SkyCiv Stiffness Method Calculator

The SkyCiv Stiffness Method Calculator implements the stiffness method for solving single-member in-plane structures (beam and truss members). The Stiffness Matrix Calculator provides a breakdown of the stiffness matrix for local and global axes. For beam elements, the stiffness method calculator will calculate the known force, displacement, and stiffness entries corresponding to each degree of freedom based on the section properties, the loads, and the boundary conditions, from this, the tool will assemble the matrix and the vector and finally solve the system to obtain the unknown displacements and reactions. The calculator is useful as a source of comparison for the stiffness matrices obtained when learning the stiffness method for solving structures.

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What is the Stiffness Method?

For structural engineers the stiffness method is a vital tool for structural analysis. The stiffness method is used to determine the displacements, internal focus and reaction of beam, truss, and frame members in a structure. The stiffness method includes multiple steps. These steps include:

  • Discretization where the structure is divided into “discrete” or smaller elements like beams or trusses.
  • Local Stiffness Matrix Creation where a stiffness matrix is created for each element.
  • Global Stiffness Matrix Creation where the global stiffness matrix represents the whole structure.
  • Load Vector Creation where the external forces are represented as a vector to be applied to the structure.
  • Displacement Vector Creation where initially all displacements are assumed to be zero and represented in a vector.
  • Equilibrium Solving where the equilibrium equations are derived with the global stiffness matrix, the displacement vector, and the load vector.
  • Solving and Reactions where the systems of equations are solved to obtain displacements are each node and then used to determine the reaction at the supports.

What is a Stiffness Matrix?

The stiffness matrix is a matrix that mathematically represents the relationship between applied forces and displacements found in each structural element. Stiffness Matrices are fundamental to the Finite Element Method (FEM) and the Stiffness Method.

What is the Difference between the Local and Global Stiffness Matrix?

The local stiffness matrix is specific to the individual elements within a structure. Conversely the global stiffness matrix deals with the entire structure.

Where to use a Stiffness Method Calculator?

Stiffness matrices are useful in a variety of engineering contexts. These contexts include:

  • In structural engineering, stiffness matrices are used in finite element analysis (FEA) to analyze complex structures and divide the structure into smaller member elements. These can then be solved to determine the overall stiffness and behavior of a structure.
  • In aerospace engineering, stiffness matrices are useful to evaluate the structural integrity of different aircraft components that is key to ensuring the integrity and safety of aircraft components during flight.
  • In automotive and mechanical engineering, a stiffness matrix can be used to model and analyze components including gears, springs, or frames.
  • In civil engineering, FEA and stiffness matrices are used to evaluate the stability and deformation of soil-structure interaction during geotechnical engineering for foundation and retaining wall structures.

How is a Stiffness Matrix Calculator Useful?

The Stiffness Matrix Calculator is useful for students learning the stiffness method for solving structures, as a source of comparison. Alongside FEA software such as SkyCiv Structural 3D and using the Stiffness Matrix Calculator students or engineers can calculate the local and global stiffness matrix as well as the transformation matrix of each element so they can compare them to what they calculated. The Stiffness Matrix Calculator also has a copy button next to each matrix in the report so that results can be pasted directly to an external spreadsheet.

Calculator FAQs

What forces are supported by the stiffness matrix calculator?

The calculator supports vertical point loads only, but it can be easily extendable to other loads by implementing the fixed forces for each degree of freedom, the assembling and solution remains the same.

Does the calculator support multi-member structures?

No, the SkyCiv Stiffness Method Calculator only supports single-member structures as of now.

Can I copy the matrices to a spreadsheet for comparison?

Yes, next to each matrix in the report, there is a copy matrix button that will copy the matrix to the clipboard.

Can I solve a complete structure using this?

Yes, for single frame elements.

Can I solve trusses with this?

No, the SkyCiv Stiffness Method Calculator will only provide the local and global stiffness matrices of the member.

Which cross sections are supported?

The SkyCiv Stiffness Matrix Calculator supports Rectangular, Circular, I-Shape and Custom (requires to enter the area and inertia directly) cross sections.

Can I get the stiffness matrix for inclined members?

Yes, you only need to define the member inclination counter-clockwise with respect to the horizon.

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