Example 4: Multibay Two Story Frame

A multi-bay reinforced concrete frame is investigated.

Example 4.1  

This example is of a reinforced concrete multibay two story frame, as shown in Figure 1, subject to gravity loads.

A model of the frame shown in Figure 1 is created. The number of objects in the model is dependent on the parameter numBay. The (numBay + 1)*3 nodes are created, one column line at a time, with the node at the base of the columns fixed in all directions. As always, our first step is to create an instance of the Model  Class:

import opensees.openseespy as ops

model = ops.Model(ndm=3, ndf=6)

model -ndm 3 -ndf 6

Three materials are constructed, one for the concrete core, one for the concrete cover and one for the reinforcement steel. Three fiber discretized sections are then built, one for the exterior columns, one for the interior columns and one for the girders.

Each of the members in the frame is modeled using inelastic beam-column elements with nip = 4 integration points and a Linear geometric transformation.

For gravity loads, a single load pattern with a linear time series and two vertical nodal loads acting at the first and second floor nodes of each column line is used. The load at the lower level is twice that of the upper level and the load on the interior columns is twice that of the exterior columns.

For the lateral load analysis, a second load pattern with a linear time series is introduced after the gravity load analysis. Associated with this load pattern are two nodal loads acting on nodes 2 and 3, with the load level at node 3 twice that acting at node 2.

As in the linear truss example, the integrator for the analysis will be LoadControl. However, in order to handle the inelastic response, a load step increment of 0.1 is used and the analysis will be performed with 10 steps.

model.integrator("LoadControl", 0.1)

integrator LoadControl 0.1;

Once the components of the analysis have been defined, the analysis object is created. For this problem a Static analysis is used and 10 steps are performed to load the model with the desired gravity load.

model.analyze(10)

analyze 10

After the gravity load analysis has been performed, the gravity loads are set to constant and the time in the domain is reset to 0.0. A new LoadControl integrator is now added. The new integrator has an initial load step of 1.0, and is allowed to vary between 0.02 and 2.0 depending on the number of iterations required to achieve convergence at each load step. 100 steps are then performed.

The output consists of the file Node41.out containing a line for each step of the lateral load analysis. Each line contains the load factor, the lateral displacements at nodes 2 and 3. A plot of the load-displacement curve for the frame is given in Figure 2.