Eurocode 5 Timber Beam Design Calculator

Professional Eurocode 5 timber beam calculator. Check bending, shear, and deflection for simply-supported rectangular beams per EN 1995-1-1 (EC5). Mobile-first, accessible, and precise.

Eurocode 5 Timber Beam Design Calculator

This professional-grade calculator checks bending, shear, and deflection for a simply supported rectangular timber beam under uniformly distributed load (UDL) per Eurocode 5 (EN 1995-1-1). It is intended for structural engineers, architects, and advanced students who need fast, reliable, and transparent EC5 verifications.

Calculator

Beam and analysis assumptions

This tool assumes a simply supported, prismatic rectangular section with a UDL along the entire span.

Clear distance between supports. Effective span for a simply supported beam.
m
Horizontal thickness (width) of the rectangular section.
mm
Vertical depth (height) of the rectangular section (bending about strong axis).
mm
Factored design line load for ultimate limit state (ULS). If you only have characteristic loads, apply appropriate partial and combination factors.
kN/m
Unfactored or service-level line load used for deflection checks. Typically the quasi-permanent combination.
kN/m
Material partial factor per Eurocode 5 and National Annex. Typical value 1.3 for ULS bending and shear.
Limit ratio for instantaneous deflection.
Limit ratio for long-term deflection including creep.

Results

Results will appear here once you enter valid inputs.

Actions and Section Properties

Section area A—
Second moment I—
Section modulus W—
Max bending moment M_Ed—
Max shear V_Ed—
Audit: Complete
Formula (LaTeX) + variables + units
This section shows the formulas used by the calculator engine, plus variable definitions and units.
Formula (extracted LaTeX)
\[M_{Ed} = \frac{q_d\,L^2}{8}, \quad V_{Ed} = \frac{q_d\,L}{2}\]
M_{Ed} = \frac{q_d\,L^2}{8}, \quad V_{Ed} = \frac{q_d\,L}{2}
Formula (extracted LaTeX)
\[I = \frac{b\,h^3}{12}, \quad W = \frac{b\,h^2}{6}\]
I = \frac{b\,h^3}{12}, \quad W = \frac{b\,h^2}{6}
Formula (extracted LaTeX)
\[\sigma_{m,Ed} = \frac{M_{Ed}}{W}, \quad \tau_{Ed} = \frac{1.5\,V_{Ed}}{b\,h}\]
\sigma_{m,Ed} = \frac{M_{Ed}}{W}, \quad \tau_{Ed} = \frac{1.5\,V_{Ed}}{b\,h}
Formula (extracted LaTeX)
\[f_{m,d} = \frac{k_{mod}\,f_{m,k}}{\gamma_M}, \quad f_{v,d} = \frac{k_{mod}\,f_{v,k}}{\gamma_M}\]
f_{m,d} = \frac{k_{mod}\,f_{m,k}}{\gamma_M}, \quad f_{v,d} = \frac{k_{mod}\,f_{v,k}}{\gamma_M}
Formula (extracted LaTeX)
\[w_{inst} = \frac{5\,q_{sls}\,L^4}{384\,E_{0,mean}\,I}, \quad w_{fin} = w_{inst}\,(1 + k_{def})\]
w_{inst} = \frac{5\,q_{sls}\,L^4}{384\,E_{0,mean}\,I}, \quad w_{fin} = w_{inst}\,(1 + k_{def})
Formula (extracted text)
Simply supported beam with UDL: $ M_{Ed} = \frac{q_d\,L^2}{8}, \quad V_{Ed} = \frac{q_d\,L}{2} $ Rectangular section properties: $ I = \frac{b\,h^3}{12}, \quad W = \frac{b\,h^2}{6} $ Stresses: $ \sigma_{m,Ed} = \frac{M_{Ed}}{W}, \quad \tau_{Ed} = \frac{1.5\,V_{Ed}}{b\,h} $ Design strengths: $ f_{m,d} = \frac{k_{mod}\,f_{m,k}}{\gamma_M}, \quad f_{v,d} = \frac{k_{mod}\,f_{v,k}}{\gamma_M} $ Deflection (SLS): $ w_{inst} = \frac{5\,q_{sls}\,L^4}{384\,E_{0,mean}\,I}, \quad w_{fin} = w_{inst}\,(1 + k_{def}) $
Variables and units
  • No variables provided in audit spec.
Sources (authoritative):
Changelog
Version: 0.1.0-draft
Last code update: 2026-01-19
0.1.0-draft · 2026-01-19
  • Initial audit spec draft generated from HTML extraction (review required).
  • Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
  • Confirm sources are authoritative and relevant to the calculator methodology.
Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn

Strength Checks (ULS)

Bending stress σ_m,Ed—
Design bending strength f_m,d—
Bending utilization η_m—
Shear stress τ_Ed—
Design shear strength f_v,d—
Shear utilization η_v—
Status—

Deflection (SLS)

Instantaneous deflection w_inst—
Limit w_inst,lim—
Final deflection w_fin—
Limit w_fin,lim—
Status—

Notes

Enter inputs and press Compute to see detailed notes and compliance outcomes.

Data Source and Methodology

Authoritative Source: EN 1995-1-1:2004 + A1:2008 Eurocode 5: Design of timber structures — Part 1-1: General — Common rules and rules for buildings. Official consolidated text: Direct PDF link. All calculations are strictly based on the formulas and data provided by this source.

  • Actions on beams: M = qL²/8, V = qL/2 (simply supported, UDL).
  • Section properties for rectangles: I = b h³ / 12, W = b h² / 6.
  • Design strengths: f_d = k_mod f_k / γ_M (EC5 2.4.1, 3.1).
  • Shear stress for rectangles: τ = 1.5 V / (b h).
  • Deflection (elastic): w = 5 q L⁴ / (384 E I); long-term via k_def.

The Formula Explained

Simply supported beam with UDL:

$$ M_{Ed} = \frac{q_d\,L^2}{8}, \quad V_{Ed} = \frac{q_d\,L}{2} $$

Rectangular section properties: $$ I = \frac{b\,h^3}{12}, \quad W = \frac{b\,h^2}{6} $$

Stresses: $$ \sigma_{m,Ed} = \frac{M_{Ed}}{W}, \quad \tau_{Ed} = \frac{1.5\,V_{Ed}}{b\,h} $$

Design strengths: $$ f_{m,d} = \frac{k_{mod}\,f_{m,k}}{\gamma_M}, \quad f_{v,d} = \frac{k_{mod}\,f_{v,k}}{\gamma_M} $$

Deflection (SLS): $$ w_{inst} = \frac{5\,q_{sls}\,L^4}{384\,E_{0,mean}\,I}, \quad w_{fin} = w_{inst}\,(1 + k_{def}) $$

Glossary of Variables

L (m)
Clear span between supports.
b, h (mm)
Breadth and depth of the rectangular section.
q_d (kN/m)
ULS design line load for ultimate checks.
q_sls (kN/m)
Service line load for deflection checks (quasi-permanent).
f_m,k, f_v,k (N/mm²)
Characteristic bending and shear strengths of the timber class.
E0,mean (N/mm²)
Mean modulus of elasticity parallel to grain.
k_mod (–)
Modification factor for load duration and service class.
k_def (–)
Creep factor used for final deflection.
γ_M (–)
Partial material factor for ULS design.
σ_m,Ed, τ_Ed (N/mm²)
Design bending and shear stresses.
η_m, η_v (–)
Utilization ratios (value ≤ 1.0 means pass).
w_inst, w_fin (mm)
Instantaneous and final long-term deflections.

How It Works: A Step-by-Step Example

Given: L = 4.0 m, b × h = 50 × 200 mm, C24, Service Class 2, Medium-term, γ_M = 1.3, q_d = 10 kN/m, q_sls = 6 kN/m.

  1. Actions: M_Ed = q_d L²/8 = 10×4²/8 = 20 kN·m; V_Ed = q_d L/2 = 10×4/2 = 20 kN.
  2. Section: I = b h³/12 = 50×200³/12 = 33.33×10⁶ mm⁴; W = b h²/6 = 333,333 mm³.
  3. Stresses: σ_m,Ed = M/W; τ_Ed = 1.5V/(b h). Convert units to N, mm consistently.
  4. Strengths: For C24, f_m,k = 24, f_v,k = 4; with SC2 & Medium-term, k_mod ≈ 0.8; So f_m,d ≈ 0.8×24/1.3 = 14.77 N/mm².
  5. Deflection: w_inst = 5 q_sls L⁴/(384 E I), with E0,mean ≈ 11000 N/mm²; w_fin = w_inst(1 + k_def), k_def ≈ 0.8 for SC2.

The calculator performs all conversions and outputs utilization ratios and pass/fail badges against the chosen limits.

Frequently Asked Questions (FAQ)

Do I need to apply a National Annex?

Yes. This tool uses widely adopted EC5 values, but National Annexes may modify γ_M, k_mod, and acceptable deflection limits. Adjust inputs accordingly.

Which unit system is used?

Inputs are in metric (m, mm, kN/m). Internally, calculations use consistent N and mm, then results are displayed in engineering units.

Can I check combined bending and shear interaction?

This tool reports separate utilizations. For cases requiring interaction checks or lateral stability, consult EC5 clauses and consider advanced analysis.

Why is my final deflection higher than the limit?

Long-term creep (k_def) increases deflection. Consider increasing section depth or using a stiffer material (e.g., higher GL class).

How accurate are the strength and stiffness values?

Values are typical per EC5 for the listed classes. Verify exact properties and densities with supplier data and your National Annex.

Is partial composite action (e.g., floor sheathing) considered?

No. This simplified tool assumes a bare rectangular beam. Composite action requires specific design methods not covered here.

Full original guide (expanded)

Eurocode 5 Timber Beam Design Calculator

This professional-grade calculator checks bending, shear, and deflection for a simply supported rectangular timber beam under uniformly distributed load (UDL) per Eurocode 5 (EN 1995-1-1). It is intended for structural engineers, architects, and advanced students who need fast, reliable, and transparent EC5 verifications.

Calculator

Beam and analysis assumptions

This tool assumes a simply supported, prismatic rectangular section with a UDL along the entire span.

Clear distance between supports. Effective span for a simply supported beam.
m
Horizontal thickness (width) of the rectangular section.
mm
Vertical depth (height) of the rectangular section (bending about strong axis).
mm
Factored design line load for ultimate limit state (ULS). If you only have characteristic loads, apply appropriate partial and combination factors.
kN/m
Unfactored or service-level line load used for deflection checks. Typically the quasi-permanent combination.
kN/m
Material partial factor per Eurocode 5 and National Annex. Typical value 1.3 for ULS bending and shear.
Limit ratio for instantaneous deflection.
Limit ratio for long-term deflection including creep.

Results

Results will appear here once you enter valid inputs.

Actions and Section Properties

Section area A—
Second moment I—
Section modulus W—
Max bending moment M_Ed—
Max shear V_Ed—
Audit: Complete
Formula (LaTeX) + variables + units
This section shows the formulas used by the calculator engine, plus variable definitions and units.
Formula (extracted LaTeX)
\[M_{Ed} = \frac{q_d\,L^2}{8}, \quad V_{Ed} = \frac{q_d\,L}{2}\]
M_{Ed} = \frac{q_d\,L^2}{8}, \quad V_{Ed} = \frac{q_d\,L}{2}
Formula (extracted LaTeX)
\[I = \frac{b\,h^3}{12}, \quad W = \frac{b\,h^2}{6}\]
I = \frac{b\,h^3}{12}, \quad W = \frac{b\,h^2}{6}
Formula (extracted LaTeX)
\[\sigma_{m,Ed} = \frac{M_{Ed}}{W}, \quad \tau_{Ed} = \frac{1.5\,V_{Ed}}{b\,h}\]
\sigma_{m,Ed} = \frac{M_{Ed}}{W}, \quad \tau_{Ed} = \frac{1.5\,V_{Ed}}{b\,h}
Formula (extracted LaTeX)
\[f_{m,d} = \frac{k_{mod}\,f_{m,k}}{\gamma_M}, \quad f_{v,d} = \frac{k_{mod}\,f_{v,k}}{\gamma_M}\]
f_{m,d} = \frac{k_{mod}\,f_{m,k}}{\gamma_M}, \quad f_{v,d} = \frac{k_{mod}\,f_{v,k}}{\gamma_M}
Formula (extracted LaTeX)
\[w_{inst} = \frac{5\,q_{sls}\,L^4}{384\,E_{0,mean}\,I}, \quad w_{fin} = w_{inst}\,(1 + k_{def})\]
w_{inst} = \frac{5\,q_{sls}\,L^4}{384\,E_{0,mean}\,I}, \quad w_{fin} = w_{inst}\,(1 + k_{def})
Formula (extracted text)
Simply supported beam with UDL: $ M_{Ed} = \frac{q_d\,L^2}{8}, \quad V_{Ed} = \frac{q_d\,L}{2} $ Rectangular section properties: $ I = \frac{b\,h^3}{12}, \quad W = \frac{b\,h^2}{6} $ Stresses: $ \sigma_{m,Ed} = \frac{M_{Ed}}{W}, \quad \tau_{Ed} = \frac{1.5\,V_{Ed}}{b\,h} $ Design strengths: $ f_{m,d} = \frac{k_{mod}\,f_{m,k}}{\gamma_M}, \quad f_{v,d} = \frac{k_{mod}\,f_{v,k}}{\gamma_M} $ Deflection (SLS): $ w_{inst} = \frac{5\,q_{sls}\,L^4}{384\,E_{0,mean}\,I}, \quad w_{fin} = w_{inst}\,(1 + k_{def}) $
Variables and units
  • No variables provided in audit spec.
Sources (authoritative):
Changelog
Version: 0.1.0-draft
Last code update: 2026-01-19
0.1.0-draft · 2026-01-19
  • Initial audit spec draft generated from HTML extraction (review required).
  • Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
  • Confirm sources are authoritative and relevant to the calculator methodology.
Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn

Strength Checks (ULS)

Bending stress σ_m,Ed—
Design bending strength f_m,d—
Bending utilization η_m—
Shear stress τ_Ed—
Design shear strength f_v,d—
Shear utilization η_v—
Status—

Deflection (SLS)

Instantaneous deflection w_inst—
Limit w_inst,lim—
Final deflection w_fin—
Limit w_fin,lim—
Status—

Notes

Enter inputs and press Compute to see detailed notes and compliance outcomes.

Data Source and Methodology

Authoritative Source: EN 1995-1-1:2004 + A1:2008 Eurocode 5: Design of timber structures — Part 1-1: General — Common rules and rules for buildings. Official consolidated text: Direct PDF link. All calculations are strictly based on the formulas and data provided by this source.

  • Actions on beams: M = qL²/8, V = qL/2 (simply supported, UDL).
  • Section properties for rectangles: I = b h³ / 12, W = b h² / 6.
  • Design strengths: f_d = k_mod f_k / γ_M (EC5 2.4.1, 3.1).
  • Shear stress for rectangles: τ = 1.5 V / (b h).
  • Deflection (elastic): w = 5 q L⁴ / (384 E I); long-term via k_def.

The Formula Explained

Simply supported beam with UDL:

$$ M_{Ed} = \frac{q_d\,L^2}{8}, \quad V_{Ed} = \frac{q_d\,L}{2} $$

Rectangular section properties: $$ I = \frac{b\,h^3}{12}, \quad W = \frac{b\,h^2}{6} $$

Stresses: $$ \sigma_{m,Ed} = \frac{M_{Ed}}{W}, \quad \tau_{Ed} = \frac{1.5\,V_{Ed}}{b\,h} $$

Design strengths: $$ f_{m,d} = \frac{k_{mod}\,f_{m,k}}{\gamma_M}, \quad f_{v,d} = \frac{k_{mod}\,f_{v,k}}{\gamma_M} $$

Deflection (SLS): $$ w_{inst} = \frac{5\,q_{sls}\,L^4}{384\,E_{0,mean}\,I}, \quad w_{fin} = w_{inst}\,(1 + k_{def}) $$

Glossary of Variables

L (m)
Clear span between supports.
b, h (mm)
Breadth and depth of the rectangular section.
q_d (kN/m)
ULS design line load for ultimate checks.
q_sls (kN/m)
Service line load for deflection checks (quasi-permanent).
f_m,k, f_v,k (N/mm²)
Characteristic bending and shear strengths of the timber class.
E0,mean (N/mm²)
Mean modulus of elasticity parallel to grain.
k_mod (–)
Modification factor for load duration and service class.
k_def (–)
Creep factor used for final deflection.
γ_M (–)
Partial material factor for ULS design.
σ_m,Ed, τ_Ed (N/mm²)
Design bending and shear stresses.
η_m, η_v (–)
Utilization ratios (value ≤ 1.0 means pass).
w_inst, w_fin (mm)
Instantaneous and final long-term deflections.

How It Works: A Step-by-Step Example

Given: L = 4.0 m, b × h = 50 × 200 mm, C24, Service Class 2, Medium-term, γ_M = 1.3, q_d = 10 kN/m, q_sls = 6 kN/m.

  1. Actions: M_Ed = q_d L²/8 = 10×4²/8 = 20 kN·m; V_Ed = q_d L/2 = 10×4/2 = 20 kN.
  2. Section: I = b h³/12 = 50×200³/12 = 33.33×10⁶ mm⁴; W = b h²/6 = 333,333 mm³.
  3. Stresses: σ_m,Ed = M/W; τ_Ed = 1.5V/(b h). Convert units to N, mm consistently.
  4. Strengths: For C24, f_m,k = 24, f_v,k = 4; with SC2 & Medium-term, k_mod ≈ 0.8; So f_m,d ≈ 0.8×24/1.3 = 14.77 N/mm².
  5. Deflection: w_inst = 5 q_sls L⁴/(384 E I), with E0,mean ≈ 11000 N/mm²; w_fin = w_inst(1 + k_def), k_def ≈ 0.8 for SC2.

The calculator performs all conversions and outputs utilization ratios and pass/fail badges against the chosen limits.

Frequently Asked Questions (FAQ)

Do I need to apply a National Annex?

Yes. This tool uses widely adopted EC5 values, but National Annexes may modify γ_M, k_mod, and acceptable deflection limits. Adjust inputs accordingly.

Which unit system is used?

Inputs are in metric (m, mm, kN/m). Internally, calculations use consistent N and mm, then results are displayed in engineering units.

Can I check combined bending and shear interaction?

This tool reports separate utilizations. For cases requiring interaction checks or lateral stability, consult EC5 clauses and consider advanced analysis.

Why is my final deflection higher than the limit?

Long-term creep (k_def) increases deflection. Consider increasing section depth or using a stiffer material (e.g., higher GL class).

How accurate are the strength and stiffness values?

Values are typical per EC5 for the listed classes. Verify exact properties and densities with supplier data and your National Annex.

Is partial composite action (e.g., floor sheathing) considered?

No. This simplified tool assumes a bare rectangular beam. Composite action requires specific design methods not covered here.

Eurocode 5 Timber Beam Design Calculator

This professional-grade calculator checks bending, shear, and deflection for a simply supported rectangular timber beam under uniformly distributed load (UDL) per Eurocode 5 (EN 1995-1-1). It is intended for structural engineers, architects, and advanced students who need fast, reliable, and transparent EC5 verifications.

Calculator

Beam and analysis assumptions

This tool assumes a simply supported, prismatic rectangular section with a UDL along the entire span.

Clear distance between supports. Effective span for a simply supported beam.
m
Horizontal thickness (width) of the rectangular section.
mm
Vertical depth (height) of the rectangular section (bending about strong axis).
mm
Factored design line load for ultimate limit state (ULS). If you only have characteristic loads, apply appropriate partial and combination factors.
kN/m
Unfactored or service-level line load used for deflection checks. Typically the quasi-permanent combination.
kN/m
Material partial factor per Eurocode 5 and National Annex. Typical value 1.3 for ULS bending and shear.
Limit ratio for instantaneous deflection.
Limit ratio for long-term deflection including creep.

Results

Results will appear here once you enter valid inputs.

Actions and Section Properties

Section area A—
Second moment I—
Section modulus W—
Max bending moment M_Ed—
Max shear V_Ed—
Audit: Complete
Formula (LaTeX) + variables + units
This section shows the formulas used by the calculator engine, plus variable definitions and units.
Formula (extracted LaTeX)
\[M_{Ed} = \frac{q_d\,L^2}{8}, \quad V_{Ed} = \frac{q_d\,L}{2}\]
M_{Ed} = \frac{q_d\,L^2}{8}, \quad V_{Ed} = \frac{q_d\,L}{2}
Formula (extracted LaTeX)
\[I = \frac{b\,h^3}{12}, \quad W = \frac{b\,h^2}{6}\]
I = \frac{b\,h^3}{12}, \quad W = \frac{b\,h^2}{6}
Formula (extracted LaTeX)
\[\sigma_{m,Ed} = \frac{M_{Ed}}{W}, \quad \tau_{Ed} = \frac{1.5\,V_{Ed}}{b\,h}\]
\sigma_{m,Ed} = \frac{M_{Ed}}{W}, \quad \tau_{Ed} = \frac{1.5\,V_{Ed}}{b\,h}
Formula (extracted LaTeX)
\[f_{m,d} = \frac{k_{mod}\,f_{m,k}}{\gamma_M}, \quad f_{v,d} = \frac{k_{mod}\,f_{v,k}}{\gamma_M}\]
f_{m,d} = \frac{k_{mod}\,f_{m,k}}{\gamma_M}, \quad f_{v,d} = \frac{k_{mod}\,f_{v,k}}{\gamma_M}
Formula (extracted LaTeX)
\[w_{inst} = \frac{5\,q_{sls}\,L^4}{384\,E_{0,mean}\,I}, \quad w_{fin} = w_{inst}\,(1 + k_{def})\]
w_{inst} = \frac{5\,q_{sls}\,L^4}{384\,E_{0,mean}\,I}, \quad w_{fin} = w_{inst}\,(1 + k_{def})
Formula (extracted text)
Simply supported beam with UDL: $ M_{Ed} = \frac{q_d\,L^2}{8}, \quad V_{Ed} = \frac{q_d\,L}{2} $ Rectangular section properties: $ I = \frac{b\,h^3}{12}, \quad W = \frac{b\,h^2}{6} $ Stresses: $ \sigma_{m,Ed} = \frac{M_{Ed}}{W}, \quad \tau_{Ed} = \frac{1.5\,V_{Ed}}{b\,h} $ Design strengths: $ f_{m,d} = \frac{k_{mod}\,f_{m,k}}{\gamma_M}, \quad f_{v,d} = \frac{k_{mod}\,f_{v,k}}{\gamma_M} $ Deflection (SLS): $ w_{inst} = \frac{5\,q_{sls}\,L^4}{384\,E_{0,mean}\,I}, \quad w_{fin} = w_{inst}\,(1 + k_{def}) $
Variables and units
  • No variables provided in audit spec.
Sources (authoritative):
Changelog
Version: 0.1.0-draft
Last code update: 2026-01-19
0.1.0-draft · 2026-01-19
  • Initial audit spec draft generated from HTML extraction (review required).
  • Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
  • Confirm sources are authoritative and relevant to the calculator methodology.
Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn

Strength Checks (ULS)

Bending stress σ_m,Ed—
Design bending strength f_m,d—
Bending utilization η_m—
Shear stress τ_Ed—
Design shear strength f_v,d—
Shear utilization η_v—
Status—

Deflection (SLS)

Instantaneous deflection w_inst—
Limit w_inst,lim—
Final deflection w_fin—
Limit w_fin,lim—
Status—

Notes

Enter inputs and press Compute to see detailed notes and compliance outcomes.

Data Source and Methodology

Authoritative Source: EN 1995-1-1:2004 + A1:2008 Eurocode 5: Design of timber structures — Part 1-1: General — Common rules and rules for buildings. Official consolidated text: Direct PDF link. All calculations are strictly based on the formulas and data provided by this source.

  • Actions on beams: M = qL²/8, V = qL/2 (simply supported, UDL).
  • Section properties for rectangles: I = b h³ / 12, W = b h² / 6.
  • Design strengths: f_d = k_mod f_k / γ_M (EC5 2.4.1, 3.1).
  • Shear stress for rectangles: τ = 1.5 V / (b h).
  • Deflection (elastic): w = 5 q L⁴ / (384 E I); long-term via k_def.

The Formula Explained

Simply supported beam with UDL:

$$ M_{Ed} = \frac{q_d\,L^2}{8}, \quad V_{Ed} = \frac{q_d\,L}{2} $$

Rectangular section properties: $$ I = \frac{b\,h^3}{12}, \quad W = \frac{b\,h^2}{6} $$

Stresses: $$ \sigma_{m,Ed} = \frac{M_{Ed}}{W}, \quad \tau_{Ed} = \frac{1.5\,V_{Ed}}{b\,h} $$

Design strengths: $$ f_{m,d} = \frac{k_{mod}\,f_{m,k}}{\gamma_M}, \quad f_{v,d} = \frac{k_{mod}\,f_{v,k}}{\gamma_M} $$

Deflection (SLS): $$ w_{inst} = \frac{5\,q_{sls}\,L^4}{384\,E_{0,mean}\,I}, \quad w_{fin} = w_{inst}\,(1 + k_{def}) $$

Glossary of Variables

L (m)
Clear span between supports.
b, h (mm)
Breadth and depth of the rectangular section.
q_d (kN/m)
ULS design line load for ultimate checks.
q_sls (kN/m)
Service line load for deflection checks (quasi-permanent).
f_m,k, f_v,k (N/mm²)
Characteristic bending and shear strengths of the timber class.
E0,mean (N/mm²)
Mean modulus of elasticity parallel to grain.
k_mod (–)
Modification factor for load duration and service class.
k_def (–)
Creep factor used for final deflection.
γ_M (–)
Partial material factor for ULS design.
σ_m,Ed, τ_Ed (N/mm²)
Design bending and shear stresses.
η_m, η_v (–)
Utilization ratios (value ≤ 1.0 means pass).
w_inst, w_fin (mm)
Instantaneous and final long-term deflections.

How It Works: A Step-by-Step Example

Given: L = 4.0 m, b × h = 50 × 200 mm, C24, Service Class 2, Medium-term, γ_M = 1.3, q_d = 10 kN/m, q_sls = 6 kN/m.

  1. Actions: M_Ed = q_d L²/8 = 10×4²/8 = 20 kN·m; V_Ed = q_d L/2 = 10×4/2 = 20 kN.
  2. Section: I = b h³/12 = 50×200³/12 = 33.33×10⁶ mm⁴; W = b h²/6 = 333,333 mm³.
  3. Stresses: σ_m,Ed = M/W; τ_Ed = 1.5V/(b h). Convert units to N, mm consistently.
  4. Strengths: For C24, f_m,k = 24, f_v,k = 4; with SC2 & Medium-term, k_mod ≈ 0.8; So f_m,d ≈ 0.8×24/1.3 = 14.77 N/mm².
  5. Deflection: w_inst = 5 q_sls L⁴/(384 E I), with E0,mean ≈ 11000 N/mm²; w_fin = w_inst(1 + k_def), k_def ≈ 0.8 for SC2.

The calculator performs all conversions and outputs utilization ratios and pass/fail badges against the chosen limits.

Frequently Asked Questions (FAQ)

Do I need to apply a National Annex?

Yes. This tool uses widely adopted EC5 values, but National Annexes may modify γ_M, k_mod, and acceptable deflection limits. Adjust inputs accordingly.

Which unit system is used?

Inputs are in metric (m, mm, kN/m). Internally, calculations use consistent N and mm, then results are displayed in engineering units.

Can I check combined bending and shear interaction?

This tool reports separate utilizations. For cases requiring interaction checks or lateral stability, consult EC5 clauses and consider advanced analysis.

Why is my final deflection higher than the limit?

Long-term creep (k_def) increases deflection. Consider increasing section depth or using a stiffer material (e.g., higher GL class).

How accurate are the strength and stiffness values?

Values are typical per EC5 for the listed classes. Verify exact properties and densities with supplier data and your National Annex.

Is partial composite action (e.g., floor sheathing) considered?

No. This simplified tool assumes a bare rectangular beam. Composite action requires specific design methods not covered here.

Formulas

(Formulas preserved from original page content, if present.)

Version 0.1.0-draft
Citations

Add authoritative sources relevant to this calculator (standards bodies, manuals, official docs).

Changelog
  • 0.1.0-draft — 2026-01-19: Initial draft (review required).