IntermediateTopic 47 of 112Civil & Structural
Matrix stiffness method
Computer-based approach that assembles element stiffness into a global system.
In depth
Formulate member stiffness matrices, transform to global axes, assemble K, apply boundary conditions and solve KΔ=F, then compute member forces. Foundation of structural analysis software (SAP2000, ETABS). Handles any frame or truss configuration and loads.
Key points
- Degrees of freedom
- Banded sparse matrices
- Direct stiffness method
ExampleA frame with 100 nodes yields a few hundred equations solved in seconds.
What is Matrix stiffness method?
Computer-based approach that assembles element stiffness into a global system.
Why is it important to understand matrix stiffness method?
The matrix stiffness method is the basis of nearly all modern structural software, so every engineer benefits from knowing how it works.
What is the stiffness matrix?
A matrix that relates nodal forces to nodal displacements for the whole structure, assembled from the element stiffness matrices.
Why use a computer for matrix analysis?
Large structures have many unknowns, and the method is systematic, so it is fast and reliable with software.
How is Matrix stiffness method used in practice?
Typical applications include analysing a large steel frame in commercial software, writing a simple frame program for teaching or checking and assembling the stiffness matrix of a bridge model for a load case.
What should I learn before Matrix stiffness method?
Study "Moment distribution method" first (topic 46 of 112 in Civil & Structural). It covers the groundwork this topic builds on.
What are the key points of Matrix stiffness method?
Degrees of freedom. Banded sparse matrices. Direct stiffness method.
Can you give an example of Matrix stiffness method?
A frame with 100 nodes yields a few hundred equations solved in seconds.
What comes after Matrix stiffness method?
The next topic is "Virtual work and energy methods", which builds directly on this one.
How difficult is Matrix stiffness method?
It is classed as Intermediate in Civil & Structural (topic 47 of 112). It is an intermediate topic. Work through the beginner topics in Civil & Structural first.