Boussinesq Stress Calculator
Directly below a 1000 kN point load at 5 m depth the vertical stress increase is 19.0986 kPa.
19.0985931710274 kPa
Full answer, then cut to fewer decimals (not rounded):
- 19.0985931710274 kPa
- 19.098593171027 kPa
- 19.09859317102 kPa
- 19.0985931710 kPa
- 19.098593171 kPa
- 19.09859317 kPa
- 19.0985931 kPa
- 19.098593 kPa
- 19.09859 kPa
- 19.0985 kPa
- 19.098 kPa
- 19.09 kPa
- 19.0 kPa
- Influence factor I
- 0.4774648293
- r/z
- 0
Step-by-step solution
- I_B = (3/2π) [1/(1 + (r/z)²)]^(5/2) = 0.4774648293
- σz = I Q/z² = 0.4774648293 × 1000 ÷ 5² = 19.09859317 kPa
Boussinesq Stress Formula
σz = (3Q / 2πz²) [1/(1 + (r/z)²)]^(5/2)
Westergaard (μ = 0): σz = (Q/πz²) [1/(1 + 2(r/z)²)]^(3/2)
Worked Example
A 1000 kN point load, directly below at 5 m depth:
- I_B = (3/2π) [1/(1 + (r/z)²)]^(5/2) = 0.4774648293
- σz = I Q/z² = 0.4774648293 × 1000 ÷ 5² = 19.09859317 kPa
r/z: 0
GATE tip
For a quick estimate under a footing use the 2:1 method, σz = Q/((B + z)(L + z)); Boussinesq is exact for a point load on an elastic half-space.
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Frequently asked questions
What is the influence factor directly below the load?
3/(2π) = 0.4775 for Boussinesq and 1/π = 0.3183 for Westergaard.
How does stress change with depth?
Under the load it falls with 1/z²: doubling the depth cuts σz to a quarter.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Boussinesq Stress Calculator. Retrieved October 29, 2026, from https://scientificconverters.com/calculators/boussinesq-stress-calculator/
IEEE
Scientific Converters, "Boussinesq Stress Calculator," scientificconverters.com. Accessed: Oct. 29, 2026. [Online]. Available: https://scientificconverters.com/calculators/boussinesq-stress-calculator/