Portal frame under combined gravity and wind
Both previous load cases at once. Superposition means the effects simply add — and gravity turns out to be what keeps the windward footing on the ground.
- Span
- 6 m
- Height
- 4 m
- 10 kN/mgravity, on the rafter
- 15 kNwind, at the eaves
- Bases
- pinned
Part 1 — Both load cases on one frame
Gravity along the rafter, wind at the eaves.
The familiar pinned portal, then both loads together:
N 0,0 N 0,4 N 6,4 N 6,0 M 1 2 M 2 3 M 4 3 S 1 P S 4 P
L 2 -10 P 2 15 0
A 10 kN/m gravity UDL on the rafter and a 15 kN lateral load at the windward eaves — the two cases solved separately in the previous examples, now acting at the same time.
Part 2, step 1 — Linear analysis means the cases simply add
Worth checking rather than assuming.
This is a linear elastic analysis, so the combined answer is the sum of the separate ones. Gravity alone gave a peak member moment of about 20.8 kN·m; wind alone about 30.0 kN·m. Together:
The solver returns 50.73 kN·m — superposition, confirmed numerically rather than taken on trust.
This is exactly why load cases are analysed separately and combined afterwards: each case is solved once, and every combination the code asks for is then arithmetic rather than a fresh analysis.
Part 2, step 2 — Gravity rescues the uplift
The reason a code asks for combinations rather than worst cases.
Under wind alone, one base wanted to lift: the vertical reactions were a pure couple of ±10 kN. Add gravity’s 30 kN of compression at each base and the picture changes completely — the reactions are now 20 and 40 kN.
Both bases stay in compression. The holding-down bolts have nothing to resist and the footing can be sized for bearing alone.
That is the whole point of a load combination: the governing case for the frame is gravity-plus-wind, but the governing case for the footing may well be wind with a reduced dead load — precisely because gravity is what keeps it down.
Hand calculation vs solver
| Quantity | By hand | StructureCalcs | |
|---|---|---|---|
| Total vertical reaction | wL = 60 kN (wind adds none) | 60 kN | |
| Total horizontal reaction | 15 kN (the applied wind) | 15 kN | |
| Peak member moment | ≈ 20.8 + 30.0 = 50.8 kN·m | 50.73 kN·m | |
| Peak sway | wind-driven | 14.09 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.