Find the instantaneous center of a bolt group under loading

Mijia Yang, North Dakota State University-Main Campus, Civil and Environmental Engineering

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In order to calculate the force of each bolt in a bolt group under loading, an instantaneous center needs to be found. Once the instantaneous center is found, the whole bolt group intends to have a pure rotation at the moment and the deformation of each bolt is proportional to the distance between the bolt and the instantaneous center. With the deformation is calculated, the force in each bolt could be calculated.

Learning Goals

The students will learn how to use advanced programming tools to perform complicated mechanics analysis. The instantaneous center is not known prior to the design. An iteration has to be performed. In the past, the process is completed by long and tedious manual calculations. It can now be done in MATLAB through a simple iteration loop. This activity involves some thinking on computational skills and needs some understanding of connection design in structural engineering.

Context for Use

The class is for senior undergraduate students and graduate students. The class size is at 15. And North Dakota State University is a public state institute. The demonstrated activity is a classroom activity, which took two class sessions. Students need to have basic MATLAB programming skills in order to complete the task. This task is an important part of connection design in advanced steel structural system. The activity introduced here can be easily adopted in typical classroom settings.

Description and Teaching Materials

Two documents are provided for this activity. One is the source code, while the other one is a homework for this activity.

Teaching Notes and Tips

Some review of basic MATLAB knowledge is helpful, such as definition of variables, programming syntax, etc.


The students performed well for the programming homework. Most of the students could perform the coding and calculate the force in each bolt accurately.

References and Resources

The resources have been uploaded in the supporting materials port.