Structural Analysis Fundamentals / module 6
Arches
The cable turned upside down: carrying load in compression, and why the shape decides whether bending appears.
What you will understand
- Explain the cable–arch analogy and why inversion turns tension into compression
- Define a funicular (linear) arch and say why it carries no bending
- Find the reactions of a three-pinned arch using the crown hinge
- Calculate normal force, shear and bending moment at an arch section
- Explain why a real arch develops bending when the loading changes
Lessons
The cable–arch analogy
Why an arch is an upside-down cable, and what a funicular shape means.
The three-pinned arch
Using the crown hinge to make an arch determinate, and finding the internal actions.
Module summary
- An arch is a cable inverted: the same shape, the same thrust, but in compression
- A three-pinned arch is statically determinate — the crown hinge supplies the fourth equation
- For a uniform load, the parabola is funicular: zero bending and zero shear everywhere
- The beam analogy: March = Mbeam − H·y
- Change the loading and the arch is no longer funicular, so bending appears
- An arch pushes outwards at its springings; the abutments must resist that thrust
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 three-pinned parabolic arch spans 24.0 m with a rise of 6.0 m under a uniform load of 10 kN/m. What is the horizontal thrust in kN?
Check yourself
What does 'funicular' mean?
Check yourself
In the beam analogy March = Mbeam − Hy, what does the term Hy represent?