Scope in one sentence: the tool checks a prismatic pultruded FRP member under one idealized load case for strong-axis bending stress, average web shear stress, and service deflection; it is a transparent preliminary-sizing aid, not a sealed structural design.
1. 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.
2. 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 web area for I-beam/channel shear, two longitudinal walls for a box section, half 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.
3. Load effects, stress, and deflection
| Load case | Maximum moment | Bending deflection | Shear correction coefficient 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.
4. What each standard contributes
- ASCE/SEI 74-23 supplies a US LRFD framework for structures made with pultruded GFRP shapes, connections, and prefabricated products. The calculator exposes this as a preliminary flexural/shear resistance path; it does not implement the standard chapter by chapter. See the official ASCE scope.
- EN 13706 is a pultruded-profile product specification series: designation, test/general requirements, and specific requirements. E17/E23 material presets use its grade language; the series is not presented here as the source of the beam equations. See theBSI series record.
- ASTM D3917-23 covers dimensional tolerances for thermosetting glass-reinforced pultruded shapes. It supports dimensional acceptance, not structural resistance or section-property formulas. See the official ASTM record.
- CEN/TS 19101:2022, GB 50608-2020, and T/CECS 692-2020 provide alternative regional design paths and application context. The interface keeps their load/resistance choices visible so users do not silently mix one region’s demand factors with another region’s material assumptions.
5. Boundaries and required engineering review
The tool does not complete lateral-torsional buckling, local plate buckling, web crippling, bearing, connection, fatigue, fire, creep rupture, sustained-load time effects, 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.