(II) How high must a pointed arch be if it is to span a space 8.0 m wide and exert one-third the horizontal force at its base that a round arch would?
Step 1 of 5</p>
Fload ; the load of the archs
FH(round); the horizontal force exerted from the base of the round arch.
FH(point); the horizontal force exerted from the base of the point arch.
W=8m (the span of the arches)
The span of the and load of the arch are the same. If the horizontal force exerted to the point arch is one third of the round arch. What must be the height y of the point arch?
y=? (height of the point arch)
Step 2 of 5</p>
The horizontal force on point arch is one third of the round arch.
Step 3 of 5</p>
We can take the half of the round arch to write the conditions of equilibrium.
According to first condition of equilibrium FH(round) from the ground is equal to the one on the top in opposite direction. Fload is equal to the reaction force N from the ground.
We can write the second condition around the point on the ground.