Structural Analysis Fundamentals / module 2
Forces, moments and equilibrium
Forces as vectors, turning effects, the three equations of equilibrium, and finding support reactions.
What you will understand
- Resolve a force into horizontal and vertical parts
- Work out the moment of a force about a point, using the perpendicular distance
- Recognise a couple and know why its moment is the same about every point
- Apply the three equations of plane equilibrium and say what each one means physically
- Say what each support restrains and what reaction it therefore provides
- Draw a free-body diagram with every force on it
- Replace a distributed load with its resultant in the right place
- Find reactions using the three equations, and check them
- Interpret a negative reaction as uplift
Lessons
Forces and resolving them
Vectors, components and resultants — the arithmetic behind everything else.
Moments, couples and equilibrium
Turning effects and the three equations that keep a body still.
Supports and free-body diagrams
What each support allows, and how to draw the picture you actually calculate from.
Finding the reactions
Using the three equations in the right order, and checking the answer.
Module summary
- A force has size, direction and a line of action
- Resolving splits a force into parts that are easier to add up
- A moment is force times perpendicular distance
- In two dimensions, equilibrium means ΣH = 0, ΣV = 0 and ΣM = 0 about any point
- Roller = 1 reaction, pin = 2, fixed = 3
- A free-body diagram shows everything acting on the piece you cut out — including reactions
- A UDL of w over length L becomes a single force wL at the middle of that length
- A negative reaction means the support is pulling down, not pushing up
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
Practice
Resolve a 40 kN force acting at 30° above the horizontal. What is its vertical component?
Check yourself
Why is a couple's moment the same about every point?
Check yourself
A single rigid body in a plane is stably restrained by four unknown reaction components. What follows?
Practice
A 10 m simply supported beam carries a UDL of 4 kN/m over its whole length. What is the reaction at each support?
Check yourself
A reaction is calculated as −7 kN (taking upwards as positive). What does that mean?
Check yourself
Which is the best point to take moments about when finding reactions?