Question

A three-hinged arch of span \(8\,\mathrm{m}\) carries a central point load of \(32\,\mathrm{kN}\). If the central rise is \(2\,\mathrm{m}\), the horizontal thrust is

• A. \(12\,\mathrm{kN}\)
• B. \(16\,\mathrm{kN}\)
• C. \(24\,\mathrm{kN}\)
• D. \(32\,\mathrm{kN}\)

Hint:

For a three-hinged arch carrying a central point load, \[ \boxed{H=\frac{WL}{4h}.} \]

Answer 1

The Correct Option is D

Step 1: Use the horizontal thrust formula for a three-hinged arch with a central point load. \[ H=\frac{WL}{4h}, \] where \[ W=32\,\mathrm{kN},\qquad L=8\,\mathrm{m},\qquad h=2\,\mathrm{m}. \]

Step 2: Substitute the values. \[ H=\frac{32\times8}{4\times2} =\frac{256}{8} =32\,\mathrm{kN}. \] Hence, \[ \boxed{32\,\mathrm{kN}} \] is the correct answer.