Module 16
Statically indeterminate structures
When equilibrium alone is not enough: compatibility, the force method, slope-deflection, moment distribution and the matrix stiffness method.
What this module covers
- Recognise indeterminacy and count its degree
- Use compatibility to supply the equations equilibrium cannot
- Analyse a propped cantilever by the force (flexibility) method
- Use fixed-end moments and the slope-deflection equations
- Distribute moments at a joint using stiffness and carry-over
- Explain how the matrix stiffness method assembles and solves a structure
Lessons
Where the missing equations come from when statics runs out.
Start lesson →The building blocks every hand method for frames is assembled from.
Start lesson →Write every end moment in terms of the joint rotations, then solve for them.
Start lesson →Balancing joints by hand, and the matrix method that replaced it.
Start lesson →Counting the other kind of unknown, and using the force method on a truss.
Start lesson →Three indeterminate structures that each need one idea you already have.
Start lesson →
Module checkpoint
Check what you have taken in
5 questions
Question 1
A propped cantilever of span 8.00 m carries a UDL of 15.0 kN/m. What is the prop reaction, in kN?
Question 2
A fixed-ended beam of span 5.00 m carries a UDL of 30.0 kN/m. What is the magnitude of the end moment, in kNm?
Question 3
In the force method, what kind of equation supplies the information that equilibrium cannot?
Question 4
Three members meet at a rigid joint with stiffnesses 2.0, 3.0 and 5.0 (same units). What is the distribution factor for the stiffest member?
Question 5
Why does a support settlement produce bending moments in an indeterminate beam but not in a determinate one?