Intze water tank: a compact design guide

What each part of the tank does, the formula that sizes it, the code table it comes from, and the rule of thumb to start with. Written so that someone new to tank design can follow it; every formula is the one the calculator uses.

Want the derivation behind a formula? See the formula reference — the same page the Theory links in the designer open.

1. How the tank carries its load

In plain words: the water pushes outward on every surface. Parts that are stretched need steel rings; parts that are squeezed need only minimum steel. The Intze shape is arranged so that the two sloping parts at the bottom push on the girder in opposite directions and nearly cancel.

The columns stand on a circle under the bottom of the cone, not under the tank wall. Everything above them — roof, wall, cone, bottom dome and all the water — is carried down to the circular girder B₃ on top of the columns. This is the RDSO standard arrangement (drawing B-1235).

Part	Along the slope / height	Round the ring	Steel
Top dome	squeezed	squeezed	minimum
Ring beam B₁	—	stretched	designed
Cylindrical wall	squeezed (light)	stretched by water	designed hoops
Ring beam B₂	—	stretched (cone + water)	designed
Conical slab	squeezed	stretched by water	designed hoops
Bottom dome (arches up)	squeezed	squeezed	minimum
Girder B₃	bends and twists between columns	small hoop force left over	designed

Girder B₃ (orange) sits on the columns at the bottom of the cone.

2. Capacity and freeboard

In plain words: decide how much water to store, then leave an empty gap at the top so an earthquake wave cannot hit the roof.

Daily demand = population × per-capita supply
Overhead storage ≈ ¼ to ⅓ of daily demand (exact value from pumping hours by the mass-curve method)

Supply standard (CPHEEO Manual)	Litres / person / day
Towns with piped sewerage	135
Towns without sewerage	70
Rural piped supply (Jal Jeevan Mission)	55

Freeboard must be at least the sloshing wave height from IS 1893 (Part 2):2014, d_max = (A_h)_c × R × D/2 (see section 14). 0.3–0.6 m is typical; the calculator checks it.

3. Proportions

In plain words: pick the ratios below, and the tank size follows from the capacity. These are starting values, not rules.

Ratio	Classic textbook	RDSO type design (B-1235)	Calculator default
Cylinder height H₁ / D	about 0.4–0.6	0.32	0.32
Bottom ring r / R	5/8 = 0.625	0.66	0.66
Cone slope from horizontal	45°	45°	45°
Top dome rise / D	1/8 = 0.125	0.165	0.165
Bottom dome rise / r	0.30–0.45	0.245	0.25 — then use the balancing value the design reports

Water volume V = πR²h_w + (πh₂/3)(R² + Rr + r²) − (πh_b/6)(3r² + h_b²)
h_w = H₁ − freeboard · h₂ = (R − r) tanθ · the last term is subtracted because the bottom dome bulges up into the water.

With the ratios fixed, V depends only on R, so R is found by trial (the calculator uses bisection).

4. Loads

Load	Value used	Source
Reinforced concrete	25 kN/m³	IS 875 (Part 1)
Water	9.81 kN/m³	—
Roof live load	1.5 kN/m² with access, 0.75 without	IS 875 (Part 2)
Finishes and fittings	5–10% of the shell weight (8% default)	practice
Wind	see section 13	IS 875 (Part 3):2015
Earthquake	see section 14	IS 1893 (Part 2):2014

Weight of a shell = surface area × thickness × 25. Surface areas: spherical dome 2πR_dh, cylinder 2πRH₁, cone π(R + r) × slant length.

5. Materials and code tables

In plain words: parts that hold water are designed so the concrete does not crack and the steel is kept at a low stress. That is why the stresses below are much lower than in ordinary buildings.

Permissible concrete stresses (N/mm²)

Grade	σ_cbc	σ_cc	direct tension σ_ct	bending tension	m
M25	8.5	6.0	1.3	1.8	10.98
M30	10.0	8.0	1.5	2.0	9.33
M35	11.5	9.0	1.6	2.2	8.12
M40	13.0	10.0	1.7	2.4	7.18

Compression: IS 456:2000 Table 21. Tension (resistance to cracking): IS 3370 (Part 2):2009 Table 1. m = 280 / (3σ_cbc).

Permissible steel stress, water-retaining parts

Bar	IS 3370 (Part 2):2009	IS 3370:1965 (older)
Deformed (HYSD)	130	150
Plain mild steel	115	115

IS 3370 (Part 2):2009 Cl. 4.4.3.1.

Minimum steel (IS 3370 Part 2:2021, Cl 8.1.1, Table 5)

Tank	Bar	L ≤ 14 m	Long members
Elevated	Fe 415 / 500	0.28%	0.42% (L ≥ 28 m)
Elevated	Fe 250	0.44%	0.66% (L ≥ 28 m)
On the ground	HYSD	0.24%	0.36% (L ≥ 22 m)

Interpolate between the limits. L is the horizontal length of the continuous member between movement joints, along the main steel. An Intze tank has no joints, so L is the circumference of each member (2πR or 2πr) — for most tanks over 100 kL that means 0.42%. An Intze tank is elevated, so the ground-tank values do not apply.

The percentage is of each surface zone, in each direction. Surface zone = half the thickness, but not more than 250 mm. Walls under 160 mm and slabs under 180 mm may have all the steel in one face (Cl 8.1.2). Why the minimum depends on length ›

Other rules

Concrete: M30 minimum for water-retaining RCC (IS 3370 Part 1).
Cover: 45 mm on faces in contact with water.
Maximum bar spacing: 300 mm, and not more than about three times the thickness.
Limit-state parts (girder, columns, footings): IS 456:2000.

Maximum shear stress τ_c,max (IS 456 Table 20)

M20	M25	M30	M35	M40+
2.8	3.1	3.5	3.7	4.0

6. Top dome

In plain words: the roof is a shallow bowl upside down. Its weight squeezes it both ways, so the concrete takes the load and the steel is only the minimum.

Dome radius R_d = (R² + h²) / 2h · sinθ = R/R_d
Load w = thickness × 25 + live load (kN/m²)
Meridional thrust T = wR_d / (1 + cosθ) (compression)
Hoop force = wR_d [cosθ − 1/(1 + cosθ)] (compression near the springing when θ < 51.8°)
Stress = T / t ≤ σ_cc
Outward push on B₁: H = T cosθ

Start with: rise D/8 to D/6, thickness 100–125 mm, minimum steel both ways.

7. Top ring beam B₁

In plain words: the dome pushes outward all round, like a barrel pushing on its hoop. Cut the ring in half: the outward push over the half is H × D, and the two cut ends share it.

Hoop tension P = H × D/2 = H × R
Steel A_st = P / σ_st
Uncracked check: P / [A_c + (m − 1)A_st] ≤ σ_ct

Start with: 250–350 × 200–300 mm. If the check fails, widen the beam.

8. Cylindrical wall

In plain words: water pressure grows with depth, so the wall is stretched most at the bottom. Horizontal bars take the stretch; the thickness is chosen so the concrete does not crack.

Pressure at depth h: p = 9.81h
Hoop tension per metre height: F = p × D/2 = 9.81 h R
Steel A_st = F / σ_st, half on each face
Thickness t ≥ F (1/σ_ct − (m−1)/σ_st), not less than 150 mm
Vertical steel = minimum steel

Note: this assumes the wall base is free to move outward. Where the wall is cast with the ring beam, the restraint causes vertical bending near the base; IS 3370 (Part 4) gives coefficients for it. Provide extra vertical steel on the water face at the bottom.

Start with: 150–300 mm. Hoop steel can be reduced in steps higher up.

9. Ring beam B₂ (where the wall meets the cone)

In plain words: the cone below is squeezed, so at its top edge it pushes this ring outward. The water pushes the same way. Both add, which is why B₂ is usually the most heavily stretched ring.

Outward push from the cone = N_φ,top × sinα (α = cone angle from the vertical)
Water on the beam face = 9.81 h_w × beam depth
Hoop tension P = (sum) × R → A_st = P/σ_st; uncracked check as for B₁

Start with: 500–800 × 350–600 mm. The ring also restrains the bottom of the wall; generous size and a haunch at the junction are normal practice.

10. Conical slab

In plain words: the cone carries the wall and the water standing on it down to the girder, so along its slope it is squeezed. Round its circumference the water stretches it — and that stretch decides its thickness.

Along the slope (compression): N_φ = W / (2πr_x cosα), W = everything above that level
Round the ring (tension): N_θ = (p / cosα + q tanα) × D_x/2
p = water pressure at that level, q = self weight per m² of slab
Check at the top (D_x = D) and the bottom (D_x = 2r); design for the larger
Thickness from the same uncracked check as the wall, not less than 200 mm

Start with: 45° slope, 200–400 mm.

11. Bottom dome

In plain words: this dome arches up into the water from the girder, like a stone arch. The water on top squeezes it, and at its edge it kicks the girder outward — exactly opposite to the cone.

R_d = (r² + h_b²)/2h_b, sinφ = r/R_d
Load W = water above it (less the bulge it displaces) + self weight
Meridional thrust N_φ = W / (2πr sinφ) (compression)
Outward push on the girder = N_φ cosφ
Stress ≤ σ_cc; minimum steel both ways, each face

Rise: 0.22r–0.30r. The rise that exactly balances the cone is h_b = r tan(φ₀/2), with tanφ₀ = W / (2πr × cone’s inward push). The calculator prints this value in section 8 of the results.

12. Circular girder B₃ and the Intze balance

In plain words: when the cone’s inward push and the dome’s outward push nearly cancel, the girder has almost no ring force. It then works like a curved beam on columns: it sags between columns, hogs over them, and twists because it is curved.

Net ring push = dome out + water on face − cone in → hoop force = net × r
W = everything above the columns (container + water + roof live load)
M_support = C₁ W R_c · M_span = C₂ W R_c · T_max = C₃ W R_c (× 1.5 for design)
Torsion: equivalent moment M_t = T(1 + D/b)/1.7 and shear V_e = V + 1.6T/b (IS 456 Cl. 41)

Columns	C₁ support	C₂ span	C₃ torsion	max torsion at
6	0.01482	0.00751	0.001507	12.73°
8	0.00827	0.00417	0.000628	9.53°
10	0.00527	0.00265	0.000320	7.62°
12	0.00365	0.00183	0.000184	6.35°

Continuous circular beam, uniform load, equally spaced supports; angle measured from a support.

Start with: width ≥ column width; depth ≈ column spacing / 6 to / 8.

13. Wind — IS 875 (Part 3):2015

In plain words: take the wind speed for your district, adjust it for height, ground roughness, slope and cyclone risk, turn it into a pressure, and multiply by the area the wind sees.

V_z = V_b k₁ k₂ k₃ k₄ · p_z = 0.6 V_z² (N/m²)
p_d = K_d K_a K_c p_z · F = C_f A p_d
Staging frame: F = C_f A_s p_d (1 + η) for the front frame plus the shielded rear frame

k₂ — height and terrain

Height (m)	Cat. 1	Cat. 2	Cat. 3	Cat. 4
10	1.05	1.00	0.91	0.80
15	1.09	1.05	0.97	0.80
20	1.12	1.07	1.01	0.80
30	1.15	1.12	1.06	0.97
50	1.20	1.17	1.12	1.10

IS 875 (Part 3):2015 Table 2 (interpolate between rows).

Other factors

Factor	Usual value
k₁ risk	1.00 (50-year life); 1.07 important, 100-year
k₃ topography	1.00 on flat ground; up to 1.36 on a hill crest
k₄ cyclone	1.00 inland; 1.15 industrial / 1.30 post-cyclone importance in cyclonic coastal belts
K_d direction	1.0 for the circular container; 0.9 for the frame
K_a area	1.0 up to 10 m², 0.9 at 25 m², 0.8 at 100 m²+
C_f container	0.7–0.8 for the usual height/diameter

Basic speeds: Kolkata 50, Delhi 47, Mumbai 44, Chennai 50, Bengaluru 33 m/s. Check the map in the code for your district.

14. Earthquake — IS 1893 (Part 2):2014

In plain words: the lower water moves with the tank (the impulsive mass) while the upper water sloshes slowly (the convective mass). Each is a weight on a spring; work each out and combine them.

Equivalent cylinder: same D, depth h = V / (πD²/4)
m_i/m = tanh(0.866 D/h) / (0.866 D/h) · m_c/m = 0.23 (D/h) tanh(3.68 h/D)
T_i = 2π√[(m_i + m_s)/K_s], m_s = container + ⅓ staging
T_c = C_c√(D/g) = 2π√[D / (3.68 g tanh(3.68 h/D))]
A_h = (Z/2)(I/R)(S_a/g); convective S_a/g × 1.75 (0.5% damping)
V = √(V_i² + V_c²), M = √(M_i² + M_c²) using h_i*, h_c* for overturning
Sloshing height d = (A_h)_c R D/2 ≤ freeboard
Check both tank full and tank empty

Zone	II	III	IV	V
Z	0.10	0.16	0.24	0.36

IS 1893 (Part 1):2016 Table 3. Kolkata III, Delhi IV, Guwahati V, Bengaluru II.

Soil	Description	S_a/g for T > plateau (5%)
I	rock / hard, N > 30	1.00/T (plateau to 0.40 s)
II	medium, N 10–30	1.36/T (plateau to 0.55 s)
III	soft, N < 10	1.67/T (plateau to 0.67 s)

Plateau value 2.5; for T < 0.1 s, 1 + 15T; beyond 4 s constant. IS 1893 (Part 1):2016.

Factor	Value
Importance I	1.5 drinking water / fire fighting; 1.0 others
R, RC frame staging (IS 13920 detailing)	2.5
R, RC shaft staging	1.8
Convective damping multiplier	1.75

IS 1893 (Part 2):2014. Confirm R for your staging type in the code table.

Staging stiffness (rigid braces): K_s ≈ β × 12 n E_c I_col N_p² / h_s³
n columns, N_p panels, β ≈ 0.85 for brace flexibility

15. Load combinations and column forces

In plain words: the sideways force tries to tip the tank. Columns on the far side get extra load, those on the near side lose load. With the tank empty, a strong enough force can even lift a column.

Column load = P/n ± M y / Σy², Σy² = (n/2) R_c²
Column moment ≈ (V/n) × panel height / 2 (portal method)

Service — for the foundation
DL + water
DL + water + wind
DL + water + earthquake
DL + earthquake, tank empty
DL + wind, tank empty

Factored — for the members
1.5 (DL + water)
1.2 (DL + water + EQ)
1.5 (DL + water) + 1.5 EQ
1.5 (DL + water) + 1.5 wind
0.9 DL + 1.5 EQ, tank empty
0.9 DL + 1.5 wind, tank empty

16. Columns and bracings

Number of columns: 6 up to about 200 kL, 8 for 200–600 kL, 10–12 above; keep 3–5 m between columns.
Column size: about 27 mm per metre of staging height to start, minimum 450 mm. Aim for 0.8–2.5% steel; above 4% make it bigger.
Design: IS 456 limit state for axial load with bending (P–M interaction). Effective length about 1.2 × panel height; if l_e/D > 12, add the slenderness moment P_uD(l_e/D)²/2000.
Bracings: a level every 3.5–4 m. Moment from the column shear shared at each joint; shear = 2M/L for a member bent in double curvature.
Detailing: IS 13920 ductile detailing — closely spaced ties at every joint — is what allows R = 2.5.

17. Foundation

In plain words: spread the load wide enough that the soil pressure stays under what the soil can safely carry, and does not drop below zero (which would mean the foundation lifts).

Ring raft: A = π(R_o² − R_i²), Z = π(R_o⁴ − R_i⁴)/(4R_o)
Net pressure p = P/A − γD_f ± M/Z
p_max ≤ SBC (× 1.25 for wind or earthquake cases, if the soil allows) · p_min ≥ 0
Raft bending as a cantilever from the column line: M_u = 1.5 p_max L²/2

Start with: raft width each side ≈ 0.3 × column circle diameter; thickness ≈ one-third of that width.

Soil (indicative only)	Safe bearing, kN/m²
Soft clay	50–100
Medium clay, loose sand	100–150
Stiff clay, dense sand	150–250
Gravel, soft rock	250 +

Never design from this table. Use the soil investigation report for the site (IS 1892, IS 6403).

18. Final checklist

Water volume matches the required capacity.
Freeboard is more than the sloshing wave height.
Wall and cone are thick enough for the uncracked check.
Ring beams B₁ and B₂ pass the tension check.
Dome stresses are below σ_cc.
Girder: balance within about 35%, bending under M_lim, shear + torsion under τ_c,max.
Columns: steel 0.8–4%, slenderness considered.
No column in net tension, or the foundation is designed for uplift.
Soil pressure under the allowed value in every case, and not negative.
Earthquake and wind both carried through; tank empty checked.
Minimum steel on every face; cover 45 mm on water faces.
A licensed structural engineer has checked and signed the design.

This guide supports the Nirmaanpro Intze tank designer. It summarises the codes for learning and preliminary design; always refer to the current editions of IS 456, IS 3370, IS 875, IS 1893, IS 11682 and IS 13920 for construction work.

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