Problem. Six wall piers, each a separate three-storey cantilever, are solved separately with MindFEM and with ETABS. They are a planar wall and a wall at 30°, an axis-aligned C core and L core, an asymmetric E core rotated by 25° and a C core with inturned lips rotated by −35°. Both programs find the six section forces, the centroid of the section and the local axis angle at every section; in the cores the lateral load does not pass through the shear centre, so torsion arises too.
Reference document. The reference is the same walls modelled in ETABS 20.1.0 with its own objects. The forces are read from its pier output, the centroid and the axis angle from its pier section properties.
Numerical model. The storey height is 3 m and the bases are fixed; the planar and the inclined walls are 0.30 m thick, the cores 0.25 m. The concrete is C30/37 and the mesh is made of 0.25 × 0.25 m quadrilateral elements.
Planar and inclined walls, axis-aligned and rotated cores
Independent calculation. ETABS 20.1.0, the same structure modelled with ETABS's own objects
107-row table · largest deviation < 0.001%
| Quantity | Reference | Computed | Deviation |
|---|---|---|---|
| EX: P1, bottom of storey 1, V2 [kN] | 60 | 60 | 0% |
| EX: P1, bottom of storey 1, M3 [kNm] | 420 | 420 | 0% |
| EX: P1, bottom of storey 2, V2 [kN] | 50 | 50 | 0% |
| EX: P1, bottom of storey 2, M3 [kNm] | 240 | 240 | 0% |
| EY: P1, bottom of storey 1, V3 [kN] | 60 | 60 | < 0.001% |
| EY: P1, bottom of storey 1, M2 [kNm] | 420 | 420 | < 0.001% |
| EY: P1, bottom of storey 2, V3 [kN] | 50 | 50 | < 0.001% |
| EY: P1, bottom of storey 2, M2 [kNm] | 240 | 240 | < 0.001% |
| G: P1, bottom of storey 1, N [kN] | -384.78 | -384.78 | < 0.001% |
| P1 centroid x [m] | 2 | 2 | 0% |
| EX: P2, bottom of storey 1, V2 [kN] | 51.9615 | 51.9615 | < 0.001% |
| EX: P2, bottom of storey 1, V3 [kN] | -30 | -30 | < 0.001% |
| EX: P2, bottom of storey 1, M2 [kNm] | -210 | -210 | < 0.001% |
| EX: P2, bottom of storey 1, M3 [kNm] | 363.731 | 363.731 | < 0.001% |
| EX: P2, bottom of storey 2, V2 [kN] | 43.3013 | 43.3013 | < 0.001% |
| EX: P2, bottom of storey 2, V3 [kN] | -25 | -24.9999 | < 0.001% |
| EX: P2, bottom of storey 2, M2 [kNm] | -120 | -120 | < 0.001% |
| EX: P2, bottom of storey 2, M3 [kNm] | 207.846 | 207.846 | < 0.001% |
| EY: P2, bottom of storey 1, V2 [kN] | 30 | 30 | < 0.001% |
| EY: P2, bottom of storey 1, V3 [kN] | 51.9615 | 51.9615 | < 0.001% |
| EY: P2, bottom of storey 1, M2 [kNm] | 363.731 | 363.731 | < 0.001% |
| EY: P2, bottom of storey 1, M3 [kNm] | 210 | 210 | < 0.001% |
| EY: P2, bottom of storey 2, V2 [kN] | 25 | 24.9999 | < 0.001% |
| EY: P2, bottom of storey 2, V3 [kN] | 43.3013 | 43.3013 | < 0.001% |
| EY: P2, bottom of storey 2, M2 [kNm] | 207.846 | 207.846 | < 0.001% |
| EY: P2, bottom of storey 2, M3 [kNm] | 120 | 120 | < 0.001% |
| G: P2, bottom of storey 1, N [kN] | -384.78 | -384.78 | < 0.001% |
| P2 centroid x [m] | 9.73205 | 9.73205 | < 0.001% |
| P2 centroid y [m] | 1 | 1 | < 0.001% |
| P2 axis angle [°] | 30 | 30 | < 0.001% |
| EX: P3, bottom of storey 1, V3 [kN] | -60 | -60 | < 0.001% |
| EX: P3, bottom of storey 1, M2 [kNm] | -420 | -420 | < 0.001% |
| EX: P3, bottom of storey 2, V3 [kN] | -50 | -50 | < 0.001% |
| EX: P3, bottom of storey 2, M2 [kNm] | -240 | -240 | < 0.001% |
| EY: P3, bottom of storey 1, V2 [kN] | 60 | 60 | < 0.001% |
| EY: P3, bottom of storey 1, T [kNm] | 2.7 | 2.7 | < 0.001% |
| EY: P3, bottom of storey 1, M3 [kNm] | 420 | 420 | < 0.001% |
| EY: P3, bottom of storey 2, V2 [kN] | 50 | 50 | < 0.001% |
| EY: P3, bottom of storey 2, T [kNm] | 2.25 | 2.25 | < 0.001% |
| EY: P3, bottom of storey 2, M3 [kNm] | 240 | 240 | < 0.001% |
| G: P3, bottom of storey 1, N [kN] | -510.974 | -510.974 | < 0.001% |
| P3 centroid x [m] | 16.375 | 16.375 | 0% |
| P3 centroid y [m] | 1.5 | 1.5 | 0% |
| P3 axis angle [°] | 90 | 90 | 0% |
| EX: P4, bottom of storey 1, V2 [kN] | 60 | 60 | < 0.001% |
| EX: P4, bottom of storey 1, T [kNm] | -1.71429 | -1.71429 | < 0.001% |
| EX: P4, bottom of storey 1, M3 [kNm] | 420 | 420 | < 0.001% |
| EX: P4, bottom of storey 2, V2 [kN] | 50 | 50 | < 0.001% |
| EX: P4, bottom of storey 2, T [kNm] | -1.42857 | -1.42857 | < 0.001% |
| EX: P4, bottom of storey 2, M3 [kNm] | 240 | 240 | < 0.001% |
| EY: P4, bottom of storey 1, V3 [kN] | 60 | 60 | < 0.001% |
| EY: P4, bottom of storey 1, T [kNm] | 1.71429 | 1.71429 | < 0.001% |
| EY: P4, bottom of storey 1, M2 [kNm] | 420 | 420 | < 0.001% |
| EY: P4, bottom of storey 2, V3 [kN] | 50 | 50 | < 0.001% |
| EY: P4, bottom of storey 2, T [kNm] | 1.42857 | 1.42857 | < 0.001% |
| EY: P4, bottom of storey 2, M2 [kNm] | 240 | 240 | < 0.001% |
| G: P4, bottom of storey 1, N [kN] | -425.812 | -425.812 | < 0.001% |
| P4 centroid x [m] | 22.9 | 22.9 | 0% |
| P4 centroid y [m] | 0.4 | 0.4 | 0% |
| EX: P5, bottom of storey 1, V2 [kN] | 25.3571 | 25.3572 | < 0.001% |
| EX: P5, bottom of storey 1, V3 [kN] | 54.3785 | 54.3784 | < 0.001% |
| EX: P5, bottom of storey 1, T [kNm] | -1.22973 | -1.22973 | < 0.001% |
| EX: P5, bottom of storey 1, M2 [kNm] | 380.649 | 380.649 | < 0.001% |
| EX: P5, bottom of storey 1, M3 [kNm] | 177.5 | 177.5 | < 0.001% |
| EX: P5, bottom of storey 2, V2 [kN] | 21.1309 | 21.131 | < 0.001% |
| EX: P5, bottom of storey 2, V3 [kN] | 45.3154 | 45.3154 | < 0.001% |
| EX: P5, bottom of storey 2, T [kNm] | -1.02478 | -1.02477 | < 0.001% |
| EX: P5, bottom of storey 2, M2 [kNm] | 217.514 | 217.514 | < 0.001% |
| EX: P5, bottom of storey 2, M3 [kNm] | 101.428 | 101.429 | < 0.001% |
| EY: P5, bottom of storey 1, V2 [kN] | -54.3785 | -54.3784 | < 0.001% |
| EY: P5, bottom of storey 1, V3 [kN] | 25.3571 | 25.3572 | < 0.001% |
| EY: P5, bottom of storey 1, T [kNm] | 2.87578 | 2.87578 | < 0.001% |
| EY: P5, bottom of storey 1, M2 [kNm] | 177.5 | 177.5 | < 0.001% |
| EY: P5, bottom of storey 1, M3 [kNm] | -380.649 | -380.649 | < 0.001% |
| EY: P5, bottom of storey 2, V2 [kN] | -45.3154 | -45.3154 | < 0.001% |
| EY: P5, bottom of storey 2, V3 [kN] | 21.1309 | 21.131 | < 0.001% |
| EY: P5, bottom of storey 2, T [kNm] | 2.39648 | 2.39648 | < 0.001% |
| EY: P5, bottom of storey 2, M2 [kNm] | 101.428 | 101.429 | < 0.001% |
| EY: P5, bottom of storey 2, M3 [kNm] | -217.514 | -217.514 | < 0.001% |
| G: P5, bottom of storey 1, N [kN] | -723.88 | -723.88 | < 0.001% |
| P5 centroid x [m] | 2.51642 | 2.51642 | < 0.001% |
| P5 centroid y [m] | 9.04616 | 9.04616 | < 0.001% |
| P5 axis angle [°] | -65 | -64.9999 | < 0.001% |
| EX: P6, bottom of storey 1, V2 [kN] | 49.1491 | 49.1491 | < 0.001% |
| EX: P6, bottom of storey 1, V3 [kN] | 34.4146 | 34.4146 | < 0.001% |
| EX: P6, bottom of storey 1, T [kNm] | 1.14433 | 1.14432 | < 0.001% |
| EX: P6, bottom of storey 1, M2 [kNm] | 240.902 | 240.902 | < 0.001% |
| EX: P6, bottom of storey 1, M3 [kNm] | 344.044 | 344.044 | < 0.001% |
| EX: P6, bottom of storey 2, V2 [kN] | 40.9576 | 40.9576 | < 0.001% |
| EX: P6, bottom of storey 2, V3 [kN] | 28.6788 | 28.6788 | < 0.001% |
| EX: P6, bottom of storey 2, T [kNm] | 0.953606 | 0.953603 | < 0.001% |
| EX: P6, bottom of storey 2, M2 [kNm] | 137.658 | 137.658 | < 0.001% |
| EX: P6, bottom of storey 2, M3 [kNm] | 196.596 | 196.596 | < 0.001% |
| EY: P6, bottom of storey 1, V2 [kN] | -34.4146 | -34.4146 | < 0.001% |
| EY: P6, bottom of storey 1, V3 [kN] | 49.1491 | 49.1491 | < 0.001% |
| EY: P6, bottom of storey 1, T [kNm] | 1.63427 | 1.63427 | < 0.001% |
| EY: P6, bottom of storey 1, M2 [kNm] | 344.044 | 344.044 | < 0.001% |
| EY: P6, bottom of storey 1, M3 [kNm] | -240.902 | -240.902 | < 0.001% |
| EY: P6, bottom of storey 2, V2 [kN] | -28.6788 | -28.6788 | < 0.001% |
| EY: P6, bottom of storey 2, V3 [kN] | 40.9576 | 40.9576 | < 0.001% |
| EY: P6, bottom of storey 2, T [kNm] | 1.36189 | 1.36189 | < 0.001% |
| EY: P6, bottom of storey 2, M2 [kNm] | 196.596 | 196.596 | < 0.001% |
| EY: P6, bottom of storey 2, M3 [kNm] | -137.658 | -137.658 | < 0.001% |
| G: P6, bottom of storey 1, N [kN] | -596.137 | -596.137 | < 0.001% |
| P6 centroid x [m] | 13.2992 | 13.2992 | < 0.001% |
| P6 centroid y [m] | 7.92145 | 7.92145 | < 0.001% |
| P6 axis angle [°] | -35 | -35 | < 0.001% |
The six piers in plan with the centroids of their sections. P1 planar, P2 at 30°, P3 a C core (3 m web, 1.5 m flanges), P4 an L core (3 m and 2 m), P5 an asymmetric E core rotated by 25° (4 m web, flanges of 1.5, 1.0 and 2.0 m), P6 a C core with lips rotated by −35° (3 m web, 1.5 m flanges, 0.5 m lips). Dimensions are in metres.
Note. G is the self weight with 10 kN/m along the walls at every floor, EX and EY a lateral load of 10, 20 and 30 kN on every piece at the floors. Local 1 points up and local 2 runs along the longest leg of the section; of equal legs the one nearest the x axis is taken. In the L core that is the 3 m leg, while the principal axis of the section is at −24.66°. For the C core with lips ETABS takes the direction of the flanges rather than the longest leg, so the label of P6 is given an angle of −35°. The values are the force on the positive face of the section; N is positive in tension, a positive M2 puts the local −3 side in tension and a positive M3 the local −2 side. Components below one per cent of the piece's largest section force are left out of the table, the torsion of the cores is kept. The centroid is the thickness-weighted centre of the section.
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.