Actions, limit states and combinations

Every design starts with the loads. This lesson sorts the actions on a building, explains characteristic values, limit states and partial factors, and builds the load combinations of SANS 10160-1 the way the STATIX calculators do.

1. Learning outcomes

After this lesson you can:

sort the actions on a building into permanent, variable and accidental;
explain a characteristic value and the difference between the ultimate and the serviceability limit state;
apply the partial factors of SANS 10160-1, including the favourable 0.9 on G;
build the combinations with a leading action and ψ on the others, and find the one that governs;
enter loads per source in STATIX and read the combinations it makes.

2. Before you start

Your copy of SANS 10160-1 (basis of design) and SANS 10160-2 (permanent and imposed loads).
The free pad footing calculator: it lists the combinations it makes.
A pocket calculator and about 45 minutes.

3. Actions

The actions on a building. Permanent actions G (the weight of the structure, finishes and fixed services) are always there. Variable actions come and go: imposed loads Q from use, and wind W. Accidental actions (impact, fire, explosion) have their own rules.

How actions change in time. G is nearly constant for the life of the building; Q changes with use; wind arrives in short gusts. Because Q and W rarely reach their peaks together, the code adds them with a reduced value for the one that does not lead.

The characteristic value. Loads vary from building to building. The characteristic value is set so that only a small fraction of real loads exceed it during the reference period. SANS 10160-2 and -3 give these values: the densities, the imposed loads by category and the basic wind speed.

4. Limit states and partial factors

Two kinds of limit state (SANS 10160-1). At the ultimate limit state the structure must not collapse, so the actions are increased by partial factors. At the serviceability limit state it must stay usable, so the actions are taken at about their characteristic values.

Partial factors for actions, SANS 10160-1 Table 3. Variable actions get a bigger factor than permanent ones because they are less certain. Where the permanent load helps (holding a roof down against wind uplift), it is reduced to 0.9.

5. Combinations

Leading and accompanying actions (SANS 10160-1 7.3.2.1, eq. (6)). One variable action is taken at its full value and the others at a reduced combination value ψ times theirs (Table 2). You repeat this with each variable action leading.

The usual set for a building (SANS 10160-1 Table 3 and eq. (10)), as STATIX lists them when G, Q and W are all present. Each line is a separate load case; the structure is checked for all of them.

ULS, STR (Table 3): 1.2 G + 1.6 Q_leading + 1.6 ψ Q_accompanying ULS, STR-P: 1.35 G + 1.0 Q_leading G favourable: 0.9 G + 1.6 W SLS (eq. (10)): G + Q_leading + ψ Q_accompanying

When G helps. Under wind uplift on a light roof, the permanent load is what keeps the frame down, so it is taken low (0.9 G) with the wind high. The column and its holding-down bolts may then be in tension: a case a G + Q check alone never shows.

Why STR-P exists. When the permanent load is large and the imposed load small (heavy roofs, thick slabs, retaining structures), 1.35 G + Q gives more than 1.2 G + 1.6 Q. STATIX works out both and the larger governs.

Serviceability. Deflection, cracking and vibration are checked with the actions at their characteristic values, the leading variable action in full and the others times ψ. These are the loads the building really carries on a bad day, not the factored ones.

6. In STATIX

In STATIX you enter the characteristic actions per source, never pre-factored: G, Q and W apart. The calculator builds the code's combinations itself and designs for every one. The pad footing calculator lists them, with the clause for each.