# Example 3: 2D RC frame subjected to earthquake base excitation

Created by: Quan Gu (Xiamen University, China), Joel P. Conte (UCSD), Michele Barbato (LSU), Yong Li (UCSD)

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This application example consists of a two-dimensional two-story two-bay reinforced concrete frame subjected to earthquake base excitation. The frame structure is modeled by using displacement based Euler-Bernoulli frame elements with distributed plasticity, each with five Gauss-Legendre integration points. Section stress resultants at the integration points are computed by discretizing the frame sections by layers. The concrete is modeled by using a uniaxial smoothed Popovics-Saenz concrete material object. Different material parameters are used for confined (core) and unconfined (cover) concrete in the columns (refer to appendix for details on the material parameters). The constitutive behavior of the steel reinforcement is modeled by using a one-dimensional Menegotto-Pinto model. The total horizontal acceleration at the base of the frame is obtained through deconvolution of a ground surface free field motion, and scaled by 10 (PGA = 14.89 m/s2).

Figure 1 Geometry, loading due to gravity and cross-sectional properties for the 2-D two-story two-bay reinforced concrete frame

- To run this example, the user needs to run Example3_Frame2D.tcl in OpenSees to perform FE response and response sensitivity analysis. To verify the DDM results using forward finite difference analysis, the user needs to run Example3_Frame2D_FFD.tcl. Finally, the user needs to run in Matlab Example3_cmp.m to visualize the results.

Figure 2 Sensitivity of roof horizontal displacement response u_roof to the core concrete strength parameter, fc, computed using DDM and forward finite difference

Figure 3 Sensitivity of roof horizontal displacement response uroof to the core concrete strength parameter, fc, computed using DDM and forward finite difference (zoom view)

## Tcl Input File Download

To execute this analysis in OpenSees the user has to download this input file:

## Reference

Gu, Q. (2008). Finite element response sensitivity and reliability analysis of soil-foundation-structure-interaction (SFSI) systems (Doctoral dissertation, UC San Diego).