A parabolic arch of span L has central rise h. Taking the springing point as the origin, its equation is given by
- Ahx(L−x)/L
- Bhx(L−x)/L²
- C4hx(L−x)/L²Correct
- D8hx(L−x)/L²
Solution
Concept
Parabola through the springings with rise h
Formula
y = 4h x (L − x) / L²
Step-by-step solution
1. y = 0 at x = 0 and L, so y = k x (L − x). 2. At x = L/2, y = h ⇒ k L²/4 = h ⇒ k = 4h/L².
Explanation
The constant is fixed by the central rise.
Why the other options are wrong
Other options do not give y = h at mid-span.
Shortcut
y = 4hx(L−x)/L².
Common mistake
Using 8h.
Correct answer: C) 4hx(L−x)/L²