Load paths and take-down

The last step joins the course together: the permanent and imposed loads of a building are followed from the slabs, through the beams and columns, down to a footing, with G and Q kept apart, and then designed in the STATIX pad footing calculator.

1. Learning outcomes

After this lesson you can:

trace the load path from slab to beam, column, footing and soil;
find tributary areas, and share slab loads to beams by span (one-way) or by the 45° rule (two-way);
add wall line loads and member self-weight;
take a column's loads down floor by floor with G and Q kept apart;
combine at the foundation and check a pad footing: SLS for bearing, ULS for the concrete.

2. Before you start

Lessons 1 to 5 of this course.
The free quick tools and pad footing calculator.
A pocket calculator and about 50 minutes.

3. The load path

The load path. Every load must find its way to the ground: the slab carries it to the beams, the beams to the columns, the columns down through each floor to the footings, and the footings spread it onto the soil. A take-down follows that path and adds up the load at each step.

Tributary areas. On a regular grid each column carries the floor halfway to its neighbours: a full bay for an interior column, half a bay at an edge, a quarter at a corner. Continuity makes the interior columns next to an edge carry a little more; the simple split is the usual first take-down.

4. Slabs to beams

One-way slabs. A slab spanning one way between two beams sends half its load to each (more to the inner support of a continuous slab). The beams then carry a uniform line load w × l/2 from each side.

Two-way slabs: the 45° rule. Lines at 45° from each corner split a panel into two triangles (to the short edges) and two trapezoids (to the long edges). The STATIX slab design engine uses this dispersion for the edge reactions, capped at half the panel load per metre of the short span, and more at restrained edges.

Line loads from walls. A wall standing on a beam adds its weight per metre (lesson 2) to the beam's slab load and self-weight; the beam passes half of its total to each column. Walls on slabs are placed where they stand.

5. The column take-down

The take-down. Work from the roof down. At each level add the floor's share (G and Q separately) and the column's own weight; the running totals at the bottom are the characteristic actions on the footing.

Why G and Q stay apart. If the take-down carries only a factored total, the footing cannot be checked at the serviceability limit state and the other combinations of lesson 1 are lost. Carry characteristic G, Q (and W) to the bottom and combine there.

Imposed load reduction. A column carrying many floors is unlikely to see every floor fully loaded together, and SANS 10160-2 (9.3.1.10) allows a reduction. The STATIX tools do not apply it, so a take-down entered into STATIX keeps the full imposed load.

per level: G += g_k × A_trib + column self-weight; Q += q_k × A_trib at the footing: the combinations of lesson 1 from ΣG, ΣQ (and W from the frame)

6. At the foundation

At the foundation. The allowable bearing pressure of the soil is a service value, so the footing's size is checked with the SLS combination, plus the footing's own weight and the soil on it. The concrete (bending, shear and punching) is designed with the ULS combinations.

Wind on the frame. The frame analysis turns the wind loads of lesson 5 into column base actions N, M and H. They go into the footing design as a separate W set, so the uplift case (0.9 G + 1.6 W) is checked too.

7. In STATIX

In STATIX: the quick tools give g_k and q_k; the take-down is a short hand table; the pad footing calculator takes the characteristic totals in its G / Q / W table, makes every combination, and checks the bearing at SLS and the concrete at ULS.