Automated Direct stiffness method for frames using Excel

This video is related to the Direct stiffness method for frames using Excel. Download the Excel spreadsheet here: https://coolcivilengineering.com/stiffness-method-for-beams/

https://docs.google.com/spreadsheets/d/1SBPwSJI-EqgGnXd7P2c1B9NRIJ4OJAj8/edit?usp=drive_web&ouid=103689545527643865042&rtpof=true

Direct stiffness method for frames

Direct stiffness method is a type of stiffness method. The stiffness method, also known as the displacement method of analysis, is the most frequent technique for analyzing structures using matrix analysis. In the stiffness approach, the number of unknowns to be solved is equal to the structural degree of kinematic indeterminacy.

The direct stiffness method is developed to achieve a basic approach to grasp the fundamental ideas of Finite element analysis (FEM) in general, and particularly displacement-based Finite Element analysis, which are frequently employed in structural analysis and computational mechanics problems.

After carefully watching the video you will be able to:

  1. Derive the stiffness matrix of the plane frame member from a global co-ordinate system to a local co-ordinate system.
  2. Easily & fastly transform the frame member stiffness matrix from a local to a global coordinate system.
  3. Fast Assemble of member stiffness matrices to generate the global stiffness matrix of the plane frame.
  4. Write the plane frame’s global load-displacement relation.
  5. Characterize and impose the given boundary conditions on the load-displacement relations.
  6. Analyze any type of plane frames using the automated direct stiffness matrix technique. I call this technique direct stiffness method for frames using excel.

Direct stiffness method frame Example

Analyse the given rigid frame shown in Fig by direct stiffness matrix method. Assume axial rigidity EA are the same for all beams. Where EI = 200 GPa, Izz = 1.33 * 10^-5, A = 0.01 m2

Direct stiffness method frame Example
Direct stiffness method frame Example Fig.

As indicated in Fig, the plane is composed of three-beam components. The numbering and nomenclature of joints and members are also shown in Fig. The number of options that nodes have is listed in Fig. The figure also displays how the global coordinate system begins at A (node 1).

Defining Nodes and members number

Form the element stiffness matrix in a local coordinate system, then transform it into a global coordinate system. At each node, three degrees of freedom are taken into account in the current example.

For Member 1:

For Member 2:

For Member 2:

Global Stiffness Matrix

Solve using the excel sheet provided

Conclusion

The direct stiffness method explains the analysis of a plane frame’s direct stiffness matrix using the direct stiffness matrix method. The local co-ordinate axes of the plane frame member are first computed, and then its global co-ordinate system is generated.

In the case of plane frames, members are oriented in different directions and, as a result, it is necessary to convert all member stiffness matrices to the same set of axes before generating the global stiffness matrix. To move from national coordinates to a world coordinate system, forces and displacements must be transformed. At the conclusion of the tutorial, several difficulties are resolved to demonstrate the technique.

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This video is related to the Direct stiffness method for frames using Excel. 

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