Structural Analysis
Analysis is the question of where a load goes once it lands on a structure. These topics animate the load path and the reactions, and make the determinate/indeterminate split visible rather than definitional.
Start from the beginning →8 topics you can watch now, 18 still to come.
Supports and determinacy
What a support actually does, and whether statics alone can solve it.
- Types of supports and reactions
- Equations of static equilibrium
- Static and kinematic indeterminacy
- Stability of structures
Trusses
A structure made entirely of members carrying only axial force.
- What a Truss Actually DoesA beam wastes the material at its middle. Move it to the edges, add one diagonal, and watch a mechanism turn rigid.
- Method of JointsSolved members fill in one at a time, spreading outward from the only joint you were allowed to start at.
- Method of SectionsOne cut, and one moment centre chosen so the two members you did not want vanish from the equation.
- Graphical and tension coefficient methods
- Space trusses
Deflections
How far the structure moves, which is often the real limit.
- Strain Energy and CastiglianoThe area under a load-extension line is a triangle, which is where the one-half comes from — and why an impact deflects twice as far.
- The Unit Load MethodTwo separate analyses of the same structure, multiplied member by member. Handles temperature and fabrication error just as easily.
- Moment area and conjugate beam methods
- Deflection of trusses by graphical methods
Indeterminate structures
When equilibrium is not enough and compatibility has to be added.
- Three-moment equation
- Slope deflection method
- Moment distribution method
- Kani method
Moving loads and arches
Structures whose worst case depends on where the load is.
- Moving load and absolute maximum bending moment
- Three-hinged and two-hinged arches
- Cables and suspension bridges
Matrix methods
The formulation every structural analysis program actually uses.
- Flexibility matrix method
- Stiffness matrix method
- Introduction to finite element analysis
About Structural Analysis
Structural analysis finds the forces inside a structure, and its first task is to ask whether equilibrium alone is enough. If it is, the structure is determinate and the work is systematic. If it is not, equilibrium has fewer equations than unknowns and the material's stiffness has to enter the calculation.
That determinacy check is the hinge of the whole subject, and doing it first saves a great deal of wasted effort. Method of joints and method of sections then handle determinate trusses — the same structure, two approaches, one better for every member and one better for a single member deep inside.
Indeterminate structures need compatibility as well as equilibrium, which is what the force method supplies. Influence lines answer a different and very practical question: not what happens under a fixed load, but where a moving load must sit to be worst.
What to know first
- Statics, and Strength of Materials
- Simultaneous equations for the indeterminate methods
Where it gets used
- Analysing trusses in bridges, roofs and towers
- Positioning moving loads to find the governing design case
- Understanding why a redundant member changes the whole force distribution