = 20 * 12  # inches, span

# Material (mean values, not reduced)
E_L = 3000  # ksi, mean longitudinal modulus
I = 100  # in^4, moment of inertia

# Instantaneous deflection (elastic)
w_total = w_D + w_L  # = 150 plf
Delta_instant = (5 * w_total * L**4) / (384 * E_L * I)
# = (5 * 150/12 * 240^4) / (384 * 3000 * 100)
# = 2.88 in

# Long-term deflection (creep under sustained load)
psi_creep = 2.0  # Creep multiplier (typical 1.5-3.0)
w_sustained = w_D  # Only dead load is sustained
Delta_creep = psi_creep * (5 * w_sustained * L**4) / (384 * E_L * I)
# = 2.0 * (5 * 50/12 * 240^4) / (384 * 3000 * 100)
# = 0.96 in

Delta_total = Delta_instant + Delta_creep  # = 2.88 + 0.96 = 3.84 in

# Check limits
L_360 = L / 360  # = 240 / 360 = 0.67 in
L_240 = L / 240  # = 240 / 240 = 1.00 in

if Delta_total > L_360:
    print(f"FAILS L/360: {Delta_total:.2f} in > {L_360:.2f} in")
    print("Increase section size or reduce span")