Results.
| Example | Reference | Records | Largest deviation |
|---|---|---|---|
| Canopy hung from rods | Independent program | 15 | 0.704% |
| Bridge with seismic shear keys | Independent program | 13 | 0.0157% |
Problem. A tension-only rod and a gap element that makes contact after a given opening are solved separately with MindFEM and with ETABS in two structures where they are used. In a fuel-station canopy hung from rods, wind suction slackens the rods, and in a bridge with seismic shear keys the transverse load closes the joint at one abutment. All cases are solved as nonlinear and the combinations are loaded together.
Reference document. The reference is the same structures modelled in ETABS 20.1.0 with its own objects. The rod is a frame with a zero compression limit, the shear key a gap link and the elastomeric bearing a point spring.
Numerical model. The canopy roof is 12 × 18 m at level 5.5 m; the three central HEB 300 columns continue as masts up to 9.0 m, and at each column a 6 m IPE 400 cantilever on either side is hung from the mast top by a Ø30 rod 1 m in from its tip; the purlins are IPE 160 at 2 m; the loads are G = self weight + 0.30 kPa, S = 0.75 kPa and an upward suction W = 0.80 kPa, and W1 is the same suction on one half only. The bridge has a continuous box-girder deck of 25 + 35 + 25 m spans, Ø1.6 m piers 10 m and 14 m tall monolithic with the deck, 4000 kN/m elastomeric bearings at the abutments and shear keys on both sides with a 50 mm opening; the loads are G = self weight + 50 kN/m and a transverse load E = 60 kN/m.
Canopy hung from rods
Independent calculation. ETABS 20.1.0, the same structure modelled with ETABS's own objects
| Quantity | Reference | Computed | Deviation |
|---|---|---|---|
| G: rod force, middle line, at mid-length [kN] | 13.4357 | 13.4357 | < 0.001% |
| G: rod force, middle line, at the upper end [kN] | 13.5309 | 13.4357 | 0.704% |
| G: rod force, end line, at mid-length [kN] | 15.5672 | 15.5672 | < 0.001% |
| G: vertical displacement of the cantilever tip, middle line [mm] | -1.34572 | -1.34572 | < 0.001% |
| G: column base axial force, middle line [kN] | 43.963 | 43.963 | < 0.001% |
| G + S: rod force, middle line, at mid-length [kN] | 32.1321 | 32.1321 | < 0.001% |
| G + S: vertical displacement of the cantilever tip, middle line [mm] | -3.18543 | -3.18543 | < 0.001% |
| G + W: rod force, middle line (slack), at mid-length [kN] | -0.0000535524 | -0.0000535525 | < 0.001% |
| G + W: vertical displacement of the cantilever tip, middle line [mm] | 4.94807 | 4.94807 | < 0.001% |
| G + W: total vertical base reaction [kN] | -32.1229 | -32.1229 | < 0.001% |
| G + W1: rod on the suction side (slack), at mid-length [kN] | -0.0000172098 | -0.0000172098 | < 0.001% |
| G + W1: rod on the other side, at mid-length [kN] | 9.02403 | 9.02403 | < 0.001% |
| G + W1: cantilever tip on the suction side [mm] | 56.1066 | 56.1066 | < 0.001% |
| G + W1: cantilever tip on the other side [mm] | -55.4442 | -55.4442 | < 0.001% |
| G + W1: column base moment, middle line [kNm] | -81.9396 | -81.9396 | < 0.001% |
Note. The rod carries tension only. When the wind suction exceeds the self weight the rods go slack and the main beam works as a cantilever from the column. In ETABS the force of an inclined rod grows from its lower to its upper end by the component of the rod's weight along its axis. The MindFEM axial element gives its weight to its two ends and its force is constant along it. That force equals the ETABS value at mid-length and is 0.7 per cent below the value at the upper end. At mid-length the force of a slack rod is very close to zero in both programs. The cases are solved as nonlinear and the loads applied together, because results of a one-way element cannot be superposed. The middle line is y = 9 m, the end line y = 3 m, and the suction side is the half x < 6 m.
Bridge with seismic shear keys
Independent calculation. ETABS 20.1.0, the same structure modelled with ETABS's own objects
| Quantity | Reference | Computed | Deviation |
|---|---|---|---|
| G: base axial force of pier P1 [kN] | 7,129.97 | 7,129.97 | < 0.001% |
| G: base axial force of pier P2 [kN] | 7,296.54 | 7,296.54 | < 0.001% |
| 0.5E: transverse deck displacement at abutment A1 [mm] | 9.3982 | 9.39932 | 0.0119% |
| 0.5E: transverse deck displacement at abutment A2 [mm] | 40.7155 | 40.7108 | 0.0115% |
| 0.5E: base moment of pier P1 [kNm] | 8,061.33 | 8,061.31 | < 0.001% |
| E: shear key force at A2 [kN] | -494.067 | -493.989 | 0.0157% |
| E: transverse deck displacement at abutment A1 [mm] | 30.0184 | 30.0166 | 0.0060% |
| E: transverse deck displacement in the middle span (x = 40 m) [mm] | 38.0629 | 38.0624 | 0.0012% |
| E: transverse deck displacement at abutment A2 [mm] | 50.4941 | 50.494 | < 0.001% |
| E: base moment of pier P1 [kNm] | 16,849 | 16,848.6 | 0.0025% |
| E: base moment of pier P2 [kNm] | 11,632.3 | 11,632.2 | < 0.001% |
| G + E: shear key force at A2 [kN] | -494.067 | -493.989 | 0.0157% |
| G + E: base moment of pier P2 [kNm] | 11,632.3 | 11,632.2 | < 0.001% |
Note. The shear key makes contact after the deck has moved 50 mm. Under 0.5E the joint is open at both abutments. Under E the joint closes at abutment A2 and the key carries force, while it stays open at A1. The results under E are therefore not twice those under 0.5E. Abutment A1 is at x = 0 and A2 at x = 85 m; pier P1 is 10 m and P2 14 m tall.
Model files
The ETABS models that produced the results in the tables can be downloaded. They open in ETABS 20 and
later with File > Import > ETABS .e2k File.
When ETABS 20.1.0 imports an .e2k file it does not assign the link properties, even in a file ETABS wrote itself, and the links show the property "None". After opening the bridge model, assign the KEY property to links K1, K2, K3 and K4 with Assign > Link/Support > Link Property. The model built this way gives the same results as the ETABS results in the tables.