Results.
| Example | Reference | Records | Largest deviation |
|---|---|---|---|
| Four-storey steel frame, linear and P-Delta | Independent program | 12 | 0.0347% |
| Four-storey steel frame, buckling | Independent program | 10 | 0.0237% |
Problem. A four-storey steel building with moment frames in X and bracing in Y is solved separately with MindFEM and with ETABS. The linear solution under vertical and lateral load, the P-Delta effect built from the vertical load and the linear buckling under vertical load are compared.
Reference document. The reference is the same building modelled in ETABS 20.1.0 with its own objects. The sections are given the same values in both programs.
Numerical model. The plan is 24 × 18 m with 8 m bays in X and 6 m bays in Y; the ground storey is 4.0 m high and the others 3.6 m. The moment frames have HEB 300 columns and IPE 450 beams, the other beams are IPE 360 and pinned, the interior columns are HEB 300 and continuous over the storeys, the braces are 168.3 × 8 mm tubes, the floors are rigid diaphragms, and the loads are G = self weight + 4 kPa, Q = 3 kPa and a lateral load growing with the storey level (EX, EY).
Four-storey steel frame, linear and P-Delta
Parameters. column, moment-beam and brace pieces = 1
Independent calculation. ETABS 20.1.0, the same building modelled with ETABS's own objects
| Quantity | Reference | Computed | Deviation |
|---|---|---|---|
| G + Q: base axial force of an interior column [kN] | 1,392.34 | 1,392.34 | < 0.001% |
| G + Q: axial force of a ground-storey brace [kN] | -57.5815 | -57.5815 | < 0.001% |
| G + Q, P-Delta: base moment of the corner column [kNm] | 17.3713 | 17.3653 | 0.0347% |
| EX: roof corner displacement in X [mm] | 34.4967 | 34.4967 | 0% |
| EX: base moment of the corner column [kNm] | 125.72 | 125.72 | 0% |
| EX, P-Delta: roof corner displacement in X [mm] | 36.9591 | 36.9669 | 0.0209% |
| EX, P-Delta: base moment of the corner column [kNm] | 135.977 | 135.998 | 0.0155% |
| EY: roof corner displacement in Y [mm] | 6.00337 | 6.00337 | 0% |
| EY: axial force of a ground-storey brace [kN] | 118.718 | 118.718 | 0% |
| EY, P-Delta: roof corner displacement in Y [mm] | 6.06854 | 6.06854 | < 0.001% |
| EX: P-Delta amplification (roof corner) | 1.07138 | 1.07161 | 0.0209% |
| EY: P-Delta amplification (roof corner) | 1.01086 | 1.01086 | < 0.001% |
Note. In the P-Delta analysis G + Q is solved to second order and the lateral loads are solved linearly with the stiffness of that solution. In ETABS these are a nonlinear vertical-load case with P-Delta and linear lateral cases that start from its end. The members are single elements; with 8 pieces the P-Delta results change by less than 0.02 per cent.
Four-storey steel frame, buckling
Independent calculation. ETABS 20.1.0, the same building modelled with ETABS's own objects
| Quantity | Condition | Reference | Computed | Deviation |
|---|---|---|---|---|
| Buckling factor 1 | ETABS mode = 1 · MAC = 1 | 9.05077 | 9.04951 | 0.0139% |
| Buckling factor 2 | ETABS mode = 2 · MAC = 1 | 9.05082 | 9.04956 | 0.0139% |
| Buckling factor 3 | ETABS mode = 3 · MAC = 1 | 10.1903 | 10.1888 | 0.0146% |
| Buckling factor 4 | ETABS mode = 4 · MAC = 1 | 10.2309 | 10.2294 | 0.0148% |
| Buckling factor 5 | ETABS mode = 5 · MAC = 1 | 10.2354 | 10.2339 | 0.0148% |
| Buckling factor 6 | ETABS mode = 6 · MAC = 1 | 10.2354 | 10.2339 | 0.0148% |
| Buckling factor 7 | ETABS mode = 7 · MAC = 1 | 13.5203 | 13.5171 | 0.0237% |
| Buckling factor 8 | ETABS mode = 8 · MAC = 1 | 14.7894 | 14.7873 | 0.0142% |
| Buckling factor 9 | ETABS mode = 9 · MAC = 1 | 14.7898 | 14.7877 | 0.0142% |
| Buckling factor 10 | ETABS mode = 10 · MAC = 1 | 20.6342 | 20.6312 | 0.0146% |
Note. In this example the columns, the moment-frame beams and the braces are divided into 8 pieces, because the buckling of a member along its own length requires the division. The first and second modes are buckling of the ground-storey braces, and the third to sixth modes buckling of the ground-storey interior columns. The seventh mode is sway in X, and the eighth and ninth modes are the second-storey braces. The modes are paired by MAC. For pairs of modes with the same factor, the MAC is computed against the shape spanned by the ETABS modes at that factor.
Model files
The ETABS models behind the tables can be downloaded. They open in ETABS 20 and later with
File > Import > ETABS .e2k File.