L02: Beam with Elastic Supports✔
- Umut Nuhat Sevinc
- Gokhan Alkan (Unlicensed)
A two-span beam is supported at an interior point by a column and with yielding elastic supports at the two exterior points. The beam is continuous and the column is pin-connected to the beam.
The beam is subjected to a vertical point load and the column is subjected to a horizontal point load. Determine the deflections and reactions.
The 2D model consists of 6 joints, 3 beam elements and 2 spring elements. This is a plane frame analysis. The translational displacement in Global Y-direction and rotations about Global X and Z-directions can be deleted from the analysis. The joints 1, 4 and 6 are fixed supports.
The material property data is given:
and sectional property data:
The spring constant for the springs is given as:
The member loads applied on beams are:
Linear static analysis with one load case is performed.
Tested Features
App
Object Link: https://openbrim.org/objid65tv28lznd34ie4efzje1.project
Library
Object Link: https://openbrim.org/objidi4segrgj8hdgrq97j7q0w.libobj
Sources
- Beaufait, F.W., et al., "Computer Methods of Structural Analysis," Prentice-Hall, 197-210.
- LARSA 4D
Result Comparison
| Output Parameters | Independent (Beaufait) | Larsa | OpenBrIM | Percent Difference (Larsa vs Independent) | Percent Difference (OpenBrIM vs Independent) |
|---|---|---|---|---|---|
| U2 (x10^-3 ft) | 0.013 | 0.013 | 0.013 | 0% | 0% |
| U3 (x10^-3 ft) | 0.013 | 0.013 | 0.013 | 0% | 0% |
| U5 (x10^-3 ft) | 0.013 | 0.013 | 0.013 | 0% | 0% |
| V2 (x10^-3 ft) | 0.021 | 0.021 | 0.021 | -0.017% | 0% |
| V3 (x10^-3 ft) | -0.002 | -0.002 | -0.002 | 0% | 0% |
| V5 (x10^-3 ft) | -0.058 | -0.058 | -0.058 | 0.004% | 0% |
| R2 (x10^-3 rad) | 0.000 | 0.000 | 0.000 | 0% | 0% |
| R3 (x10^-3 rad) | -0.000 | -0.000 | 0.000 | 0% | 0% |
| R5 (x10^-3 rad) | 0.000 | 0.000 | 0.000 | 0% | 0% |
| Reaction V @ Joint 1 (kip) | -2.1 | -2.144 | -2.144 | 2.095% | 2.052% |
| Reaction H @ Joint 4 (kip) | -5.0 | -5.0 | -5.0 | 0% | 0% |
| Reaction V @ Joint 4 (kip) | 11.3 | 11.360 | 11.360 | 0.531% | 0.531% |
| Reaction M @ Joint 4 (kip) | -360 | -360 | -360 | 0% | 0% |
| Reaction V @ Joint 6 (kip) | 5.8 | 5.7845 | 5.8 | -0.267% | 0% |
U denotes the displacement in horizontal direction and V denotes the displacement in vertical direction. R is the rotation. Reaction V is the vertical force at the support joint and Reaction H is the horizontal force. Reaction M is the support moment.