Description
A three-story plane frame is analyzed for the additional bending moments and forces generated by the vertical loads acting through the deflected shape of the frame.
Geometry
Dimensions: as shown above.
Sections: UB 533x210x122 (British steel I-beam)
Material: Steel – Elastic modulus = 204,100 [kN/mm2]
Supports: pinned.
Loads
as shown above
Reference
G.L. Kulak, P.F. Adams, M.I Gilmor, Limit States Design in Structural Steel, 4th Edition 1990 (Chapter 9.4), Canadian Institute of Steel Construction.
Calculations
Mf = Mfg +U2 Mft
where:
| Mf | = | total factored moment at the beam end including 2nd order effects |
| Mfg | = | first-order moment due to factored gravity load |
| Mft | = | first-order moment due to factored lateral load |
| U2 | = | 1/(SCfDf/SVfh) |
| Vf | = | Total first-order lateral shear |
| Cf | = | Total vertical axial load |
| h | = | story height |
| Df | = | relative lateral deflection within the story height, produced by the first-order lateral shear only. |
Comparison of Results
| Beam | Result type | Result | Deviation | |
| Theoretical | STRAP | |||
| 15 | Mf | 388 kN | 389 | 0.26% |