Select a grid line and a load combination
Full 3D space frame — 12 DOF per member, six per node, fixed at foundation level. Four base solves (DL, LL, lateral X, lateral Y) superposed into every IS 456 Table 18 combination.
1.5 DL + 1.5 LL · Ultimate limit state — Table 18
Spans
3
Direction
X
Max UDL
29.81kN/m
Edge line
Perimeter
Grid plan — selected line highlighted
Floor 2 · Grid A runs along X. Click any grid line on the plan to switch.
metres · 0.014 m/px
— — orange dashed = buildable footprint after setbacks■ solid = column at a grid intersection, sized as designedhatched = bay not built on this storey — no slab, beam, column or loadX grid 1,2,3… · Y grid A,B,C…
Bending moment diagram
Sagging positive, kNm · 1.5 DL + 1.5 LL · Ultimate limit state — Table 18
Shear force diagram
kN · 1.5 DL + 1.5 LL · Ultimate limit state — Table 18
Span results
Floor 2 · Grid A · 1.5 DL + 1.5 LL
| Span | L (m) | w (kN/m) | M+ | M− | V |
|---|---|---|---|---|---|
| 1 | 3.50 | 29.81 | 21.43 | 35.25 | 58.13 |
| 2 | 3.50 | 29.81 | 13.89 | 32.00 | 52.30 |
| 3 | 3.50 | 29.81 | 21.55 | 35.28 | 58.21 |
Support reactions
Foundation level, 1.5 DL + 1.5 LL — forces kN, moments kNm
| Node | Fx | Fy | Fz | Mx | My | Mz |
|---|---|---|---|---|---|---|
| A1 | 2.12 | 1.00 | 125.62 | -1.27 | 2.66 | 0.00 |
| A2 | -0.61 | 1.04 | 229.79 | -1.32 | -0.84 | 0.00 |
| A3 | 0.49 | 1.02 | 230.96 | -1.29 | 0.55 | 0.00 |
| A4 | -2.23 | 1.34 | 134.78 | -1.71 | -2.87 | 0.00 |
| B1 | 2.79 | 0.02 | 234.69 | -0.02 | 3.49 | 0.00 |
| B2 | -0.51 | 0.10 | 362.97 | -0.13 | -0.77 | 0.00 |
| B3 | 0.43 | 0.07 | 340.59 | -0.10 | 0.39 | 0.00 |
| B4 | -2.33 | -1.28 | 135.68 | 1.61 | -3.01 | 0.00 |
| C1 | 2.09 | -1.04 | 126.76 | 1.32 | 2.61 | 0.00 |
| C2 | -0.06 | -1.12 | 245.68 | 1.42 | -0.16 | 0.00 |
| C3 | -2.17 | -1.15 | 129.38 | 1.45 | -2.80 | 0.00 |
| Σ | -0.00 | 0.00 | 2296.89 | |||
Column design forces
Worst of every ultimate combination, including the lateral ones
| Column | Type | At (m²) | P (kN) | Pu (kN) | Mux | Muy | Governing combination |
|---|---|---|---|---|---|---|---|
| A1 | corner | 2.63 | 106.9 | 160.3 | 18.79 | 23.00 | 1.5(DL-LATY) |
| A2 | edge | 5.25 | 172.5 | 258.7 | 32.29 | 27.47 | 1.5(DL+LATX) |
| A3 | edge | 5.25 | 173.9 | 260.8 | 32.01 | 27.90 | 1.5(DL-LATX) |
| A4 | corner | 2.63 | 116.1 | 174.2 | 19.15 | 24.66 | 1.5(DL-LATY) |
| B1 | edge | 5.25 | 174.8 | 262.2 | 30.26 | 28.73 | 1.5(DL+LATY) |
| B2 | interior | 10.50 | 264.0 | 396.0 | 49.36 | 33.64 | 1.5(DL+LATX) |
| B3 | interior | 7.88 | 249.1 | 373.6 | 48.96 | 34.14 | 1.5(DL-LATX) |
| B4 | corner | 2.63 | 116.6 | 174.9 | 18.94 | 24.65 | 1.5(DL+LATY) |
| C1 | corner | 2.63 | 106.3 | 159.5 | 19.28 | 23.01 | 1.5(DL+LATY) |
| C2 | edge | 5.25 | 182.1 | 273.2 | 33.17 | 27.48 | 1.5(DL+LATX) |
| C3 | corner | 2.63 | 107.8 | 161.8 | 19.27 | 23.11 | 1.5(DL+LATY) |
Equilibrium verification — every case and combination
Σ applied load vs Σ support reactions in all three global directions
| Case / combination | Applied ΣFz | Reaction ΣFz | Applied ΣFx | Reaction ΣFx | Applied ΣFy | Reaction ΣFy | Balance |
|---|---|---|---|---|---|---|---|
| DL | 1331.8 | 1331.8 | 0.00 | 0.00 | 0.00 | -0.00 | OK |
| LL | 199.5 | 199.5 | 0.00 | 0.00 | 0.00 | 0.00 | OK |
| DL+LL | 1531.3 | 1531.3 | 0.00 | 0.00 | 0.00 | -0.00 | OK |
| LATX | 0.0 | 0.0 | 97.39 | 97.39 | 0.00 | -0.00 | OK |
| LATY | 0.0 | 0.0 | 0.00 | 0.00 | 97.39 | 97.39 | OK |
| 1.5DL | 1997.6 | 1997.6 | 0.00 | 0.00 | 0.00 | -0.00 | OK |
| 1.5(DL+LL) | 2296.9 | 2296.9 | 0.00 | 0.00 | 0.00 | -0.00 | OK |
| 1.2(DL+LL+LATX) | 1837.5 | 1837.5 | 116.87 | 116.87 | 0.00 | -0.00 | OK |
| 1.2(DL+LL-LATX) | 1837.5 | 1837.5 | -116.87 | -116.87 | 0.00 | 0.00 | OK |
| 1.2(DL+LL+LATY) | 1837.5 | 1837.5 | 0.00 | 0.00 | 116.87 | 116.87 | OK |
| 1.2(DL+LL-LATY) | 1837.5 | 1837.5 | 0.00 | -0.00 | -116.87 | -116.87 | OK |
| 1.5(DL+LATX) | 1997.6 | 1997.6 | 146.09 | 146.09 | 0.00 | -0.00 | OK |
| 1.5(DL-LATX) | 1997.6 | 1997.6 | -146.09 | -146.09 | 0.00 | 0.00 | OK |
| 1.5(DL+LATY) | 1997.6 | 1997.6 | 0.00 | 0.00 | 146.09 | 146.09 | OK |
| 1.5(DL-LATY) | 1997.6 | 1997.6 | 0.00 | -0.00 | -146.09 | -146.09 | OK |
| 0.9DL+1.5LATX | 1198.6 | 1198.6 | 146.09 | 146.09 | 0.00 | -0.00 | OK |
| 0.9DL-1.5LATX | 1198.6 | 1198.6 | -146.09 | -146.09 | 0.00 | 0.00 | OK |
| 0.9DL+1.5LATY | 1198.6 | 1198.6 | 0.00 | 0.00 | 146.09 | 146.09 | OK |
| 0.9DL-1.5LATY | 1198.6 | 1198.6 | 0.00 | -0.00 | -146.09 | -146.09 | OK |
Forces are in kN. Bending moments and shears come from the same four base solves by the same superposition, so a case that balances here has consistent BMD/SFD and reactions. Column self weight is not part of the frame load — it is added in the column design step, so it does not appear in these sums.
Imposed load audit — where the LL total comes from
IS 875 Part 2, per room, level by level
| Level | Built area (m²) | LL intensity (kN/m²) | Σ LL (kN) | Occupancies |
|---|---|---|---|---|
| Floor 2 | 52.50 | 2.00 – 3.00 | 120.8 | Master bedroom, Bedroom 2, Bedroom 3, Study, Landing |
| Roof (roof) | 52.50 | 1.50 – 1.50 | 78.8 | roof / terrace |
| Σ imposed load on the frame | 199.5 |
A panel with no room above it is a roof / terrace slab and takes the roof imposed load from the Loads step — currently 1.50 kN/m². Every other panel takes the IS 875 Part 2 value of the room sitting on it — not an average.
Model diagnostics
- Vertical equilibrium — Σ reactions vs Σ applied member loadsOK
Ultimate case 1.5(DL+LL): applied 2296.9 kN, support reactions 2296.9 kN.
- Lateral equilibrium — Σ horizontal reactions vs applied storey shearOK
Seismic along X: applied storey forces 97.39 kN (32.9 + 64.5), Σ support Fx -97.39 kN.
- Load audit — frame loads vs independent slab + wall hand calculationOK
Hand calculation 2296.9 kN (slab 1165.5 + walls & beam self weight 1131.4), frame 2296.9 kN, difference 0.00 %. Column self weight is added separately in the column design.
- Equilibrium check — max residual force at a free degree of freedomOK
3D space frame: 33 nodes, 52 members, 198 degrees of freedom, fixed at foundation level. Four base solves (DL, LL, lateral X, lateral Y) superposed into 19 cases and combinations. Worst unbalanced force 1.56e-13 kN.
- Panel aspect ratios within Table 26 range (β ≤ 2)OK
Largest β = 1.17. Above 2.0 the panel is treated as one-way.
- Every load case and combination balances at the supportsOK
19 cases checked in all three global directions. Worst normalised out-of-balance 8.95e-12 %.
- Imposed load on the frame vs Σ (room area × IS 875 Pt 2 load)OK
Frame LL case 199.5 kN, room-by-room hand calculation 199.5 kN (Floor 2 120.8, Roof 78.8). Roof/terrace panels use the roof imposed load set on the Loads step (1.50 kN/m²) — set it to 0.75–1.5 kN/m² if your STAAD model loads the roof.
- Storey drift allowance (h/250)OK
Permissible drift 28 mm over the full height — verify with a full frame analysis before construction.
The frame is solved four times — dead load, imposed load, lateral load along X and lateral load along Y (the governing of wind / seismic storey forces) — and every IS 456 Table 18 combination is obtained by superposition, exactly as STAAD builds combinations of primary cases. Member design uses the worst of all ultimate combinations. Mass is lumped at floor level with no rigid diaphragm. The solver is verified against closed-form fixed, simply supported, continuous and portal-frame solutions. A licensed engineer must still review the model before you build.