Snow load on roofs
Snow loads on monopitch and duopitch roofs, with all load cases, to EN 1991-1-3.
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Tool information
What this calculator computes
The tool determines the snow load on a roof to EN 1991-1-3 (Eurocode 1, part 1-3), for monopitch and duopitch roofs, with every load case the code requires.
The base expression, for persistent and transient design situations:
\(s = \mu_i \cdot C_e \cdot C_t \cdot s_k\)
The four factors and what each does
They are often confused, but they do completely different things.
\(s_k\) is the characteristic load on the ground, from the national zoning map. It is the only term that comes from the site as an input.
\(\mu_i\) converts the ground load into a roof load. It is about shape: snow slides off steep pitches and accumulates in valleys.
\(C_e\) is about exposure to wind (Table 5.1):
| Exposure | \(C_e\) |
|---|---|
| Windswept — open on all sides | 0.8 |
| Normal | 1.0 |
| Sheltered — among taller buildings or trees | 1.2 |
The spread between extremes is 50%. An exposed site loses snow to the wind; a sheltered one collects it. The value 0.8 applies only if the site is genuinely open, with no shelter from terrain, buildings or vegetation — clause 5.2(7) is restrictive here.
\(C_t\) is about heat escaping through the roof and melting the snow. Normally 1.0; below 1.0 only with justification, per clause 5.2(8).
The shape coefficient
For simple roofs, Table 5.2 gives:
\(\mu_1 = \begin{cases} 0.8 & 0° \le \alpha \le 30° \\ 0.8 \cdot \dfrac{60 - \alpha}{30} & 30° < \alpha < 60° \\ 0 & \alpha \ge 60° \end{cases}\)
Up to 30° the snow stays put. Above 60° it slides off completely — the coefficient becomes zero.
But note: zero on the roof does not mean zero load. The snow that slides has to go somewhere. If there is a lower roof or a snowguard below the eaves, a load appears there which the code covers in clauses 6.2 and 6.4 — not in this calculation.
The table also gives \(\mu_2\), for snow accumulating in a valley, rising from 0.8 to 1.6 between 0° and 30°. It applies to multi-span roofs; the page exposes it but does not apply it.
Why three load cases
For a duopitch roof, clause 5.3.3 requires checking three situations:
- (i) undrifted — \(\mu_1(\alpha_1)\) on both slopes;
- (ii) \(0.5 \, \mu_1(\alpha_1)\) on the left, \(\mu_1(\alpha_2)\) on the right;
- (iii) \(\mu_1(\alpha_1)\) on the left, \(0.5 \, \mu_1(\alpha_2)\) on the right.
Cases (ii) and (iii) model wind sweeping the snow off one slope onto the other. On a symmetric roof they do not change the maximum value, but they produce an asymmetric load — and it is the asymmetry that governs. A truss loaded on one half sees moments that a uniform load never produces.
For a monopitch roof there is a single case.
Input data
- \(s_k\) — from the national zoning map.
- Exposure — for \(C_e\).
- Roof type and pitches — one or two, in degrees.
- Advanced — \(C_t\) and an additional site factor.
About the national annex
National annexes are not just a different map: some introduce further factors that do not exist in EN 1991-1-3. Romania's CR 1-1-3/2012, for instance, adds an importance factor \(\gamma_{Is}\). That is why the page has a separate "additional factor" field rather than assuming a value.
Always check \(s_k\) and any annex factors against the version in force — those are exactly the values that change between revisions.
Assumptions and limitations
Covered: monopitch (clause 5.3.2) and duopitch (clause 5.3.3) roofs, in persistent and transient design situations.
Not covered: multi-span and cylindrical roofs (clauses 5.3.4, 5.3.5), drifting against taller constructions and obstructions (clause 6.2), snow overhanging the eaves (6.3), loads on snowguards (6.4) and accidental situations with exceptional snow (clause 5.2(3)).
Related calculators
- Wind action — the other climatic action, EN 1991-1-4
- Portal frame — where the loads end up, asymmetric cases included
- Timber member design — snow is a short or medium-term action, which changes \(k_{mod}\)
- Timber deflections — snow below 1000 m has \(\psi_2 = 0\), so it produces no creep