Module 16 · Lesson 16.1
The load path, end to end
Every previous module answered a question about one member. This one follows the load from where it lands to where it stops.
Why this matters
Every module so far has designed one member in isolation, with its loading handed to it. Real design does not work that way: the loading on a beam is a result of the slab decision above it, and the column below cannot be started until the beam is settled. Most of what goes wrong in practice goes wrong at these joins — a load counted twice, a load not counted at all, or a member designed against loading that a later decision changed.
By the end of this lesson you should be able to
- Follow one load from the floor finish to the ground
- Convert an area load to a line load, and a line load to a point load
- Account for self-weight exactly once
- Accumulate axial load down a column and reduce the variable part
What you should already know
- Actions and combinations (Module 2)
- Slab behaviour and one-way spanning (Module 9)
- Beam and column design (Modules 8 and 10)
- Pad foundations (Module 11)
The building
One floor of a three-storey office building, in in-situ reinforced concrete. The frame is a regular grid:
- Columns on a 7.5 m by 5.0 m grid, storey height 3.5 m
- Beams span the 7.5 m direction, at 5.0 m centres
- A one-way slab spans the 5.0 m between beams
- C30/37 concrete, 500 MPa reinforcement throughout
- Allowable bearing pressure 200 kN/m²
That is the whole structure. Four members, and the load has exactly one way to reach the ground:
slab → beam → column → pad → ground
Each arrow is a change of units as well as a change of member. The slab carries an area load in kN/m². It delivers a line load in kN/m to the beam. The beam delivers a point load in kN to the column. The column delivers a point load to the pad, which spreads it back into a pressure in kN/m².
Getting those conversions right is most of a load take-down, and every one of them is equilibrium — there is no code in any of it.
Worked example
The load take-down, slab to ground
Given
- One-way slab 200 mm thick spanning 5.0 m onto beams
- Finishes, services and ceiling 1.5 kN/m²; partitions 1.0 kN/m² (permanent)
- Office imposed load 3.0 kN/m²; roof imposed 1.5 kN/m²
- Beams 350 × 550, spanning 7.5 m at 5.0 m centres
- Columns 400 × 400, storey height 3.5 m, three storeys
Find
The design load at every stage, from the slab down to the pad.
Assumptions
- Reinforced concrete at 25 kN/m³
- Simply supported members, which is conservative for a monolithic frame
- γG = 1.35 and γQ = 1.5 — in general UK use, not verified against the National Annex here
Practice
The slab carries gk = 7.5 kN/m² and the beams are at 5.0 m centres. The beam is 350 × 550 with a 200 mm slab. What is the total permanent line load on the beam, in kN/m?
Practice
With gk = 40.56 kN/m and qk = 15.0 kN/m, what is the design moment on the 7.5 m simply supported beam, in kNm?
Practice
An internal column on a 7.5 m × 5.0 m grid carries a floor with gk = 7.5 kN/m², plus 29.5 kN of beam weight per bay. What permanent axial load arrives from one floor, in kN?
Check yourself
Why must the permanent and variable loads be tracked separately all the way down the column, instead of being combined at each floor?
Where the units change is where the mistakes are
Three conversions carry the whole take-down, and each has its own characteristic error.
Area to line — the tributary width. The error is using the beam spacing where the slab spans in the other direction, or forgetting that an edge beam picks up half a bay rather than a full one. The check is that all the tributary widths across a floor must add up to the floor.
Line to point — the tributary area. The error is the same one a level up. An internal column on a regular grid takes one full bay; a corner column takes a quarter. Again the areas must add up to the floor.
Point to pressure — the pad. The error is factoring the load. The bearing pressure is compared against an allowable pressure, which is a serviceability quantity derived with its own factor of safety already inside it. Factoring the load as well applies the safety twice, and gives a pad perhaps 35% larger than it needs to be.
Every one of these is checked the same way: add the parts up and see whether they equal the whole. It takes a minute and it catches almost everything.
Summary
- slab → beam → column → pad → ground, and each arrow changes the units
- Tributary widths and areas across a floor must add up to the floor
- Self-weight is counted once, at the member that carries it — the beam takes its downstand only
- Permanent and variable are tracked separately all the way down
- The multi-storey reduction applies to the variable load only, and saved 5% here
- The foundation is sized on CHARACTERISTIC load — factoring it applies the safety twice
This is educational material. It uses simplified examples to teach principles, and must not be relied on for real design or safety-critical decisions. Module overview and checkpoint