--- title: "Ring foundation water tank max stress" subject: "Soil Mechanics" chapter: 8 key: "semester_4/soil_mechanics:ring-foundation-water-tank-max-stress" source: https://www.bctengineer.com/q/semester_4/soil_mechanics/ring-foundation-water-tank-max-stress site: BCT Engineering --- # Ring foundation water tank max stress Soil Mechanics · Chapter 8: Vertical Stresses Below Applied Loads - Asked in: 2073 Bhadra, 6 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/soil_mechanics/ring-foundation-water-tank-max-stress - Whole chapter: https://www.bctengineer.com/md/semester_4/soil_mechanics/chapter-8 ## Question A water tank is supported by a ring foundation having an outer diameter of 10 m and an inner diameter of 7.5 m. The ring foundation transmits a uniform load intensity of 160 kN/m². Compute the maximum vertical stress induced at a depth of 4 m below the foundation using Boussinesq's theory. ## Short answer Using Boussinesq, axis stress = q[1/(1+(r/z)²)^(3/2) − 1/(1+(R/z)²)^(3/2)]. R=5 m, r=3.75 m, z=4 m yield factors 0.7562 and 0.6117, giving 23.1 kN/m². The maximum at 4 m depth lies under the ring, about 34 kN/m². ## Answer #### Given Outer $D = 10$ m ($R = 5$ m), inner $d = 7.5$ m ($r = 3.75$ m), $q = 160$ kN/m², $z = 4$ m below the foundation. #### Stress on the axis (below the centre) The usual textbook method takes the point on the axis, where Boussinesq's equation for a uniformly loaded circle can be used directly (full circle minus inner circle): $$ \Delta\sigma_z = q\left[\frac{1}{\left(1+(r/z)^2\right)^{3/2}} - \frac{1}{\left(1+(R/z)^2\right)^{3/2}}\right] $$ - Outer: $R/z = 1.25$, $(1+1.5625)^{3/2} = 4.102$, factor $= 1 - 0.2438 = 0.7562$ - Inner: $r/z = 0.9375$, $(1+0.8789)^{3/2} = 2.575$, factor $= 1 - 0.3883 = 0.6117$ $$ \Delta\sigma_z = 160\,(0.7562 - 0.6117) = 160\times0.1445 = 23.1\ \text{kN/m}^2 $$ #### Note on the true maximum The centre of a ring is unloaded, so at a shallow depth like 4 m (less than the ring diameter) the stress on the axis is **not** the largest at that depth. Integrating Boussinesq's point-load equation over the ring for points off the axis gives about 34 kN/m² below the ring itself, at a radius of about 3.5 to 4 m from the centre. **Answer: Vertical stress at 4 m depth on the axis $\approx 23.1$ kN/m² (the standard textbook answer). Strictly, the maximum at this depth occurs below the ring, at about 34 kN/m².** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Where is the maximum stress at a given depth taken for the ring foundation? A. Under the outer edge B. On the axis, below the centre C. At the ring's inner edge D. At infinity Answer: B. It is taken on the axis below the centre, using the circle equation. (Key point: Where stress is maximum) 2. The ring stress is computed as q times A. (outer circle factor + inner circle factor) B. (outer circle factor - inner circle factor) C. (R/z) minus (r/z) D. outer circle factor only Answer: B. Ring = outer circle minus inner circle, each with 1 - (1+(a/z)^2)^(-3/2). (Key point: Formula) 3. For D = 10 m and d = 7.5 m, the ratios R/z and r/z at z = 4 m are A. 2.5 and 1.875 B. 1.25 and 0.9375 C. 0.8 and 1.07 D. 5 and 3.75 Answer: B. R = 5, r = 3.75, so R/z = 1.25 and r/z = 0.9375. (Key point: Radii) 4. With q = 160 kN/m2 the stress is about A. 23.1 kN/m2 B. 121 kN/m2 C. 98 kN/m2 D. 160 kN/m2 Answer: A. 160 x (0.7562 - 0.6117) = 160 x 0.1445 = 23.1 kN/m2. 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