A symmetric parabolic arch of span 20 m and rise 5 m is hinged at the springings. It supports a uniformly distributed load of 2 tonnes per meter run of the span. The horizontal thrust in tonnes at each of the springing is
- A8
- B16
- C20Correct
- DZero
Solution
Concept
Horizontal thrust in a two-hinged parabolic arch under UDL
Formula
H = w L² / (8 h)
Step-by-step solution
1. w = 2 t/m, L = 20 m, h = 5 m. 2. H = w L² / (8h) = 2 × 400 / (8 × 5) = 20 t.
Explanation
For a symmetrical parabolic two-hinged arch under a UDL over the whole span, the horizontal thrust is wL²/8h. The result is the same as for the three-hinged arch.
Shortcut
H = wL²/8h (UDL, full span, parabolic arch).
Common mistake
Using L instead of L² in the formula.
Correct answer: C) 20