Curved and tapered glulam
A simple-span glulam beam of one of two kinds, by NDS 2024 5.3.8 to 5.3.10, 5.2.8, 5.2.9, 5.4.1 and 5.4.2 under uniform loads. LRFD or ASD.
- a curved beam of constant section;
- a double-tapered curved (pitched-tapered) beam, Figure 5C.
Inputs of the curved beam #
- Beam: curved with constant section (5.4.1) or double-tapered curved (5.4.2).
- Stress class: the Supplement Table 5A values in the library (read against the 2024 Supplement, p. 80).
- Width and depth: for a pitched-tapered beam, the depth at the ends de and at the peak dc, the roof slope φT and the soffit slope at the ends φB.
- Lamination thickness t and radius R: t is the lamination thickness in the curved part, R the radius of its inside face. Curved members usually use 3/4 in. laminations; t/R is limited to 1/100 for Southern Pine and hardwoods and 1/125 for other softwoods (5.3.8).
- The moment (curved beam):
- Flattens the curve: radial tension, checked against Frt'. Gravity on a crowned or pitched beam does this.
- Sharpens the curve: radial compression, checked against Frc' = Fc⊥y'.
- Span: span of the beam.
- Loads: dead, roof live, snow, live and downward wind in plf. Wind matters for radial tension: with wind or earthquake, Douglas Fir-Larch and the western species take (1/3) Fvx Cvr instead of 15 psi (Table 5.2.8).
- Deflection limits: L/ for live load and total load (IBC Table 1604.3 roof values prefilled; your choice).
- Service conditions: wet service and temperature. Load duration is in the code options.
Auto-design (editor toolbar) varies the width and the depth in lamination steps (the peak depth of a pitched-tapered beam). Objective: the least wood.
Checks performed #
| Check | Basis |
|---|---|
| t/R | ≤ 1/100 Southern Pine, ≤ 1/125 other softwoods (5.3.8) |
| Bending | Curved: 6M/(bd²). Pitched: Kφ 6M/(b dc²), Kφ = 1 + 2.7 tan φT (Eq. 5.4-2). Both against Fb' with Cc (Eq. 5.3-3) and CV (CL = 1.0 with the top braced, 5.3.5) |
| Radial stress | Curved: fr = 3M/(2 Rm b d) (Eq. 5.4-1). Pitched: fr = Krs Crs 6M/(b dc²) (Eq. 5.4-3) with Krs and Crs (uniform load, dc/Rm ≤ 0.3). Against Frt' (Table 5.2.8, with CD, CM and Ct of Fv) and never more than F'v/3, or against Frc' = Fc⊥y' (5.2.9) |
| Straight-tapered part | The largest 6M/(bd²) along the taper against Fb' with the lesser of CI (Eq. 5.3-4, taper φT − φB on the compression face) and CV |
| Shear | (2/3) F'v b d at the support (de for a pitched beam) with Cvr = 0.72, without the reduction for loads near supports |
| Deflection | Curved: as a straight beam (5.4.1.4). Pitched: Eq. 5.4-4 with dequiv. Dead load × Kcr = 1.5 (3.5.2) in the total |
| Horizontal movement | Pitched: ΔH = 2hΔc/ℓ (Eq. 5.4-5), a note for the support detail; curved: a note (5.4.1.4) |
The drawings are the beam elevation (the arc, or the Figure 5C shape with its depths and slopes) and the section with the laminations.
Limitations #
- Glulam reference values: Supplement Table 5A (p. 80), read 2026-11-12. Table 5A Expanded combinations are not offered here.
- Lateral stability: the compression edge is taken as braced (CL = 1.0).
- Not covered:
- unbraced beams;
- Tudor and three-hinged arches (5.4.3);
- radial reinforcement design (only its F'v/3 cap is checked);
- point loads and unsymmetrical members.
- Pitched beam geometry: ℓc is taken as 2R sin φB, the horizontal length of a circular soffit between the tangent points. The bending stress along the straight-tapered part uses the vertical depth.
Verification examples #
Verification status: 17 values compared in 2 examples (0 published, 2 hand calculations from the cited equations): 17 within tolerance, 0 recorded deviations. No published example: every value is a hand calculation. That checks the program against this reading of the code, not the reading itself. Code basis: not yet recorded for this module.
No worked example of a curved or pitched-tapered beam is on disk. The values are hand calculations of the NDS equations with the library's 24F-1.8E values:
- Curved beam: Cc, CV, bending, radial stress against 15 psi × CD, shear and deflection.
- Pitched-tapered beam: Kφ, Krs, Crs, the peak bending and radial stresses, dequiv, Δc and ΔH.
The AITC / APA glulam design manuals are listed as needed.