# Dynamic Analyses of 1-Story Moment Frame with Viscous Dampers

Example posted by: Sarven Akcelyan & Prof. Dimitrios G. Lignos (McGill University)

This example demonstrates how to use the viscous damper material within a simple single story shear frame.

The files needed to analyze this structure in OpenSees are included here:

Supporting files

• TakY.th – uses the JR Takatori record from the Kobe 1995 earthquake (available in the zip file below)

All files are available in a compressed format here: Viscous_Damper_Example.zip

The rest of this example describes the model and shows the analysis results.

## Model Description

Figure 1. Schematic representation of a viscous damper installed in the single story moment resisting frame.

The viscous damper is modeled with a Two Node Link Element. This element follows a Viscous damper hysteretic response. An idealized schematic of the model is presented in Figure 1.

The units of the model are mm, kN, and seconds.

### Basic Geometry

The single bay single story frame shown in Figure 1 has 5000mm bay width and 3000mm story height (centerline). The period of the system is 0.7sec. Columns and beams of the frame are modeled with elastic beam-column elements.

A Two Node Link Element is used to link the two nodes that define the geometry of the viscous damper.

### Constraints

the Nodes at the base of the frame are fixed. The beam (element 3 in Figure 1) is considered to be rigid.

### Viscous Damper Material

To model the viscous damper the ViscousDamper is used. The input parameters that are selected for the damper example are as follows: Axial Stiffness K = 25 kN/mm, Damping Coefficient Cd=20.74 kN(s/mm)0.35 and exponent a=0.35.

The single story frame with viscous damper is subjected to the 50% JR Takatori record from the Kobe 1995 earthquake in Japan.

### Recorders

The recorders used in this example include:

• The Element recorder to track the damper axial force and axial displacement.
• The Node recorder to track the Frame displacement history at its roof.

### Analysis

A uniform excitation option is selected with application of ground acceleration history as the imposed motion. The Newmark integration scheme is selected for integration of the equations of motion with a time step dt = 0.001sec. Two percent mass proportional damping is used.

## Results

### Simulation Results for the 50% JR Takatori Record

Figure 2. Displacement history at the roof of the single story MRF
• The force - displacement relationship from the viscous damper are shown in Figure 3. A comparison with results from a SAP2000 model is also shown in Figure 3. Results are nearly identical between the two models.
Figure 3. Force - displacement relationship of the viscous damper and comparison with identical model in SAP2000