Shear Strength Calculator
A soil with c = 10 kPa and φ = 30° under a normal stress of 100 kPa has a shear strength of 67.735 kPa.
67.7350269189626 kPa
Full answer, then cut to fewer decimals (not rounded):
- 67.7350269189626 kPa
- 67.735026918962 kPa
- 67.73502691896 kPa
- 67.7350269189 kPa
- 67.735026918 kPa
- 67.73502691 kPa
- 67.7350269 kPa
- 67.735026 kPa
- 67.73502 kPa
- 67.7350 kPa
- 67.735 kPa
- 67.73 kPa
- 67.7 kPa
- Failure plane angle to the major principal plane
- 60 °
Step-by-step solution
- τf = c + σ tan φ = 10 + 100 × tan 30° = 67.73502692 kPa
Shear Strength Formula
τf = c + σ tan φ; σ₁ = σ₃ Nφ + 2c√Nφ
Nφ = tan²(45° + φ/2); failure plane at 45° + φ/2
Worked Example
A soil with c = 10 kPa and φ = 30° under σ = 100 kPa:
- τf = c + σ tan φ = 10 + 100 × tan 30° = 67.73502692 kPa
GATE tip
Use effective c′ and φ′ with effective stresses for drained (CD) tests, and total cu with φu = 0 for undrained clays.
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Frequently asked questions
What does an unconfined compression test give?
With σ₃ = 0 and φ = 0, σ₁ = qu = 2c, so the undrained cohesion is half the unconfined compressive strength.
At what angle does the failure plane form?
At 45° + φ/2 to the major principal plane: 60° for φ = 30°.
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). Shear Strength Calculator. Retrieved October 29, 2026, from https://scientificconverters.com/calculators/shear-strength-calculator/
IEEE
Scientific Converters, "Shear Strength Calculator," scientificconverters.com. Accessed: Oct. 29, 2026. [Online]. Available: https://scientificconverters.com/calculators/shear-strength-calculator/