It has been mentioned that the buttresses are 1' thick. What about the walls? We need the weight of all the concrete for the resisting moment.
It is unusual for a concrete buttress to be only one-foot thick if the stability depends on it.
Perhaps more information is contained in the 'axon' drawing. You will need to extract more information, or scan the drawing so we can see it.
In the mean time, we can calculate the overturning moment due to hydrostatic pressure, and to be resisted by the buttresses by integration.
Let h=height of wall=8'
w=spacing between buttresses=6'
The lateral pressure at x' high is
f(x)=62.5(h-x) #/ft² (#=pounds)
Lateral moment dm on each buttress over a strip of height dx
dm=w*x*f(x)dx
Moment M over full height
=∫dm
=∫w*x*f(x)dx
=∫w*x*(h-x)dx from 0 to h
It is hard to calculate the resisting moment if the geometric configuration of the buttresses is not known.
In general, the walls would be monolithic with the bottom of the pool, thereby resisting the lateral forces and some bending moments. Also, the stability would be much improved if part of the wall is underground, engaging the weight of the adjacent soil.
The buttresses would spaced at 6' to minimize the horizontal reinforcement required for the walls.
Will look forward to additional information from you.
1. Aquarium (Retaining Buttresses)
Background:
In a liquid, pressure develops from the weight of the liquid above any point. That pressure is called Hydrostatic pressure and acts equally in all directions. The pressure at any given depth is given by the following formula: p = wh, where p = pressure (in
lb/ft2), w = weight per unit volume (in lb/ft3), and h = vertical height between the surface of the water and the point for which the pressure is being calculated. In the case of water,
water weighs 62.5 pounds per cubic foot. Using the formula above, at the surface, there is no pressure in the water; at 1 foot deep, the pressure is 62.5 psf; at 2 feet deep, the
pressure is 125 psf; etc.
Problem - Part 1:
In the following problem, 10-foot high concrete buttresses of constant cross section retain water in a large aquarium that is 8 feet deep. The buttresses are 1’ thick, and are placed
6’ apart from each other (the axon drawing on the following page shows a small portion of the aquarium).
Given a density for concrete to be 150 pounds per cubic foot, do the concrete buttresses resist the overturning moment caused by the water pressure? If the concrete buttresses do not resist the overturning moment, provide some suggestions to improve their moment
resistance.
2 answers
Let h=height of wall=8'
w=spacing between buttresses=6'
ρ=density of water=62.5 #/ft³
The lateral pressure at x' high is
f(x)=ρ(h-x) #/ft² (#=pounds)
Lateral moment dm on each buttress over a strip of height dx
dm=ρw*x*f(x)dx
Moment M over full height
=∫dm
=∫ρ*w*x*f(x)dx
=∫ρ*w*x*(h-x)dx from 0 to h
w=spacing between buttresses=6'
ρ=density of water=62.5 #/ft³
The lateral pressure at x' high is
f(x)=ρ(h-x) #/ft² (#=pounds)
Lateral moment dm on each buttress over a strip of height dx
dm=ρw*x*f(x)dx
Moment M over full height
=∫dm
=∫ρ*w*x*f(x)dx
=∫ρ*w*x*(h-x)dx from 0 to h
2 answers