Pitched Cambered Beam Design to Eurocode 5

Worked example

GL24c pitched cambered beam, h_ap 1.00 m, R 20 m, with cantilevers

Material: GL24c glulam per EN 14080
Apex height h_ap: 1.00 m
Curvature radius R: 20 m (inside face)
Cantilevers: 1.5 m each end

Verify the apex zone of a pitched cambered glulam beam GL24c, b = 250 mm, h_ap = 1.00 m, R = 20 m (to the inside face), delta = 15 degrees, t = 40 mm, service class 2, gamma_M = 1.3, apex zone volume V = 2.68 m3, M_ap,d = 143.7 kNm.

Calculate the example with Mia

Required inputs

Geometry: span l, support widths l_{a/l_b}, beam width b, upper/lower edge slope angles, beam heights (h_s, h_a, h_First, h_ap), curvature radius R and its reference face; optional cantilever length/end slope/bottom-edge slope on either end
Glulam strength class (or f_m,k / f_t,0,k / f_t,90,k / f_c,0,k / f_c,90,k / f_v,k), lamination thickness t, E_0,05 and G_0,05 for lateral-torsional buckling
Service class, load-duration class(es), gamma_M, and the shear crack factor k_cr per your National Annex
For the ridge check: M_ap,d directly, or roof loads (permanent/snow/wind) plus a tributary width for a symmetric span case
For every other check (shear, tension/compression+bending, tapered-edge bending, lateral-torsional buckling, support pressure): N_d, V_d, M_d at that section, from your own analysis (e.g. an RFEM model). This skill does not perform frame/arch analysis itself

What you receive

Utilisation ratio and governing EN 1995-1-1 clause for every check run
The governing check named across the whole beam
Deflection results against the applicable National Annex limits

Start from an input template

These templates prefill the form with typical inputs. They are not calculated results; the calculation runs in CALC.

Prepare your calculation

Configure the apex (ridge) check

Structural calculation to standard

System sketch

l = 24.65 mh_a = 0.717 mh_ap = 1.45 mh_First = 1.86 mδ = 12β = 8R = 26 mg_k = 0.5 kN/m²s_k = 0.65 kN/m²w_k = 0.3 kN/m²

Glulam strength class

Span between supports l

m

Support width l_a

m

Beam width b

m

Upper-edge (roof) slope angle delta

°

Lower-edge slope angle at support beta

°

Beam height at outer edge h_s

m

Beam height at support centreline h_a

m

Total height at ridge h_First (incl. ridge wedge)

m

Apex height h_ap (excl. ridge wedge)

m

Apex zone geometry

Curved apex, ridge wedge not load-bearing (α_ap = 0)

Straight tapered top to a sharp ridge (α_ap = δ)

Curvature radius of the bottom chord R

m

Lamination thickness t

m

Service class

Service class 1

Service class 2

Service class 3

National Annex

Tributary width (Lasteinzugsbreite)

m

Characteristic permanent roof load g_k

kN/m²

Characteristic snow load s_k

kN/m²

Characteristic wind load w_k

kN/m²

All required fields completed

Inputs completeReady to calculate

What this skill checks

Apex bending and tension-perpendicular interaction (6.4.3)

Checks the ridge-zone bending stress (k_l) and the combined tension-perpendicular-to-grain/shear interaction (k_dis, k_vol). The apex angle alpha_ap is taken as the true local edge slope at the apex (0 for a smoothly curved ridge, not the support-end taper angle), matching verified RX-TIMBER output.

General section checks (6.1.7, 6.2.2-6.2.4, 6.4.2)

Shear (with the crack-reduction factor), combined tension/compression and bending at any section including cantilevers, and bending on straight tapered edges (tension and compression side).

Lateral-torsional buckling (6.3.3)

Computes the relative slenderness and k_crit from the critical bending stress, given the section's lateral and torsional stiffness and effective buckling length.

Support pressure at an angle (6.2.2)

Checks compression at an angle to the grain at raked supports, with the effective contact length and k_c,90.

Deflection (Table 7.2)

Instantaneous, net-final (creep-adjusted), and combined characteristic/quasi-permanent deflection at midspan and at any cantilever tip, against the National Annex limits.

Normative basis

Standards & references

The checks follow these standards. Nationally determined parameters come from the National Annex selected in the form.

EN 1995-1-1

Eurocode 5: Design of timber structures – Part 1-1: General – Common rules and rules for buildings

Edition used: DIN EN 1995-1-1:2010-12 (EN 1995-1-1:2004 + AC:2006 + A1:2008) + DIN EN 1995-1-1/A2:2014-07

Withdrawn

§6.4.2
§6.4.3

DIN MediaNewer edition: DIN EN 1995-1-1:2026-09 (EN 1995-1-1:2025)

National Annexes
Country	National Annex	Factors	Source
DE	DIN EN 1995-1-1/NA:2013-08Current	γ_M (glulam) = 1.30	DIN Media
EN	Recommended valuesEN 1995-1-1:2004 + AC:2006 + A1:2008 + A2:2014	γ_M (glulam) = 1.25	–

Status checked on 2026-09-30

EN 1991-1-3

Eurocode 1: Actions on structures – Part 1-3: General actions – Snow loads

Edition used: DIN EN 1991-1-3:2010-12 (EN 1991-1-3:2003 + AC:2009) + DIN EN 1991-1-3/A1:2015-12

Current

DIN Media

Status checked on 2026-09-30

EN 1991-1-4

Eurocode 1: Actions on structures – Part 1-4: General actions – Wind actions

Edition used: DIN EN 1991-1-4:2010-12 (EN 1991-1-4:2005 + A1:2010 + AC:2010)

Current

DIN Media

Status checked on 2026-09-30

EN 1990

Eurocode: Basis of structural design

Edition used: DIN EN 1990:2021-10 (EN 1990:2002 + A1:2005 + A1:2005/AC:2010)

Current

§6.4.3.2

DIN MediaNewer edition: EN 1990:2023 (CEN; coexistence with the first generation until 2028-03-30)

National Annexes
Country	National Annex	Factors	Source
EN	Recommended valuesEN 1990:2002 + A1:2005 + A1:2005/AC:2010	γ_G = 1.35γ_Q = 1.50	–

Status checked on 2026-09-30

Frequently asked questions

InputsWhich inputs are required?

Full geometry (including any cantilevers), the glulam strength class and elastic properties, service/load-duration classes, and the internal forces (N,d, V,d, M,d) at each section you want checked. For the ridge check alone, roof loads plus a tributary width can stand in for a directly given M_ap,d.

ScopeDoes this replace a full structural analysis?

No. This skill checks stresses and capacities at sections you specify. For a curved or cantilevered beam under wind, deriving the internal forces at every section generally needs a real 2D/frame analysis (e.g. an RFEM model, skill 000005-rfem-model-design). Only the simple symmetric-UDL ridge moment can be derived by hand statics here.

VerificationWhy is alpha_ap not just the roof pitch angle?

For a beam whose top and bottom edges are both curved (a smoothly rounded ridge, not a sharp angular apex), the edge slope AT the apex itself is 0 regardless of the overall roof pitch measured at the supports. Using the support-end slope there would overstate the apex bending check. Tell Mia explicitly if your beam instead has a straight tapered top maintained to a sharp ridge line.

ScopeCan this check a beam with cantilevers?

Yes. Describe the cantilever length, end slope, and bottom-edge slope on either side; the same section checks apply at cantilever locations, including the cantilever-specific deflection limits.

Question not answered?Ask Mia directly in CALC. She answers for this skill and your inputs.Ask Mia

Design pitched cambered timber beams to Eurocode 5

GL24c pitched cambered beam, h_ap 1.00 m, R 20 m, with cantilevers

Required inputs

What you receive

Start from an input template

GL24h, h_ap 1.45 m, R 26 m

System sketch

What this skill checks

Apex bending and tension-perpendicular interaction (6.4.3)

General section checks (6.1.7, 6.2.2-6.2.4, 6.4.2)

Lateral-torsional buckling (6.3.3)

Support pressure at an angle (6.2.2)

Deflection (Table 7.2)

Standards & references

Eurocode 5: Design of timber structures – Part 1-1: General – Common rules and rules for buildings

Eurocode 1: Actions on structures – Part 1-3: General actions – Snow loads

Eurocode 1: Actions on structures – Part 1-4: General actions – Wind actions

Eurocode: Basis of structural design

Frequently asked questions

Related skills

Ready for your first check?

Design pitched cambered timber beams to Eurocode 5

GL24c pitched cambered beam, hap 1.00 m, R 20 m, with cantilevers

Required inputs

What you receive

Start from an input template

GL24h, hap 1.45 m, R 26 m

System sketch

What this skill checks

Apex bending and tension-perpendicular interaction (6.4.3)

General section checks (6.1.7, 6.2.2-6.2.4, 6.4.2)

Lateral-torsional buckling (6.3.3)

Support pressure at an angle (6.2.2)

Deflection (Table 7.2)

Eurocode 5: Design of timber structures – Part 1-1: General – Common rules and rules for buildings

Eurocode 1: Actions on structures – Part 1-3: General actions – Snow loads

Eurocode 1: Actions on structures – Part 1-4: General actions – Wind actions

Eurocode: Basis of structural design

Related skills

Ready for your first check?

GL24c pitched cambered beam, h_ap 1.00 m, R 20 m, with cantilevers

GL24h, h_ap 1.45 m, R 26 m