Wind action on buildings
Peak velocity pressure and external pressure zones for a rectangular building, to EN 1991-1-4.
Advanced
Secondary members — line loads
Each member picks up the strip between itself and its neighbours, so the surface pressure becomes kN/m. Its loaded area A = spacing × span also decides which coefficient applies: below 10 m² the code interpolates towards c_pe,1.
Tool information
What this calculator computes
The tool determines the wind action on a rectangular building to EN 1991-1-4 (Eurocode 1, part 1-4): the peak velocity pressure \(q_p(z)\) and the net pressures on the wall and roof zones — flat, monopitch or duopitch.
The output is what goes straight into the model: a pressure in kN/m² for each zone, plus the total force along the wind direction.
From basic velocity to pressure
The chain has four links, each with its own role:
\(v_b = c_{dir} \cdot c_{season} \cdot c_{prob} \cdot v_{b,0}\)
\(v_{b,0}\) is the velocity from the national wind map. The recommended values for \(c_{dir}\) and \(c_{season}\) are 1.0; \(c_{prob}\) corrects for a return period other than 50 years and is exactly 1.0 at 50.
\(c_r(z) = k_r \ln(z/z_0), \qquad k_r = 0.19\left(\frac{z_0}{z_{0,II}}\right)^{0.07}\)
The logarithmic velocity profile. Terrain category II is the reference, hence the 0.19 coefficient.
\(I_v(z) = \frac{k_l}{c_o \ln(z/z_0)}, \qquad q_p(z) = \left[1 + 7 I_v(z)\right] \cdot \tfrac{1}{2}\rho \, v_m^2\)
The factor \((1 + 7 I_v)\) is what turns the mean velocity into a peak pressure — the gust.
What happens below $z_
Each terrain category has a minimum height below which the profile is frozen: the velocity stops decreasing, because the logarithmic model no longer holds among obstacles.
| Category | \(z_0\) [m] | \(z_{min}\) [m] |
|---|---|---|
| 0 — sea, exposed coast | 0.003 | 1 |
| I — lakes, flat land | 0.01 | 1 |
| II — grass, isolated obstacles | 0.05 | 2 |
| III — suburbs, forests | 0.3 | 5 |
| IV — dense urban | 1.0 | 10 |
The practical consequence: an 8 m building in a city (category IV, \(z_{min} = 10\) m) gets the same pressure over its whole height — there is no point looking for a varying profile.
A second effect is worth noticing. Urban terrain gives higher turbulence (so a larger gust factor, above 2.2 against roughly 1.7 in open country), but a much lower mean velocity. Net, the pressure stays lower — but not in proportion to the velocity.
The pressure zones
The zone geometry starts from a single characteristic length:
\(e = \min(b, 2h)\)
where \(b\) is the crosswind dimension. On the side face, of depth \(d\):
- \(e < d\) → zones A (0…\(e/5\)), B (\(e/5\)…\(e\)), C (\(e\)…\(d\))
- \(e \ge d\) → zones A and B; C disappears
- \(e \ge 5d\) → A only, over the full depth
Zone A sits at the upstream edge, where the flow separates and produces the largest suction, \(c_{pe} = -1.2\). That is why facade fixings fail at the corners first, not in the middle of the wall — an observation borne out by any post-storm damage report.
The faces perpendicular to the wind are D (pressure) and E (suction), with coefficients depending on the slenderness \(h/d\):
| \(h/d\) | D | E |
|---|---|---|
| ≤ 0.25 | +0.7 | −0.3 |
| 1 | +0.8 | −0.5 |
| ≥ 5 | +0.8 | −0.7 |
Linear interpolation between rows. Note that the leeward suction doubles from a low building to a slender one, while the windward pressure barely changes.
Internal pressure is not a detail
The net pressure on a cladding element is:
\(w = q_p(z_e) \cdot (c_{pe} - c_{pi}) \cdot c_s c_d\)
When the opening ratio is not known, clause 7.2.9(6) requires checking both extremes, \(c_{pi} = +0.2\) and \(-0.2\). The difference between them is \(0.4 \, q_p\) — on a zone A with \(c_{pe} = -1.2\), the net suction goes from \(1.0 \, q_p\) to \(1.4 \, q_p\), that is 40% more. Not a correction you can skip.
The page shows both columns and bolds the governing value in each pair.
Splitting the wall into parts
When the building is taller than its crosswind width, clause 7.2.2 requires splitting it into parts, each with its own reference height \(z_e\):
- \(h \le b\) → a single part, \(z_e = h\)
- \(b < h \le 2b\) → two parts
- \(h > 2b\) → a bottom part, intermediate strips, a top part
The reason is economy, not safety: using a single \(q_p\) taken at the top would overestimate the total load by tens of percent on a tall building.
Pitched roofs
For monopitch roofs (clause 7.2.4, Tables 7.3a and 7.3b) and duopitch roofs (clause 7.2.5, Tables 7.4a and 7.4b) the page reports every relevant wind direction, not just one. The reason is that on a monopitch roof \(\theta = 0°\) (wind up the slope) and \(\theta = 180°\) (wind down it) give completely different results, and the second is often the more severe: at 15°, zone F reaches \(c_{pe,10} = -2.5\) with the wind coming down the slope, against \(-0.9\) the other way round.
The sign changes, and does not mix
On the windward slope, between \(+5°\) and \(+45°\), the pressure changes rapidly from positive to negative. The code gives both sets of values and requires two separate cases: one with all positive values, one with all negative. Note 1 to Table 7.3a is explicit — mixing the two signs on the same face is not allowed. The page shows the pairs marked (−) and (+) precisely so you do not combine them by accident.
For duopitch roofs, Note 1 to Table 7.4a goes further: four cases must be considered, combining the extreme values in zones F, G, H with those in I and J.
Below 5° there is no interpolation
Linear interpolation on \(\alpha\) is permitted only between values of the same sign (Note 2). Between \(+5°\) and \(-5°\) there is no interpolation at all: for pitches in that range the code refers you to the flat roof of clause 7.2.3. The page refuses the calculation and tells you to switch the roof shape — it does not invent an intermediate value.
The \(0.0\) entries in the tables are not an accident: they are there as interpolation anchors for intermediate angles.
\(c_{pe,1}\) is not a detail
The tables give two columns. \(c_{pe,10}\) applies to loaded areas of at least 10 m², that is to the primary structure. \(c_{pe,1}\) applies to areas below 1 m² — a purlin, a fixing, a panel. The difference frequently exceeds 20%: on a monopitch roof at 15°, \(\theta = 90°\), zone F has \(c_{pe,10} = -2.4\) but \(c_{pe,1} = -2.9\).
For pitched roofs the page shows both columns. Sheeting fixings torn off by wind are a common failure mode, and they come from exactly this — using \(c_{pe,10}\) where the code asks for \(c_{pe,1}\).
The zones
With \(e = \min(b, 2h)\), as for the walls:
| Direction | Zones |
|---|---|
| Monopitch, \(\theta = 0°\) / \(180°\) | F at the two upwind corners (\(e/4\) wide, \(e/10\) deep), G the strip between them, H the remainder |
| Monopitch, \(\theta = 90°\) | \(F_{up}\) at the high eaves, \(F_{low}\) at the low eaves — with different coefficients — G between them, H to \(e/2\), I to the downwind edge |
| Duopitch, \(\theta = 0°\) | F, G over \(e/10\); H up to the ridge; J over \(e/10\) beyond the ridge; I to the downwind edge |
| Duopitch, \(\theta = 90°\) | F at the corners, G the rest of the strip, H to \(e/2\), I to the downwind edge |
Zone J belongs to the duopitch roof alone: the strip on the leeward slope immediately past the ridge, where the flow reattaches. It has no counterpart on a monopitch roof.
Input data
- \(v_{b,0}\) — from the national wind map.
- Terrain category — of the upwind surface, for the wind direction being analysed.
- Geometry — \(b\), \(d\), \(h\). The wind is implicitly perpendicular to side \(b\); for the other direction, run again with \(b\) and \(d\) swapped.
- Roof — flat, monopitch or duopitch, with the pitch angle \(\alpha\). Negative means the roof pitches inwards (valley or butterfly roof) and applies to duopitch roofs only.
- Internal pressure — extremes, a single value, or none.
- Advanced — \(c_{dir}\), \(c_{season}\), \(c_o\), \(c_s c_d\), return period, \(\rho\).
Assumptions and limitations
Covered: peak velocity pressure, vertical walls (Table 7.1), flat roofs with sharp eaves (Table 7.2) and monopitch and duopitch roofs (Tables 7.3 and 7.4), for every wind direction.
Not covered: hipped roofs (clause 7.2.6, Table 7.5) and multispan roofs (clause 7.2.7), parapets, rounded or bevelled eaves, canopies, free-standing walls, isolated cylinders and prisms, friction forces (clause 7.5) and the calculation of the structural factor \(c_s c_d\) (section 6).
The hipped roof is missing for a concrete reason: the zones in Figure 7.9 are trapezia and triangles bounded by the sloping hips, not strips across the depth — they cannot be described by the same (start, extent) pair as the rest.
Other limitations:
- \(c_s c_d = 1.0\) is permitted only for buildings up to 15 m (clause 6.2(1)(a)). Above that it must be determined per section 6 and entered manually — the page flags the case.
- The orography factor \(c_o\) is entered manually; its calculation (Annex A.3) is not implemented. Hills and escarpments accelerate the wind locally.
- For walls and flat roofs only \(c_{pe,10}\) is shown. \(c_{pe,1}\) currently appears for pitched roofs only.
- The loaded area of each zone is not computed, so neither is the logarithmic interpolation between \(c_{pe,1}\) and \(c_{pe,10}\) for areas between 1 and 10 m² (clause 7.2.1(1)). The two values are given separately.
- Clause 4.3.2 covers heights up to 200 m.
- The national annex may change the recommended values (\(c_{dir}\), \(c_{season}\), \(k_l\), \(\rho\)) — which is why all of them are editable.
Related calculators
- Portal frame — where the pressures computed here end up
- Timber member design — wind is a short-term action, with a favourable \(k_{mod}\)
- Timber deflections — wind has \(\psi_2 = 0\), so it produces no creep