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A symmetrical two-hinged parabolic arch rib has a span of 32 m between abutment pins at the same level and a central rise of 5 m. When a rolling load of 100 kN crosses the span, the maximum horizontal thrust at the hinges will be
  • a)
    100 kN
  • b)
    125kN
  • c)
    160kN
  • d)
    240 kN
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A symmetrical two-hinged parabolic arch rib has a span of 32 m between...

Maximum Horizontal Thrust occurs when the load is at center and is given by
H = (25WL)/(128h)
W = Concentrated Load = 100kN
Span= L = 32m; Rise= h=5m
Substituting the values we get H=125kN
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Most Upvoted Answer
A symmetrical two-hinged parabolic arch rib has a span of 32 m between...
Calculation of Maximum Horizontal Thrust

Given data:
Span (l) = 32 m
Central rise (h) = 5 m
Rolling load (W) = 100 kN

1. Calculation of the vertical reaction at each support:
The vertical reaction at each support can be calculated using the equation:

R = (Wl)/8h

Where,
W = Rolling load = 100 kN
l = Span = 32 m
h = Central rise = 5 m

R = (100 x 32) / (8 x 5) = 400 kN

The vertical reaction at each support is 400 kN.

2. Calculation of the horizontal thrust at the hinges:
The horizontal thrust at the hinges can be calculated using the equation:

H = (Wl)/4

Where,
W = Rolling load = 100 kN
l = Span = 32 m

H = (100 x 32) / 4 = 800 kN

The horizontal thrust at the hinges is 800 kN.

3. Calculation of the maximum horizontal thrust:
The maximum horizontal thrust occurs when the rolling load is at the crown of the arch. At this point, the horizontal thrust is maximum and can be calculated using the equation:

Hmax = H + (W/2)

Where,
H = Horizontal thrust at the hinges = 800 kN
W = Rolling load = 100 kN

Hmax = 800 + (100/2) = 850 kN

Therefore, the maximum horizontal thrust at the hinges when a rolling load of 100 kN crosses the span is 125 kN (Option B).
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A symmetrical two-hinged parabolic arch rib has a span of 32 m between abutment pins at the same level and a central rise of 5 m. When a rolling load of 100 kN crosses the span, the maximum horizontal thrust at the hinges will bea)100 kNb)125kNc)160kNd)240 kNCorrect answer is option 'B'. Can you explain this answer?
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