Stair vibration, comparison with SAP2000

Results.

Problem. The modes of a steel U stair, a concrete U stair, a concrete spiral stair and a steel U stair whose landing column is braced, all drawn on the floor plan, are solved with MindFEM and with SAP2000. Both programs' modes go through the same footfall calculation, and the SCI P354 response factor and the AISC DG11 peak acceleration are compared as well. The frequencies and the response factor use SCI P354's concrete modulus, the AISC DG11 accelerations 1.35 times the static modulus.

Reference document. The reference is the same stairs modelled in SAP2000 27.1.0 with its own objects, on a mesh refined to 2×2 shells and 0.1 m frame elements.

Numerical model. The MindFEM model is the stair taken from the storey's analytical model as the app takes it, on the app's own mesh with shell elements at most 0.25 m and frame elements at most 0.5 m. On the steel U stairs the treads are plates connected to two channel stringers, the landings of the U stairs bear on a wall and a column, the spiral stair's plate is flat triangles running from its first riser at the base to its last riser at the floor above, and on the braced stair the brace enters at its full length, its far end pinned under SCI P354 and fixed under AISC DG11.

Steel U stair#

Independent calculation. SAP2000 27.1.0, the same stair modelled with SAP2000's own objects on a refined mesh

Concrete U stair#

Independent calculation. SAP2000 27.1.0, the same stair modelled with SAP2000's own objects on a refined mesh

Note. The frequency deviation comes from the app's shell mesh. On the same refined mesh the two programs' fundamental frequencies agree within 0.15 %.

Spiral stair#

Independent calculation. SAP2000 27.1.0, the same stair modelled with SAP2000's own objects on a refined mesh

Braced steel U stair#

Independent calculation. SAP2000 27.1.0, the same stair modelled with SAP2000's own objects on a refined mesh

Model files#

The SAP2000 models that produced the results in the tables can be downloaded. They open in SAP2000 27 and later with File > Import > SAP2000 .s2k Text File.

• Steel U stair, SCI P354 (.s2k)
• Steel U stair, AISC DG11 (.s2k)
• Concrete U stair, SCI P354 (.s2k)
• Spiral stair, SCI P354 (.s2k)
• Spiral stair, AISC DG11 (.s2k)
• Braced steel U stair, SCI P354 (.s2k)
• Braced steel U stair, AISC DG11 (.s2k)