Two-story frame — how story shear accumulates downward
Add a storey and something new appears: the lateral load from every level above accumulates as it travels down. This is why the bottom columns of any building are the hardest working ones — and why codes limit drift per storey rather than total movement.
- Bay
- 6 m
- Story height
- 4 mtwo stories, 8 m overall
- 8 kN/mon each floor beam
- Lateral
- 12 kNat each floor level
- 200 GPa
- 100 × 10⁶ mm⁴all members
- Bases
- fixed
Part 1, step 1 — Six nodes, two stories
Build it story by story, exactly as it would be erected.
Two bays of column and two floor beams. Place the left column line first, then the right — bottom to top on both, so the local axes agree:
N 0,0 N 0,4 N 0,8 N 6,0 N 6,4 N 6,8
Then the members — each column in two lifts, split at the floor level, because the floor beam has to frame into a node:
M 1 2 M 2 3 M 4 5 M 5 6 M 2 5 M 3 6
The last two are the floor and roof beams. A node is not just a point — it is where members can connect and where loads can be applied, so the column must be split at every level that has a beam.
Part 1, step 2 — Fix the bases, load both floors
Gravity on the beams, wind at each level.
Fixed bases, as a real multi-story frame would usually have:
S 1 F S 4 F
Gravity on both beams, and a 12 kN lateral load at each floor level:
L 5 -8 L 6 -8 P 2 12 0 P 3 12 0
Two lateral loads of 12 kN — one at the first floor, one at roof level. That total of 24 kN is the number to watch as it travels down.
Part 2, step 1 — Story shear accumulates downward
The single most important idea in multi-story framing.
Consider a horizontal cut just below the roof. Only the roof load, 12 kN, is above it — so the upper columns share 12 kN of shear between them.
Now cut just above the bases. Both lateral loads are above that cut:
The solver confirms the total: 24 kN reaches the foundations. The lower columns carry twice the story shear the upper ones do, from an identical load at each level.
You can see it directly in the member end moments: the lower column lift peaks at 27.17 kN·m against 5.421 kN·m in the lift above it.
Part 2, step 2 — Story drift, not just total sway
The number that governs a multi-story frame.
Total sway at roof level is 11.74 mm, and at the first floor 5.881 mm. But the number that matters for a multi-story frame is story drift — the RELATIVE movement between one floor and the next:
That is what cracks partitions, jams doors and shears façade fixings — not the absolute movement of the roof, which the building experiences as a whole and nobody inside can feel.
Hand check vs solver
| Quantity | By hand | StructureCalcs | |
|---|---|---|---|
| Total lateral reaction | 12 + 12 = 24 kN | 24 kN | |
| Total vertical reaction | 8 × 6 × 2 = 96 kN | 96 kN | |
| Peak moment, LOWER column lift | indeterminate | 27.17 kN·m | |
| Peak moment, upper column lift | indeterminate | 5.421 kN·m | |
| Base moment (fixed) | indeterminate | 34.24 kN·m | |
| Peak sway (roof) | indeterminate | 11.74 mm |
Every value was worked by hand with the classical method, then checked against this site’s solver — the same engine the Try it button opens. This agreement is re-run automatically on every build.
Now make it yours
Open this exact model in the calculator — then change a load, drag a support, and watch every diagram update in real time. The best way to build intuition is to break it and see what happens.
Take it with you
Export this worked example as a PDF, or download it as a .screport and open it in the Report Builder — the model travels inside the file, so you can reconstruct it, re-solve, and build your own report from it.