Frame22 – Two-Dimensional Moment Frame with Static and Dynamic Loads

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.

The independent solution uses the modal time history analysis technique with 5% damping for all modes. Two time history load cases are run in this model. The first is a modal time history analysis technique with 5% damping for all modes. The second is a direct integration time history using the Hilber-Hughes-Taylor alpha method for time integration with an alpha factor of zero.
The challenge that arises when including the direct integration time history in this example is to get a good match between the 5% damping used in the modal time history analysis and the mass and stiffness proportional damping specified for the direct integration time history. In this example a mass proportional damping coefficient of 0.3686 and a stiffness proportional coefficient of 0.005127 were used. These coefficients are calculated by assuming that the damping for the first two modes is 5%; that is, that the damping at periods of 1.2732 and 0.4313 seconds is 5%. The table below shows a comparison of the modal and proportional damping for all seven modes. Note that the proportional damping has considerably more damping in the higher modes but the modal participating mass ratio for the higher modes is low. Thus the higher damping should have only a small influence on the results.

In this model, time history analyses the output sampling time interval used is 0.02 seconds and response is calculated for the first 8 seconds of the record. The independent analysis has an output sampling time interval of 0.1 seconds.
Important Note: The AISC section properties in the database file SECTIONS8.PRO are not used in this example and the required section properties are explicitly entered. This is intentional because most of the sections used in the example are older sections not in the current AISC database.

Library 

Object Link : https://bim.aecbolt.com/objidyhniv5dyhdc55kn6lk8x5.libobj

Results Comparison

Static Lateral Analysis Results (Load case LAT)

Response Spectrum Analysis Results (Load case SPECSRSS)

Response Spectrum Analysis Results (Load case SPECCQC)

Tested Features

•  Diaphragm constraint
•  Joint force assignments
•  Joint mass assignments
•  Modal analysis for eigenvalues
•  Response spectrum analysis
•  Modal time history analysis for base excitation
•  Direct integration time history analysis for base excitation