AdvancedFrameMulti-storyWindStory shear

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.

Figure 1.A two-story rigid frame: 8 kN/m on each floor and 12 kN of lateral load at each level.
Given
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
1

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.

Figure 2.The left column line — two lifts, split at the floor level.
Figure 3.Both columns and both beams: the frame is complete but unsupported.
2

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.

Figure 4.The complete two-story model: 8 kN/m on each floor, 12 kN of lateral load at each level, fixed bases.
3

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.

Figure 5.The solved frame. All 24 kN of lateral load reaches the two fixed bases, along with the gravity load from both floors.
4

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.

Figure 6.The sway mode: each story leans relative to the one below. The DIFFERENCE between levels is what damages the building fabric.

Hand check vs solver

Verified — hand calculation vs the solver, to round-off
QuantityBy handStructureCalcs
Total lateral reaction12 + 12 = 24 kN24 kN
Total vertical reaction8 × 6 × 2 = 96 kN96 kN
Peak moment, LOWER column liftindeterminate27.17 kN·m
Peak moment, upper column liftindeterminate5.421 kN·m
Base moment (fixed)indeterminate34.24 kN·m
Peak sway (roof)indeterminate11.74 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.

Verifying your link…