Reinforcement of a curved or tapered beam to SIA 265
Checks the reinforcement of a curved beam, a variable-inertia (pitched-cambered) beam or an arch against tension perpendicular to the grain at the ultimate limit state, to SIA 265:2021, annex E.5. Every step shows its formula and the clause it comes from.
Pro SIA 265:2021
Part of the Pro plan
This module is included in the Pro plan and above, with its calculation note.
About this check
clauses, worked example and questions
Checks the reinforcement of a curved beam, a variable-inertia (pitched-cambered) beam or an arch against tension perpendicular to the grain at the ultimate limit state, to SIA 265:2021, annex E.5. Every step shows its formula and the clause it comes from.
What it checks
- Stress across the grain, SIA 265 clause 5.1.3, equation (54): σt,90,d = (MEd / W) · h / (4·r), with W = b · h² / 6 and the radii ra and ri (figure 15). For a variable-inertia beam it comes from the apex moment with the coefficient kp of SIA D0185 §7.3, 7.5 and 7.6 (SIA 265 gives no model for that shape); for an arch, or any case only a frame analysis settles, it is entered directly.
- Tension on one element, clause E.5.1, equation (146): Ft,90,Ed = kB · (b · a1 / n) · σt,90,d, with kB = 1.0 in the two inner quarters of the tension zone.
- Check 1, clause E.5.1: Ft,90,Ed ≤ Rax,d, with ηt and ηw (clauses 2.2.6 and 3.2.1.3, table 4) applied where withdrawal or the bonded length governs.
- Check 2, clause E.5.2: 250 mm ≤ a1. Closer elements interfere and restrain the shrinkage of the section.
- Check 3, clause E.5.2: a1 ≤ 0.75·h. Beyond this the timber between two elements is held by neither.
What you enter and what you get
You enter the member (wood type, strength class, load duration, service class, b, and h, the apex depth for a variable-inertia beam); the type of beam and the quarters the elements sit in; the source of σt,90,d; MEd, the radius r at the neutral axis and the sense of the moment; the spacing a1, the number of elements n over it and the type of reinforcement; and Rax,d of one element, with what governs it.
You get the stress, the force on each element and the three checks with their utilisations, each with its clause. With the Pro plan, it prints as an A4 calculation note.
Assumptions and limits
- A moment that opens the curvature puts the timber across the grain in compression; no reinforcement for tension is called for.
- With reinforcement, the perpendicular tensile resistance of the timber is neglected entirely (clause E.1.4).
- Internal elements run the whole depth, stopping short only of one edge lamination (clause E.5.2). Clause E.1.2 admits glued threaded rods or ribbed bars up to 20 mm, or fully threaded self-drilling screws with no plain shank; the section they remove is deducted where the section is in tension along the grain.
- Tension in the steel is sized to SIA 263, without ηt and ηw.
- Reinforce the whole tension zone, and repeat the check for the outer quarters, where kB falls to 0.67.
Worked example
A curved glulam beam GL24h, 200 × 900 mm, in service class 1, with a moment of 300 kN·m closing the curvature at a radius of 12,000 mm, reinforced in the inner quarters with two internal elements every 400 mm, each with a withdrawal resistance of 20 kN. These are the module's own results for its worked example, computed when this page was built.
| Input | Value | Ref. |
|---|---|---|
| Wood type | Glulam | |
| Strength class | GL24h | |
| Load duration ηt | Short to permanent | § 2.2.6 |
| Service class ηw | 1 | § 3.2.1.3 t.4 |
| Section width b | 200 mm | |
| Section depth h | 900 mm | |
| Type of beam | Curved beam | § E.5.1 |
| Position of the reinforcement in the tension zone | Inner two quarters of the zone | § E.5.1 |
| The stress σt,90,d is | Computed from the moment and the radius — eq. (54) | § 5.1.3 (54) |
| Design bending moment MEd | 300 kN·m | § 5.1.3 (54) |
| Radius of curvature at the neutral axis r | 12000 mm | § 5.1.3 (54) |
| Sense of the moment | Closes the curvature (M⁺ of figure 15) | § 5.1.3 f.15 |
| Spacing of the reinforcement along the beam a1 | 400 mm | § E.5.1 |
| Elements over the length a1 n | 2 | § E.5.1 |
| Type of reinforcement | Internal — glued rods or fully threaded screws | § E.5.2 |
| What governs that resistance | Withdrawal from the timber, or the bonded length | § 2.2.6 · 3.2.1.3 t.4 |
| Axial withdrawal or tensile resistance of one element Rax,d | 20 kN | § 6.4 · annexe E.1 |
| Step | Value | Ref. |
|---|---|---|
| Section modulusW = b · h² / 6, from the width and depth of the Member panel | W = 27,000,000 mm³ | |
| Radius at the extradosra = r + h/2 | ra = 12,450.0 mm | § 5.1.3 f.15 |
| Radius at the intradosri = r − h/2 | ri = 11,550.0 mm | § 5.1.3 f.15 |
| Curvature termthe sharper the curve, the larger the share of the bending that turns into stress across the grain | h / (4·r) = 0.01875 | § 5.1.3 (54) |
| Stress across the grainσt,90,d = |+ (MEd / W) · h / (4·r)| = 0.2083 N/mm². Positive inside the absolute value is tension, negative compression, per figure 15. The moment closes the curvature here, so this plane is in tension. | σt,90,d = 0.2083 N/mm² | § 5.1.3 (54) |
| Step | Value | Ref. |
|---|---|---|
| Distribution coefficientkB = 1.0 in the two inner quarters of the tension zone, where it is full | kB = 1.00 | § E.5.1 |
| Plan area one element coverseach element carries the perpendicular tension over the share of the beam it is responsible for | b · a1 / n = 40,000 mm² | § E.5.1 |
| Tension acting on one elementFt,90,Ed = kB · (b · a1 / n) · σt,90,d. It acts at the level of the beam axis and must be anchored each side over the length lad. It is an action, so ηt and ηw do not enter it. | Ft,90,Ed = 8.3333 kN | § E.5.1 (146) |
| Step | Value | Ref. |
|---|---|---|
| Load duration factorfrom the load duration chosen in the Member panel | ηt = 1.00 | § 2.2.6 |
| Moisture factorfrom the service class chosen in the Member panel | ηw = 1.00 | § 3.2.1.3 t.4 |
| Resistance used, with the two factors appliedRax,d · ηt · ηw = 20.00 · 1.00 · 1.00 = 20.00 kN. Withdrawal and the bonded length are timber properties, so the duration of the action and the moisture content reach them. | Rax,d = 20.00 kN | § 2.2.6 · 3.2.1.3 t.4 |
| Reinforcement element in axial tensionFt,90,Ed ≤ Rax,d | η = 0.417 · Pass42 % of the capacity used | § E.5.1 |
| Step | Value | Ref. |
|---|---|---|
| Minimum spacing of the elements250 mm ≤ a1 | η = 0.625 · Pass63 % of the capacity used | § E.5.2 |
| Step | Value | Ref. |
|---|---|---|
| Upper limit of the spacing0.75 · 900 mm, h being the depth from the Member panel | 0.75·h = 675 mm | § E.5.2 |
| Maximum spacing of the elementsa1 ≤ 0.75·h | η = 0.593 · Pass59 % of the capacity used | § E.5.2 |
How this module is verified
Verified clause by clause against SIA 265:2021 (and SIA D0185 for the apex coefficient) and against independent calculations used on real projects, before release.
Questions
Do I enter R_ax,d with η_t and η_w?
No. Enter it for ηt = ηw = 1.0. The module applies both factors where withdrawal or the bonded length governs, and neither where steel tension governs.
Does it cover an arch?
Yes. Equation (54) covers any curved member of constant depth, an arch included, if the radius is known.
Which plan includes this module?
The Pro plan, with its calculation note.
Related
- Bearing reinforced with fully threaded screws
- Beam in biaxial bending, ultimate limit state
- Timber design to SIA 265: all timber modules
- SIA 265: modules and clauses
Norm: SIA 265:2021 · Page updated: 21 October 2026