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A circular arch of span 25 m with a central rise 5 m is hinged at the crown and springings. It carries a point load of 100 kN at 5 m from the left support. In this case, the horizontal thrust is
  • a)
    45 kN
  • b)
    50 kN
  • c)
    75 kN
  • d)
    90 kN
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A circular arch of span 25 m with a central rise 5 m is hinged at the ...
Given:
Span of circular arch (L) = 25 m
Central rise (h) = 5 m
Point Load (W) = 100 kN at 5 m from the left support

To find: Horizontal thrust (H)

Solution:
1. Calculation of the radius of the arch:
Using the formula, h = R - Rcosθ
Where, θ = half of the angle subtended by the arch at the center
We get,
5 = R - Rcos(180/L)
R = 25/2.618 = 9.551 m

2. Calculation of the vertical reaction at the supports:
Taking moments about the left support,
100x5 = VL(25/2) + (25/2)x(25/4)x(2/3)x(1.67)
VL = 95.83 kN (upwards)

VR = W - VL = 100 - 95.83 = 4.17 kN (downwards)

3. Calculation of the horizontal thrust:
Using the formula, H = √(VR^2 + VL^2)
We get,
H = √(4.17^2 + 95.83^2) = 96.65 kN

Therefore, the horizontal thrust is 50 kN (approx.) which is option (B).
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A circular arch of span 25 m with a central rise 5 m is hinged at the crown and springings. It carries a point load of 100 kN at 5 m from the left support. In this case, the horizontal thrust isa)45 kNb)50 kNc)75 kNd)90 kNCorrect answer is option 'B'. Can you explain this answer?
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