Hibbeler — Statics and Mechanics of Materials
Ogua hot tub — same wall math, different depth
The Uktena cistern with the lid off — a short entry, since base moment scales with depth cubed, so a shallower tub needs far less wall steel.
See the build: ogua →Concepts pulled in
- Base moment scaling with depth cubed
The build: the Ogua is an open-top masonry hot tub built from the same moon-eye bricks with rebar channels as the Uktena, on the same kind of reinforced platform, with a bench and a firebox for heat.
Why a short entry: it's the cistern with the lid off. Ch. 10 already treated the wall top as free (a cantilever off its base), so an open top changes nothing about the check. Everything there carries over: reinforced pad, filled channels, bars doweled into the base.
What does change: water depth and people. A new rule falls out: base moment scales with depth cubed (M = γh³/6), so a shallower tub needs far less wall steel than a deep cistern.
Assumed (replace with real dimensions): 5×5 ft interior, 3 ft of water, four adults (about 800 lb), same 8"-class block, walls about 3.5 ft tall, bench built from the same block.
Weight on the platform: water 75 cu ft × 62.4 ≈ 4,700 lb, people ≈ 800 lb, masonry and bench ≈ 4,800 lb. Total ≈ 10,300 lb over about 39 sq ft ≈ 260 psf. That's about 17% of the 1,500 psf default allowable and lighter than the Snawfus. Same reinforced-pad rule as Ch. 9.
Wall check at 3 ft of water
- Thrust: ½ × 62.4 × 3² ≈ 281 lb/ft
- Base moment: about 281 lb-ft ≈ 3,400 lb-in per ft, which is 42% of the cistern's
- Required steel: about 0.05 in² per ft, versus 0.12 for the cistern. Whatever rebar pattern clears the cistern clears this by better than 2×.
- Base connection: friction from the wall's weight covers only about 100 of the 281 lb/ft, so the dowels still carry the rest.
As specified (Zach)
Water depth is 2.5 ft at most, with the benches displacing some of the water, so the tub holds well under the cistern's volume. The 3 ft numbers above are conservative. At 2.5 ft: thrust ≈ ½ × 62.4 × 2.5² ≈ 195 lb/ft; base moment ≈ 163 lb-ft ≈ 1,950 lb-in per ft, which is 24% of the cistern's (depth cubed: (2.5 ÷ 4)³); required steel ≈ 0.03 in² per ft, versus 0.12 for the cistern; base connection: friction from the wall's weight covers about half of the thrust, so the dowels still carry the rest.
Answer
The same blocks, platform, and rebar pattern as the Uktena work for a tub up to the cistern's 4 ft water depth. Always check against the deepest water level the tub will hold.
Out of scope — call a specialist: the firebox and how it heats the water (thermal design, draft, and hot/cold cycling on the geopolymer and mortar joints). Same category as the Snawfus flue design.
Open items for a later pass
Actual dimensions and water depth, real strength numbers for the geopolymer, an overflow and drain, and the firebox design.
Modern Monticello · Technical Library · Worked calculation
Ogua hot tub — same wall math, different depth
Hibbeler — Statics and Mechanics of Materials · Chapter 11
Project or part: (not named)
Try your own numbers
Starts on this chapter's Ogua hot tub at 2.5 ft of water. Change the depth, wall or steel to test your own tank. Wall bending and steel only: the slab, sliding, waterproofing and the real strength of cast geopolymer are separate questions.
- Pressure at the base: 62.4 × 2.5 = 156 psf
- Thrust per ft of wall: ½ × 62.4 × 2.5² = 195 lb/ft, acting 0.83 ft above the base
- Base moment per ft: M = 195 × 0.83 ft ≈ 1,950 lb-in (it scales with depth cubed)
- Section modulus per ft: 12 × 7.625² ÷ 6 = 116 in³, so bending tension = 1,950 ÷ 116 = 17 psi
- Steel needed: As = M ÷ (fs × 0.9 × d) = 1,950 ÷ (20,000 × 0.9 × 3.81) = 0.028 in² per ft (bars centered, d = half the wall)
- Steel provided: 3/8" bars every 8 in = 0.165 in² per ft
The masonry tension is under even the low end of what an unreinforced wall can take (roughly 25 to 70 psi), though the filled, reinforced channels are still the plan.
That 25 to 70 psi is an order-of-magnitude range for ordinary block, and cast geopolymer needs real test numbers. The steel only works if the channels are grouted solid, the bars are doweled into the base, and the top and corners are tied together. Walls spanning sideways between corners help, so this cantilever case is the conservative one, but only if the corners are tied. This is a water tank: a failure releases a lot of water, so get a pro's sign-off before it holds water, and thrust grows with depth squared, so deeper tanks go to an engineer.
Worked example from the Modern Monticello Technical Library, using published design values and simplified checks. Not a stamped engineering design: your site, materials and loads will differ, and anything that could hurt someone if it fails deserves a licensed engineer's review. Provisional or example values are placeholders, not measurements of your material. Sources for every number: modernmonticellobuild.com/technical-library/ogua-hot-tub
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