E07: 2D Frame (Wilson & Bathe) Eigenvalues
- Gokhan Alkan (Unlicensed)
This 2D frame structure has 10 equal bays and 9 stories. The bottom ends of the base columns are fixed. All members have the same section properties. Determine the frame's three lowest natural frequencies.
The material properties of the beams and columns are:
The sectional properties of the beams and columns are:
The geometry of the structure is based on:
The frame is modeled in the global XZ plane with Z as the vertical direction. The joints are numbered such that the footing level is 1 to 11. First level joints are from 101-111, second level joints are from 201-211, etc. The joints along the base are completely fixed. Columns are numbered 1 to 99 from bottom to top and left to right. The beams are numbered 100-189. The local z-axis of all beams and columns is normal to the plane of the frame.
This is a plane (2D) model, the degrees of freedom for the out-ofplane translational displacement (in Y) and in-plane rotations (about X and Z) are removed from the analysis. The joints can move in Global X and Z directions and rotate about the Global Yaxis.
Tested Features
Reference
- Ref [3] - Peterson, F.E., "EASE2, Elastic Analysis of Structural Engineering, Example Problem Manual," Engineering Analysis Corporation, Berkeley, California, 1981.
Sources
- LARSA 4D
- Bathe,K.J., Wilson,E.L., "Large Eigenvalue Problems in Dynamic Analysis", Journal of the Eng.Mech.Div., ASCE, Vol.98, No. EM6, Proc.Paper 9433, Dec 1972.
- Computers & Structures Inc., "SAP90 Structural Analysis Verification Manual", October 1990, 2-1.