How Much Steel?
Calculus
What if you varied the angle? - Explore the mathematical principles and create your own unique investigation.
Introduction
A steel arch bridge like the Forth Bridge is a lattice of trusses following a single supporting curve. Fit a curve to the arch, then work out how much steel it takes to build it, and how that changes if the arch is taller for the same span.
Guiding Questions
- Look at a steel arch bridge. Which curve is the arch — parabola, catenary, circle? Fit candidates to a photo you take or find.
- Estimate the length of steel in the main arch by breaking the curve into short straight segments and summing their lengths. How does your estimate change as you use more, shorter segments?
- How does the amount of steel change if the arch is made taller for the same span?
- Add the deck hangers: predict their lengths and total them. Check against the real bridge if data exists.