Structural Analysis Fundamentals / module 3
Internal forces and structural diagrams
What happens inside a member, and how shear force and bending moment vary along it.
What you will understand
- Explain the difference between an external load and an internal action
- Use the cut-section method to find internal forces at any point
- Identify normal force, shear force and bending moment on a free body
- Apply a consistent sign convention and read sagging and hogging correctly
- Sketch the shape of a shear force and bending moment diagram before calculating
- Draw both diagrams for point loads, UDLs and overhangs
- Use the relationships between load, shear and moment
- Find the maximum moment by locating zero shear
- Identify points of contraflexure and say why they matter
Lessons
Cutting the member open
How internal forces arise, and how to find them at any section.
Sign conventions, sagging and hogging
Getting signs right, and knowing which face of the beam is in tension.
Building the diagrams
Predict the shape, then calculate the values.
Relationships, overhangs and contraflexure
The calculus behind the shapes, and what happens when a beam hangs over its support.
Module summary
- Cut the member, keep one side, and put back whatever forces are needed to hold it still
- One external load usually creates several internal actions at once
- Internal forces vary along the member — that is why we draw diagrams of them
- Sagging is positive bending; hogging is negative
- Shear steps at a point load and slopes under a UDL
- Moment is the area under the shear diagram
- Maximum moment occurs where shear passes through zero
- Contraflexure is where the moment changes sign and the tension face swaps over
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
A simply supported beam of 6.0 m carries a central point load of 20 kN. What is the bending moment at midspan?
Check yourself
Why does calculating from the right-hand side give the same bending moment?
Check yourself
Where does reinforcement go in a sagging reinforced-concrete beam?
Practice
A cantilever 4.0 m long carries a UDL of 6 kN/m over its whole length. What is the magnitude of the bending moment at the fixed end?
Check yourself
Under a uniformly distributed load, what shape is the shear force diagram?
Check yourself
What is a point of contraflexure?