Concept explainers
Height of the pointed arch.
Answer to Problem 56P
Solution:
Explanation of Solution
Considering the centers of gravities of the left half of the circular positions is same as that of right halves from below diagram.
Given:
Fis the load of the arch
Calculations:
The horizontal force exerted to the point arch is one third of the round arch.
From the given statement
A round arch is simply a semicircle (top half of a circle, diameter 8m) resting on 2 supports. The arch itself can be thought of as 2 halves.
From diagram, the line of action of F (pointing left and acting through the top of L) is a distance
If the height of the pointed arch above the base is h.
The horizontal force exerted to the point arch is one third of the round arch.
From the given statement,
Moment about this force is =
These two must be equal as they balance the moment
Conclusion:Height of the pointed arch must be
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