FRP profile calculator methodology
A reproducible account of the geometry equations, load cases, resistance factors, shear-deflection correction, material assumptions, standards boundaries and exclusions behind the free calculator.
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Calculation sequence and units
Inputs are converted to a consistent N–mm system. The engine first validates the wall geometry, then computes gross area A, strong-axis second moment Ix, elastic section modulus Wx, and an effective shear area Av. It applies the selected load-case coefficients to service moment and shear, applies the chosen load factor only to strength demand, and compares those factored stresses with reduced material resistance. Deflection remains a service-load calculation. Keeping strength and serviceability paths separate prevents a load factor from being applied twice.
The interactive calculator and the crawlable FRP span tables import the same section-property functions. A geometry update therefore changes both outputs together, and the validation benchmarks are recomputed from that shared engine during the site build.
Section-property equations
I-beams and channels use the outer rectangle minus the web-side voids: Ix = [B·H³ − (B − tw)·(H − 2tf)³] / 12. Rectangular tubes use the outer rectangle minus the concentric inner rectangle. Round tubes use Ix = π·(Ro⁴ − Ri⁴) / 4 and A = π·(Ro² − Ri²). Angles are resolved as two non-overlapping rectangles; the centroid is found first and the parallel-axis theorem is applied to both legs. Wx equals Ix divided by the farthest extreme-fiber distance. For unsymmetrical angles, that distance is measured from the calculated centroid rather than assumed to be H/2.
These are classical geometry identities, not equations supplied by EN 13706 or ASTM D3917. The tool uses the clear web area for I-beam and channel shear, the two side walls between the flanges for a box section (2·(H − 2t)·t), half the gross annular area for a round tube, and the vertical leg for an angle. That Av model is intentionally simple and is one reason the result remains a preliminary check.
Load effects, stress and deflection
| Load case | Maximum moment | Bending deflection | Shear correction c |
|---|---|---|---|
| Simple span, UDL | wL²/8 | 5wL⁴/(384EIx) | 9.6 |
| Simple span, mid-point load | PL/4 | PL³/(48EIx) | 12 |
| Cantilever, tip load | PL | PL³/(3EIx) | 3 |
| Cantilever, UDL | wL²/2 | wL⁴/(8EIx) | 4 |
Bending stress is M/Wx and the average shear check is V/Av. Total deflection uses a load-case-matched Timoshenko correction: δtotal = δbending·[1 + c·E·Ix/(G·Av·L²)]. This matters for pultruded GFRP because longitudinal E and in-plane G are very different. The selected L/n criterion is then applied to the service-load deflection. For wet service both moduli are reduced by the stiffness factor of that environment (0.90) before the deflection is calculated.
Resistance, load duration and environment
The design strength is φ · λ · Fk · Cenv, compared with the factored stress. Fk is min(FtL, FcL) for bending and the shear strength for shear. On the ASCE path, λ is the time-effect factor of the selected load duration (0.8 occupancy live load, 0.6 storage, 0.4 permanent, 1.0 wind or earthquake, from the ASCE LRFD Pre-Standard of 2010 on which ASCE/SEI 74-23 builds), and the load factor follows ASCE 7-22 (1.6 live, 1.4 permanent, 1.0 strength-level wind or earthquake). The CEN path uses γM= 1.5 with the EN 1990:2023 variable-action factor 1.5 for consequence class CC2; the creep conversion factor for permanent loads is not applied, so permanent loads need a separate check. The EN 13706 E17 and E23 datasets use the standard's minimum modulus, tensile strength and interlaminar shear strength (15 and 25 MPa, standing in for the in-plane shear strength that EN 13706 does not give); GLT and FcL are stated assumptions.
| Environment | Strength | Stiffness | Basis |
|---|---|---|---|
| Indoor, dry, ≤ 30 °C | 1.00 | 1.00 | Reference; no knockdown |
| Outdoor, exposed (UV + humidity) | 0.85 | 1.00 | In line with the moisture conversion factor CEN/TS 19101 uses for outdoor exposure not continuously wet |
| Wet / immersion | 0.75 | 0.90 | ASCE/SEI 74-23 wet-service adjustment for a polyester matrix: 0.75 on strength, 0.90 on stiffness |
| Mild chemical (acid/alkali) | 0.75 | 1.00 | F1 screening value; resin-specific chemical data are needed |
| Elevated temperature (32–60 °C) | 0.70 | 1.00 | F1 screening value; stiffness also falls, so ask for resin data. ASCE/SEI 74-23 limits service temperature to T_g − 22 °C |
What each standard contributes
ASCE/SEI 74-23
A US LRFD framework for structures made with pultruded GFRP shapes, connections and prefabricated products. The calculator exposes it as a preliminary flexural and shear resistance path; it does not implement the standard chapter by chapter. Official ASCE scope
EN 13706
A product specification series for pultruded profiles: designation, test and general requirements, and specific requirements. The E17 and E23 material presets use its grade language; the series is not the source of the beam equations. BSI series record
ASTM D3917-23
Dimensional tolerances for thermosetting glass-reinforced pultruded shapes. It supports dimensional acceptance, not structural resistance or section-property formulas. Official ASTM record
CEN/TS 19101:2022
The European technical specification for fibre-polymer composite structures. CEN has agreed to turn it into a Eurocode, expected by 2028; until then a project has to adopt it explicitly. Its actions come from EN 1990, now in its second generation (EN 1990:2023), where the partial factors are 1.35 kF and 1.5 kF with kF = 1.0 for consequence class CC2.
GB 50608-2020 and T/CECS 692-2020
The Chinese design path. The interface keeps each method's load and resistance factors together, so a user does not silently mix one code family's demand factors with another family's resistance factors.
Codes by market
| Market | Loads and main combinations | Pultruded FRP design | Related documents |
|---|---|---|---|
| United States | ASCE 7-22 through the IBC: 1.4D; 1.2D + 1.6L | ASCE/SEI 74-23 (LRFD for pultruded GFRP shapes and connections) | OSHA 29 CFR 1910 Subpart D for workplace access; ASTM D3917 dimensional tolerances |
| European Union | EN 1990:2023 and EN 1991: 1.35·k_F·G; 1.5·k_F·Q (k_F = 1.0 for CC2), national annexes | CEN/TS 19101:2022, Eurocode expected by 2028 | EN 13706 product specification; EN ISO 14122 for machinery access |
| United Kingdom | BS EN 1990 and BS EN 1991 with UK National Annexes | PD CEN/TS 19101:2022 | BS EN 13706; BS EN ISO 14122 for machinery access |
| Canada | NBC Part 4 (NBC 2020; NBC 2025 published December 2025, adopted by each province on its own timetable: check the edition in force): 1.4D; 1.25D + 1.5L | No standard specific to pultruded shapes; CSA S806 covers self-supporting FRP components and FRP-reinforced or strengthened concrete in buildings and is the usual Canadian reference | CSA S6:25 for bridges; CSA S807 for FRP bars |
| Australia | AS/NZS 1170.0 and 1170.1: 1.35G; 1.2G + 1.5Q | No Australian standard for pultruded shapes; published Australian design guides use the ASCE LRFD approach with AS/NZS 1170 loads | AS 1657:2018 for platforms, walkways, stairs and ladders; AS 5204:2023 for FRP bars |
| New Zealand | AS/NZS 1170.0 and 1170.1 through NZBC B1: 1.35G; 1.2G + 1.5Q | No New Zealand standard for pultruded shapes; the resistance model is agreed with the building consent authority | NZBC D1 and F4 for access routes and barriers |
The calculator's ASCE option applies 1.6 to live load, which is conservative against the 1.5 used by AS/NZS 1170.0 and the NBC. Use the CEN option for European and UK projects.
Boundaries and required engineering review
The tool does not complete lateral-torsional buckling, local plate buckling, web crippling, bearing, connection, fatigue, fire, creep deflection, creep rupture, vibration, combined axial and flexural loading, biaxial bending, principal-axis angle design, continuous beams, frames, or second-order effects. Environmental factors are screening inputs, not project-specific durability predictions. Catalog dimensions also require tolerance review before final capacity is accepted.
Use the result to compare candidate shapes, reproduce assumptions and prepare an RFQ. A qualified engineer must establish governing loads, combinations, restraint, code edition, material qualification, connection details and final limit states for the actual project.
Send the member and loads for a checked section
Send the span, loads, support conditions and design code with the candidate section. We reply within one business day.