Structural Analysis Questions and Answers – Arches

This set of Structural Analysis Multiple Choice Questions & Answers (MCQs) focuses on “Arches”.

1. An arch is a beam except for ____
a) It does not resist inclined load
b) It does not resist transverse forces
c) It does not allow rotation at any point
d) It does not allow horizontal movement

Explanation: An arch is a curved member in which horizontal displacements are prevented at the supports/springings/abutments.

2. An arch is more economical than a beam for a shorter span length.
a) True
b) False

Explanation: Bending Moment for an arch is given by the bending moment produced in simply supported for same loading minus bending moment produced due to horizontal thrust. Since the bending moment produced is lower for the same loading, it is more economical than the beam.

3. Two hinged arches is a determinate structure.
a) True
b) False

Explanation: Two hinged arches is an indeterminate structure. We can calculate vertical reactions by using ∑M = 0 and ∑V = 0 but the horizontal reaction cannot be computed by any of equilibrium equations. Thus, two hinged arches is an indeterminate structure.

4. Calculate the horizontal thrust for the two hinged parabolic arch loaded uniformly throughout with distributed load.

a) $$\frac{WL^2}{32H}$$
b) $$\frac{WL^2}{16H}$$
c) $$\frac{WL^2}{8H}$$
d) $$\frac{WL^2}{2H}$$

Explanation: ∑H = 0
H = $$\frac{∫M.y dy}{∫y^2 dy}$$
Where, y=$$\frac{4 H x ( L-x )}{L^2}$$
Hence, H = $$\frac{WL^2}{8H}$$

5. Calculate the horizontal thrust for the two hinged parabolic arch loaded uniformly for the left half span of the arch with distributed load.

a) $$\frac{WL^2}{32H}$$
b) $$\frac{WL^2}{16H}$$
c) $$\frac{WL^2}{8H}$$
d) $$\frac{WL^2}{2H}$$

Explanation: ∑H = 0
H = $$\frac{∫M.y dy}{∫y^2 dy}$$
Where, y=$$\frac{4 H x ( L-x )}{L^2}$$
Hence, H = $$\frac{WL^2}{16H}$$
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6. Calculate the horizontal thrust for the two hinged semicircular arch loaded uniformly throughout with distributed load.

a) $$\frac{W}{\pi}$$
b) $$\frac{W}{\pi}$$ sin2
c) $$\frac{4RW}{3\pi}$$
d) $$\frac{W}{2\pi}$$

Explanation: ∑H = 0
H = $$\frac{∫M.y dy}{∫y^2 dy}$$
Y = $$\sqrt{R^2- x^2} – \sqrt{R^2-(\frac{L^2}{2})}$$
Hence, H = $$\frac{4RW}{3\pi}.$$

7. Calculate the horizontal thrust for the two hinged semicircular arch loaded with point load at its crown.

a) $$\frac{W}{\pi}$$
b) $$\frac{W}{\pi}$$ 2
c) $$\frac{4RW}{3\pi}$$
d) $$\frac{W}{2\pi}$$

Explanation: ∑H = 0
H = $$\frac{∫M.y dy}{∫y^2 dy}$$
Y = $$\sqrt{R^2- x^2} – \sqrt{R^2-(\frac{L^2}{2})}$$
Hence, H = $$\frac{W}{\pi}$$

8. Calculate the horizontal thrust for the two hinged parabolic arch loaded with point load at its crown.

a) $$\frac{W}{\pi}$$
b) $$\frac{W}{\pi}$$sin2
c) $$\frac{4RW}{3\pi}$$
d) $$\frac{25WL}{128H}$$

Explanation: ∑H = 0
H = $$\frac{∫M.y dy}{∫y^2 dy}$$
Where, y=$$\frac{4 H x (L-x)}{L^2}$$
Hence, H = $$\frac{25WL}{128H}.$$

9. Calculate the horizontal thrust for the two hinged semicircular arch loaded with point load at inclination of α with horizontal axis on the left span.

a) $$\frac{W}{\pi}$$
b) $$\frac{W}{\pi}$$sin2
c) $$\frac{4RW}{3\pi}$$
d) $$\frac{25WL}{128H}$$

Explanation: ∑H = 0
H = $$\frac{∫M.y dy}{∫y^2 dy}$$
Y = $$\sqrt{R^2- x^2} – \sqrt{R^2-(\frac{L}{2^2})}$$
Hence, H = $$\frac{W}{\pi}$$sin2∞.

10. Identify the incorrect statement according to the hinged arches.
a) Three hinged arch is a statically determinate structure
b) To analyze three hinged arch, equlibrium equations are sufficient
c) For three hinged parabolic arch subjected to u.d.l over the entire span, the bending moment is constant throughout the span
d) For two hinged parabolic arch subjected to u.d.l over the entire span, the bending moment is zero throughout the span

Explanation: For three hinged parabolic arch subjected to u.d.l over the entire span, the bending moment and radial shear at any section is zero throughout the span.

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