Computational Engineering / module 7
Finite-element building blocks
Freedoms, elements, restraints, releases and offsets — the five things you actually set, and what each one does to the answer.
What you will understand
- Count the degrees of freedom a model has and say what each one means
- Choose an element family from the outputs the question needs
- Predict what a joint between two families will and will not transfer
- Distinguish a restraint from a release, and say which belongs where
- Compute what an end release does to the moments and the deflection
- Explain why a rigid offset adds exactly V·e to the supporting member
Lessons
Freedoms and families
What a degree of freedom is, what each element family carries, and what happens where two families meet.
Restraints and releases
How the model is held to the world, and what happens inside it — with the moments and deflections for every case.
Offsets and eccentricity
The rigid arm between a node and the member it actually connects to, and the moment it carries.
Module summary
- A degree of freedom is a direction the model is allowed to move in; a model fails in directions the structure has no load in
- Element families differ by what they carry, and a joint transfers only what both sides have a freedom for
- A beam meeting a solid shares three freedoms and transfers no moment at all
- Restraints join the model to the world; releases describe what happens inside it
- Fixing both ends divides the deflection by exactly five and moves the peak moment to the supports
- A release is a spring of zero stiffness — there is one idea here, not two
- A rigid offset shortens the clear span and adds exactly V·e to the supporting member
- Three of the four common restraint mistakes solve cleanly and give a full set of results
Teaching basis and review status
These are educational models and exercises. Check their assumptions before using the results. The full technical content and every diagram have not yet been independently verified.
Concrete and steel calculations retain their stated first-generation Eurocode teaching basis. Use the standards and amendments specified for your project; do not mix generations without an appropriate design basis.
Read the lesson register and outstanding review notesCheck your understanding
Check yourself
Why does a beam connected to a solid mesh at one node transfer no moment?
Practice
A 10 m span carries 15 kN/m. What is the midspan moment if both ends are fully fixed?
Practice
A beam's end shear is 64.89 kN and it frames into a column at an eccentricity of 0.30 m. The beam's own end moment is 44.99 kN·m. What moment does the column top see?