Example Description
This example is a seven-story, two-dimensional, fixed base frame structure subjected to lateral earthquake loads. The lateral earthquake load is modeled in four different ways: as a static lateral load, as a response spectrum, as a modal time history and as a direct integration time history. The results are compared with the results from another computer program presented in the reference by Engineering/Analysis Corporation and Computers/Structures International.
The earthquake excitation used in this example is the N-S component of the 1940 El Centro earthquake. The response spectrum function for this earthquake, shown later, is input directly into the model. The digitized base acceleration is in the file named ELCENTRO, which is read by the model when the analysis is run.
Important Note: Only the Ux, Uz and Ry degrees of freedom are active in this model. Also, only bending and axial deformations are considered in the analysis. Shear deformations are ignored. This is achieved in this example by setting the shear area to 0 for all frame objects.
All framing and loads in this example are identical to those used in the above mentioned reference. Static lateral loads are input as joint loads. The lateral (X) displacements of the columns at each story level are constrained together using a separate diaphragm constraint at each story level. Also 0.49 kip-sec2/in masses are specified only in the lateral (X) direction at each story level. These modeling techniques are commonly used to reduce the size of the equation system and were used in the independent solution by Engineering/Analysis Corporation and Computers/Structures International. The diaphragm constraints eliminate all axial deformations in the beams. This and the absence of mass specification in the vertical direction reduce the dynamic problem to seven modes of vibration. All seven modes are included in the response spectrum analysis and the modal time history analysis.
The independent solution uses the SRSS (square root sum of the squares) modal combination technique for the response spectrum analysis. Two response spectrum analyses are run in this model, one using the SRSS modal combination technique and the other using the CQC (complete quadratic combination) modal combination technique. The CQC modal combination method is the default for this model and is the recommended method.
...
| Output Parameter | OpenBrIM | SAP2000 | Independent | Pecent Difference OpenBrIM - Independent | Pecent Difference SAP2000- Independent |
|---|---|---|---|---|---|
| Mode 1 period (sec) | 1.2727 | 1.2732 | 1.2732 | 0.04% | 0% |
| Mode 2 period (sec) | 0.4311 | 0.4313 | 0.4313 | 0.05% | 0% |
| Mode 3 period (sec) | 0.242 | 0.2420 | 0.2420 | 0% | 0% |
| Mode 4 period (sec) | 0.1601 | 0.1602 | 0.1602 | 0.06% | 0% |
| Mode 5 period (sec) | 0.119 | 0.1190 | 0.1190 | 0% | 0% |
| Mode 6 period (sec) | 0.0951 | 0.0951 | 0.0951 | 0% | 0% |
| Mode 7 period (sec) | 0.0796 | 0.0795 | 0.0795 | 0.1% | 0% |
Static Lateral Analysis Results (Load case LAT)
...