Frame14 - Eigenvalue Problem✔
- Gokhan Alkan (Unlicensed)
- Umut Nuhat Sevinc
Example Description
This model eigenvalue computations are verified using vibrations of a cantilever beam.
This example uses several models of an eight foot long cantilever concrete beam with I22 != I33. Each of the models has a different discretization. The first five bending Eigen modes for each model are compared with the independent solution provided in Clough and Penzien 1975.
Important Note: Only bending modes are calculated and compared. Shear deformations are ignored by setting the frame property modification factor for shear area to zero. Axial and torsional modes are excluded by excluding the Ux and Rx degrees of freedom from the analysis.
Tested Features
- Eigenvalue analysis of a frame with unequal moment of inertia values (I22 != I33) for bending modes
- Automatic frame subdivision
App
Object Link: https://openbrim.org/objidtknzvco15mzx0yalkyr1.project
Library
Object Link: https://openbrim.org/objid47wnwbqova7mrmnpr94w5a.libobj
Mode | Output Parameter | Model | SAP 2000 | OpenBrIM | Independent | Percent Difference (SAP 2000 vs Independent) | Percent Difference (OpenBrIM vs Independent) |
|---|---|---|---|---|---|---|---|
1 First mode for bending about the Z-axis | Period, sec | A(1 elem) | 0.054547 | 0.0548 | 0.038005 | +43.53% | +44.19% |
B(2 elems) | 0.042333 | 0.0425 | +11.39% | +11.83% | |||
C(4 elems) | 0.039090 | 0.0393 | +2.85% | +3.41% | |||
D(6 elems) | 0.038485 | 0.0387 | +1.26% | +1.83% | |||
E(8 elems) | 0.038273 | 0.0385 | +0.71% | +1.30% | |||
F(10 elems) | 0.038175 | 0.0384 | +0.45% | +1.04% | |||
G(96 elems) | 0.038003 | 0.0382 | -0.01% | +0.51% | |||
2 First mode for bending about the Y-axis |
| A(1 elem) | 0.036364 | 0.0367 | 0.025337 | +43.52% | +44.85% |
| B(2 elems) | 0.028222 | 0.0285 | +11.39% | +12.48% | |||
| C(4 elems) | 0.026060 | 0.0264 | +2.85% | +4.20% | |||
| D(6 elems) | 0.025657 | 0.0260 | +1.26% | +2.62% | |||
| E(8 elems) | 0.025516 | 0.0259 | +0.71% | +2.22% | |||
| F(10 elems) | 0.025450 | 0.0258 | +0.45% | +1.83% | |||
| G(96 elems) | 0.025335 | 0.0257 | -0.01% | +1.43% | |||
3 Second mode for bending about the Z-axis |
| A(1 elem) | N.A. | N.A. | 0.006064 | N.A. | N.A. |
| B(2 elems) | 0.008218 | 0.0085 | +35.52% | +40.17% | |||
| C(4 elems) | 0.006651 | 0.0069 | +9.68% | +13.79% | |||
| D(6 elems) | 0.006330 | 0.0066 | +4.39% | +8.84% | |||
| E(8 elems) | 0.006214 | 0.0065 | +2.47% | +7.19% | |||
| F(10 elems) | 0.006160 | 0.0064 | +1.58% | +5.54% | |||
| G(96 elems) | 0.006065 | 0.0063 | +0.02% | +3.89% | |||
4 Second mode for bending about the Y-axis | Period, sec | A(1 elem) | N.A. | N.A. | 0.004043 | N.A. | N.A. |
| B(2 elems) | 0.005479 | 0.0059 | +35.52% | +45.93% | |||
| C(4 elems) | 0.004434 | 0.0048 | +9.67% | +18.72% | |||
| D(6 elems) | 0.004220 | 0.0046 | +4.38% | +13.78% | |||
| E(8 elems) | 0.004143 | 0.0045 | +2.47% | +11.30% | |||
| F(10 elems) | 0.004107 | 0.0045 | +1.58% | +11.30% | |||
| G(96 elems) | 0.004043 | 0.0044 | 0% | +8.83% | |||
5 Third mode for bending about the Z-axis | Period, sec | A(1 elem) | N.A. | N.A. | 0.002165 | N.A. | N.A. |
| B(2 elems) | N.A. | N.A. | N.A. | N.A. | |||
| C(4 elems) | 0.002511 | 0.0028 | +15.98% | +29.33% | |||
| D(6 elems) | 0.002321 | 0.0025 | +7.21% | +15.47% | |||
| E(8 elems) | 0.002254 | 0.0025 | +4.11% | +15.47% | |||
| F(10 elems) | 0.002222 | 0.0024 | +2.63% | +10.85% | |||
| G(96 elems) | 0.002166 | 0.0024 | +0.05% | +10.85% |