Timber deflections

What this calculator checks

This tool computes the deflections of a timber member and compares them with the limits recommended by EN 1995-1-1 §7.2. It checks three distinct quantities, defined by Figure 7.1 of the code:

• \(w_{inst}\) — the instantaneous deflection, under the characteristic combination of actions;
• \(w_{fin}\) — the final deflection, once creep has taken place;
• \(w_{net,fin}\) — the net final deflection, that is \(w_{fin}\) minus the precamber.

In timber, the serviceability limit state frequently governs the design. A beam can sit at a bending utilisation of 0.6 and still fail on deflection, because timber has a modulus of elasticity roughly twenty times lower than steel and, on top of that, creeps over time.

Creep and the factor $k_

Timber keeps deforming under sustained load. The code models this with \(k_{def}\) (Table 3.2), which depends only on the product and the service class:

In service class 3 the deformation triples relative to the instantaneous value. Moisture is not a comfort detail: it is the dominant factor in long-term behaviour.

There is one correction that is easy to miss. Clause 3.2(4) requires that for timber placed at or near fibre saturation which will dry out under load, \(k_{def}\) be increased by 1.0. A service class 1 member installed green therefore reaches 1.60 instead of 0.60 — nearly tripling the creep. The calculator has a dedicated switch for it.

Watch for the classic confusion: \(k_{mod}\) belongs to strength, \(k_{def}\) to stiffness. They do not substitute for one another and never appear in the same expressions.

Why \(\psi_2\) matters, not \(\psi_0\)

This is where it gets interesting. Creep is not produced by the whole variable load, only by the part that stays on the member long enough. The code quantifies that through the quasi-permanent factor \(\psi_2\) from EN 1990:

\(w_{fin} = u_{inst,G}(1 + k_{def}) + u_{inst,Q1}(1 + \psi_{2,1} k_{def}) + \sum_i u_{inst,Qi}(\psi_{0,i} + \psi_{2,i} k_{def})\)

The consequence is counter-intuitive at first. Wind has \(\psi_2 = 0\): a beam loaded purely by wind has a final deflection equal to the instantaneous one, whatever the service class. At the other end, a storage area (category E, \(\psi_2 = 0.8\)) produces creep almost as large as self-weight — 10 mm instantaneous becomes 14.8 mm in service class 1, against 16 mm if the same deflection came from a permanent load.

Some common coefficients from EN 1990 Table A1.1:

These are the values recommended by EN 1990; the national annex may change them, which is why the calculator also accepts a \(\psi_0\) / \(\psi_2\) pair entered by hand.

The characteristic combination

The instantaneous deflection is computed under the characteristic combination (§2.2.3(2)): the leading variable action enters in full, the accompanying ones with \(\psi_0\):

\(w_{inst} = u_{inst,G} + u_{inst,Q1} + \sum_i \psi_{0,i} \, u_{inst,Qi}\)

Order matters: the first variable action in the list is treated as the leading one. If you are unsure which governs, run the calculation with each in first position and keep the worst case.

The limits in Table 7.2

The code gives ranges, not single values — the first figure is the most permissive:

The calculator starts from the permissive end and switches the values automatically when you change the static scheme. You can edit them, and setting a limit to zero skips that check.

Cantilever limits look more generous, but they refer to the cantilever length rather than an equivalent span — for the same visible deformation, a 2 m cantilever has roughly half the budget of a 4 m beam.

Input data

Instantaneous deflections are inputs, not something the page computes: that would mean assuming a static scheme and a load distribution. You obtain them from analysis or from beam formulas.

One point is essential: instantaneous deflections are computed with the mean modulus \(E_{0,mean}\) (§2.2.3(2)), not the 5th percentile \(E_{0,05}\) used for buckling and lateral torsional buckling checks. Confusing the two puts results 25-35% out.

• Strength class and service class — determine \(k_{def}\).
• Span \(l\) and static scheme — determine the limits.
• Precamber \(w_c\) — subtracted from \(w_{net,fin}\) only.
• Deflection from permanent actions \(u_{inst,G}\).
• Variable actions — each with its category (which gives \(\psi_0\) and \(\psi_2\)) and its own instantaneous deflection.

Assumptions and limitations

• The serviceability limit state is checked. For strength see the timber member check.
• Floor vibration (§7.3) is not covered — in long-span timber floors it often governs before deflection does.
• Deformation from slip in connections (§2.3.2.2) is not accounted for; it matters in built-up members.
• The formula assumes all actions deflect the member in the same direction. If an action lifts the member, enter its real effect rather than its magnitude.
• The \(\psi\) coefficients are those recommended by EN 1990; check your national annex.

Related calculators

• Timber member design — the ultimate limit state, EN 1995-1-1.
• Single-span beams — where the instantaneous deflections come from.
• Continuous beam — for multi-span schemes.