Course · lesson 3 of 6

Timber floors, fire and members

How the STATIX timber beam calculator checks a timber floor for vibration and deflection, what load sharing does and does not do, how a timber beam is checked in fire by charring, and axial force and bolted ends in outline.

1. Learning outcomes

After this lesson you can:

check a residential timber floor for vibration as the calculator does, and read why it fails;
set the deflection limits and use load sharing where it applies;
check a timber beam in fire by the reduced cross-section method;
see when axial force and the bolted end check come in.

2. Before you start

Lesson 1 (the floor joist, k_mod, k_def) and lesson 2 (restraint, glulam).
The free timber beam calculator.
A pocket calculator and about 50 minutes.

3. Floor vibration

Why timber floors bounce. A timber floor is light and stiff enough to carry its load, but a footstep can still make it spring or ring. EN 1995-1-1 7.3.3 checks a residential floor three ways: its first natural frequency, its deflection under a 1 kN point load, and its response to the impulse of a heel strike. The calculator runs all three when you tick the residential floor joist box.

The first natural frequency. A stiff, short, light floor vibrates fast and walking does not excite it; a long, heavy or soft one vibrates slowly and does. (EI)_l is the joist stiffness per metre of floor width and m the mass per square metre of the empty floor. Below 8 Hz the simple rules do not apply.

The point-load deflection w. A 1 kN load at mid-span must not deflect the floor more than a (mm). EN 1995-1-1 takes w with the load spread by the deck across several joists; the calculator puts the whole 1 kN on one joist, which is conservative and makes this check stricter than the code. The limit a is a national choice; the page uses the recommended range of Figure 7.2.

The impulse velocity v. A heel strike sets the floor moving; a heavier, wider floor moves less. n₄₀ counts the modes below 40 Hz, which needs the stiffness of the deck across the joists, (EI)_b. The calculator asks for it and does not guess it; with damping ζ 0.01 the limit follows from b_v, also a national choice in Figure 7.2.

4. Deflection and load sharing

Deflection limits. Timber creeps: the final deflection adds k_def times the quasi-permanent part (k_def 0.6 in service class 1, more when wetter). The calculator checks the instant and the final deflection against limits you set; the defaults are L/300 and L/250, inside the ranges of EN 1995-1-1 Table 7.2. Brittle ceilings and tiled floors call for tighter values.

Load sharing. Where four or more similar joists are tied by a continuous deck, a weak one is helped by its neighbours, and EN 1995-1-1 6.6 lets the strength rise by k_sys 1.1. It is a strength factor only; stiffness and the vibration checks are not raised by it.

5. Fire

Fire by charring. Timber burns slowly from the outside in, and the char layer insulates what is left. EN 1995-1-2 4.2.2 removes d_ef = β_n t + k₀ × 7 mm from each exposed face and treats the rest as sound timber. The calculator does this for 3 sides (top protected by the floor) or 4.

Checking the residual section. In a fire the load is lower (an accident with only part of the imposed load), the strength is the 20% fractile raised by k_fi (1.25 solid, 1.15 glulam) with γ_M,fi 1.0, and the beam is the smaller, burnt section. The calculator checks bending, shear and lateral-torsional buckling on it.

Size decides fire resistance. The char depth is the same on a thin joist as on a wide beam, so a 38 mm joist loses nearly all of its width in a short fire while a wide glulam beam keeps a strong core. Exposed thin joists get their fire resistance from a lining or ceiling, which the calculator does not model: it checks the bare member.

6. Members and connections, in outline

Axial force with bending, in outline. A top chord, a post or a rafter with a thrust carries axial force as well as bending. The calculator takes N_Gk, N_Qk and N_Wk, the two buckling lengths and the net area for a tie, and combines them with the bending in each load combination; on cantilevers and continuous beams it says NOT CHECKED.

Bolted ends and the one route. The calculator has one bolted end connection check to SANS 10163-1 13.11, given here in outline. This lesson works the EN 1995-1-1 route (with EN 1995-1-2 for fire) and the SANS load combinations throughout; vibration and fire are EN checks, so run the beam in that route rather than mixing.