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 and elevated-temperature service both moduli are reduced by the stiffness factor of that environment (0.90 and 0.74) 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, as in the ASCE/SEI 74-23 table and the 2010 Pre-Standard before it), 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 a screening 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 | F1 screening value for outdoor exposure that is not continuously wet; a CEN/TS 19101 design uses the standard's own moisture conversion factor |
| Wet / immersion | 0.75 | 0.90 | ASCE/SEI 74-23 sustained-moisture factor C_M: 0.75 on strength, 0.90 on stiffness, the same for polyester and vinyl ester |
| Mild chemical (acid/alkali) | 0.75 | 1.00 | F1 screening value; resin-specific chemical data are needed |
| Elevated temperature (32–49 °C) | 0.70 | 0.74 | ASCE/SEI 74-23 temperature factor C_T for a polyester matrix at 49 °C (120 °F): 1.9 − 0.010T on strength and 1.7 − 0.008T on stiffness, T in °F. At 60 °C these fall to 0.50 and 0.58, so ask for resin data. Service is limited 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/TC 250 approved its conversion into Eurocode 11 (prEN 19101-1-1, -1-2 and -2) as new projects in July 2026, with no publication date yet; until then a project has to adopt the TS 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; its conversion to Eurocode 11 (prEN 19101) started as a CEN project in July 2026, with no publication date yet | 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 S806:26 (third edition, 2026) covers FRP building 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.