Results.
| Example | Reference | Records | Largest deviation |
|---|---|---|---|
| Single-cell box girder, 30 m | Closed form | 12 | < 0.001% |
| Comparison with SAP2000 | Independent program | 12 | < 0.001% |
Problem. A section cut produces the resultant section forces of the elements a user plane cuts. In a simply supported single-cell box girder the shear force, the bending moment and the torsional moment are compared at three sections.
Reference document. Static equilibrium is used.
When a load uniform along the girder acts at a distance from the girder axis, statics gives these values at the section . The values are the force on the positive face of the section, and a positive puts the bottom of the section in tension.
Numerical model. The girder spans 30 m and is built from shell elements. The top slab is 6 m wide and 0.25 m thick, the bottom slab 3 m wide and 0.20 m, the webs 2 m deep and 0.40 m thick, there is a 0.50 m diaphragm at each end and the mesh is 0.50 m quadrilateral elements.
Single-cell box girder, 30 m
Closed form. Static equilibrium
| Quantity | Reference | Computed | Deviation |
|---|---|---|---|
| G: V2 at x = 1 m [kN] | -1,269.96 | -1,269.96 | < 0.001% |
| G: M3 at x = 1 m [kNm] | 1,315.32 | 1,315.32 | < 0.001% |
| G: V2 at x = 7.5 m [kN] | -680.336 | -680.336 | < 0.001% |
| G: M3 at x = 7.5 m [kNm] | 7,653.78 | 7,653.78 | < 0.001% |
| G: M3 at x = 15 m [kNm] | 10,205 | 10,205 | < 0.001% |
| Q: V2 at x = 1 m [kN] | -350 | -350 | < 0.001% |
| Q: T at x = 1 m [kNm] | -612.5 | -612.5 | 0% |
| Q: M3 at x = 1 m [kNm] | 362.5 | 362.5 | < 0.001% |
| Q: V2 at x = 7.5 m [kN] | -187.5 | -187.5 | < 0.001% |
| Q: T at x = 7.5 m [kNm] | -328.125 | -328.125 | < 0.001% |
| Q: M3 at x = 7.5 m [kNm] | 2,109.38 | 2,109.37 | < 0.001% |
| Q: M3 at x = 15 m [kNm] | 2,812.5 | 2,812.5 | < 0.001% |
Note. The bearings are at the nodes where the bottom slab meets the webs. The two bearings at each end are held vertically, and torsion is carried by the force couple of these two bearings. Q is a 10 kPa load on a 2.5 m wide strip on one side of the girder, 1.75 m from the girder axis. The sections are at x = 1, 7.5 and 15 m and cut every shell of the box. Local axis 1 runs along the girder, local axis 2 points up, and the moment is taken about the centroid of the section. N, V3 and M2, zero by statics, stay below 10⁻⁸ in MindFEM.
Comparison with SAP2000
Independent calculation. SAP2000 27.1.0, the same model, Section Cut by SAP2000's own group definition
| Quantity | Reference | Computed | Deviation |
|---|---|---|---|
| G: V2 at x = 1 m [kN] | -1,269.96 | -1,269.96 | < 0.001% |
| G: M3 at x = 1 m [kNm] | 1,315.32 | 1,315.32 | < 0.001% |
| G: V2 at x = 7.5 m [kN] | -680.336 | -680.336 | < 0.001% |
| G: M3 at x = 7.5 m [kNm] | 7,653.78 | 7,653.78 | < 0.001% |
| G: M3 at x = 15 m [kNm] | 10,205 | 10,205 | < 0.001% |
| Q: V2 at x = 1 m [kN] | -350 | -350 | < 0.001% |
| Q: T at x = 1 m [kNm] | -612.5 | -612.5 | < 0.001% |
| Q: M3 at x = 1 m [kNm] | 362.5 | 362.5 | < 0.001% |
| Q: V2 at x = 7.5 m [kN] | -187.5 | -187.5 | < 0.001% |
| Q: T at x = 7.5 m [kNm] | -328.125 | -328.125 | < 0.001% |
| Q: M3 at x = 7.5 m [kNm] | 2,109.38 | 2,109.37 | < 0.001% |
| Q: M3 at x = 15 m [kNm] | 2,812.5 | 2,812.5 | < 0.001% |
Note. The SAP2000 model is built with the same nodes and elements, the shells are Shell-Thick and SAP2000 does not mesh them further. The Section Cut uses SAP2000's own definition, a group of the summed elements and the section nodes, and the moment is taken about the same point.
Model files
The model of the SAP2000 comparison can be downloaded. It opens in SAP2000 27 and later with
File > Import > SAP2000 .s2k Text File and carries the Section Cut definitions.