Problem. An office floor of flat-plate and twelve-metre beam-and-slab construction, with walls and openings, is solved separately with MindFEM and with ETABS. The deflections under self weight, the total weight and the vertical modes of the floor are compared.
Reference document. The reference is the same building modelled in ETABS 20.1.0 with its own objects and its own mesh.
The modes are compared after pairing the vertical mode shapes of the two programs at the floor nodes with the Modal Assurance Criterion (MAC). It measures how alike two shapes are regardless of scale and sign, is one for identical shapes and zero for unrelated ones, and a value above 0.9 is taken as the same mode.
Numerical model. The floor is 34.5 × 15 m, with 450 × 450 mm columns, 400 × 900 and 300 × 600 mm beams and 250 and 200 mm slabs. It is held by half-storey columns and walls pinned at their far ends, and in both programs the columns join the slab at a single point.
Office floor: flat plate and 12 m beam-and-slab, walls, openings
Independent calculation. ETABS 20.1.0, the same building modelled with ETABS's own objects
| Quantity | Condition | Reference | Computed | Deviation |
|---|---|---|---|---|
| Floor mode 1 frequency [Hz] | ETABS mode = 1 · MAC = 0.998 | 7.22708 | 7.23495 | 0.109% |
| Floor mode 2 frequency [Hz] | ETABS mode = 2 · MAC = 0.997 | 8.05264 | 8.06337 | 0.133% |
| Floor mode 3 frequency [Hz] | ETABS mode = 3 · MAC = 0.997 | 8.71165 | 8.54573 | 1.90% |
| Floor mode 4 frequency [Hz] | ETABS mode = 4 · MAC = 0.992 | 10.0491 | 9.9799 | 0.688% |
| Floor mode 5 frequency [Hz] | ETABS mode = 5 · MAC = 0.993 | 10.2648 | 10.1572 | 1.05% |
| Floor mode 6 frequency [Hz] | ETABS mode = 6 · MAC = 0.996 | 11.7634 | 11.7322 | 0.265% |
| Deflection in the flat-plate part, (3.0; 11.5) [mm] | -4.59358 | -4.78094 | 4.08% | |
| Deflection in the beam-and-slab part, (28.5; 4.0) [mm] | -6.8777 | -6.88677 | 0.132% | |
| Deflection at mid-span of the 12 m beam, (28.5; 7.5) [mm] | -5.16959 | -5.16877 | 0.0157% | |
| Total weight [kN] | 4,664.16 | 4,664.16 | < 0.001% |
Note. The two programs use different shell elements and different meshes, and ETABS lumps the mass at the nodes. In MindFEM the beam is divided into frame elements at the mesh nodes, and the mass of each element goes to its own nodes through the consistent mass matrix. ETABS divides a beam built as a single object at the slab nodes for the analysis, but in this model the self mass of the beam is lumped at the two ends of the object. The beams are therefore built in ETABS as 0.5 m objects. In the flat-plate part the slab rests on point columns, so its deflection and frequency change with mesh refinement in both programs. The tolerances are a regression band that locks the measured difference.
MindFEM and ETABS frequencies of the first six floor modes. Each point is a mode pair matched by shape, and a point below the line means MindFEM finds the lower frequency.
MAC matrix between the first twelve modes of the two programs. Dark cells along the diagonal show that the modes pair in order, and dark cells off the diagonal show two modes that changed places. A row left empty is a mode that moves the walls or columns more than the floor and has no counterpart among the first twelve ETABS modes.
Model files
The ETABS model that produced the results in the table can be downloaded. It opens in ETABS 20
and later with File > Import > ETABS .e2k File.