The locus of reaction of a two hinged semi-circular arch, is
A. Straight line
B. Parabola
C. Circle
D. Hyperbola
Answer: Option D
Solution (By Examveda Team)
1. Locus of Reactions:The reaction locus refers to the path traced by the reaction forces at the hinge supports as the load moves along the arch.
2. Two-Hinged Semi-Circular Arch Behavior:
A two-hinged arch is statically indeterminate to one degree, meaning it requires additional equations (beyond equilibrium equations) to determine its reactions.
The horizontal thrust at the hinges plays a crucial role in defining the locus of reactions.
3. Mathematical Justification:
When deriving the equation of the reaction locus, it is found to follow the equation of a hyperbola rather than a circle.
This happens because the reactions depend on the horizontal thrust, which varies with the load position in a hyperbolic manner.
4. Why Not a Circle?
If the locus were a circle, it would imply a uniform reaction distribution independent of the load position.
However, in a two-hinged arch, the reactions change non-linearly, leading to a hyperbolic relationship rather than a circular one.
Conclusion:
The correct answer is Hyperbola (Option D), as it accurately represents the mathematical and structural behavior of the reaction locus in a two-hinged semi-circular arch.
This Question Belongs to Civil Engineering >> Theory Of Structures
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Comments (2)
A. $$\frac{2}{3}$$
B. $$\frac{3}{2}$$
C. $$\frac{5}{8}$$
D. $$\frac{8}{5}$$
Principal planes are subjected to
A. Normal stresses only
B. Tangential stresses only
C. Normal stresses as well as tangential stresses
D. None of these
A. $$\frac{{\text{M}}}{{\text{I}}} = \frac{{\text{R}}}{{\text{E}}} = \frac{{\text{F}}}{{\text{Y}}}$$
B. $$\frac{{\text{I}}}{{\text{M}}} = \frac{{\text{R}}}{{\text{E}}} = \frac{{\text{F}}}{{\text{Y}}}$$
C. $$\frac{{\text{M}}}{{\text{I}}} = \frac{{\text{E}}}{{\text{R}}} = \frac{{\text{F}}}{{\text{Y}}}$$
D. $$\frac{{\text{M}}}{{\text{I}}} = \frac{{\text{E}}}{{\text{R}}} = \frac{{\text{Y}}}{{\text{F}}}$$
A. $$\frac{{\text{M}}}{{\text{T}}}$$
B. $$\frac{{\text{T}}}{{\text{M}}}$$
C. $$\frac{{2{\text{M}}}}{{\text{T}}}$$
D. $$\frac{{2{\text{T}}}}{{\text{M}}}$$
Two hinged arch is statically indeterminate structure of one degree having two hinge support at its end.
The locus of the reaction of a two hinged semi-circular arch is a straight line whereas the locus of the reaction of a two-hinged parabolic arch is a parabolic curve.