**Problem 4: Soil Shear Strength Analysis**The shear strength in kilopascals (kPa) of a sandy soil sample is defined by the equation:\[ SS_1 = 8 + \sigma' \tan 34^\circ \]For a different, more silty soil sample, the shear strength is given by:\[ SS_2 = 31 + \sigma' \tan 20^\circ \]**Objective:** Determine the effective normal stress ($\sigma'$) at which both soil samples exhibit the same shear strength. Provide the answer rounded to the nearest kPa.**Explanation:**To find the effective normal stress where both shear strengths are equal, set $SS_1$ equal to $SS_2$:\[ 8 + \sigma' \tan 34^\circ = 31 + \sigma' \tan 20^\circ \]This equation can be solved to find the value of $\sigma'$.

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4. The shear strength in kPa of a sandy soil sample is given by SS₁ = 8 + o'tan 34°, while the shear strength of a different more silty soil sample is given by SS₂ = 31 + o' tan 20°. At what effective normal stress would the samples have the same shear strength, to the nearest kPa?

4. The shear strength in kPa of a sandy soil sample is given by SS₁ = 8 + o'tan 34°, while the shear strength of a different more silty soil sample is given by SS₂ = 31 + o' tan 20°. At what effective normal stress would the samples have the same shear strength, to the nearest kPa?

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Concept explainers

Test for Determination of Shear Strength

The term shear strength is often associated with the soil. Shear strength is defined as the resistance to the deformation of soil particles due to the continuous action of shear stress. In short, shear strength is the maximum shear stress that a soil can sustain.

Question

**Problem 4: Soil Shear Strength Analysis**

The shear strength in kilopascals (kPa) of a sandy soil sample is defined by the equation:

\[ SS_1 = 8 + \sigma' \tan 34^\circ \]

For a different, more silty soil sample, the shear strength is given by:

\[ SS_2 = 31 + \sigma' \tan 20^\circ \]

**Objective:**
Determine the effective normal stress ($\sigma'$) at which both soil samples exhibit the same shear strength. Provide the answer rounded to the nearest kPa.

**Explanation:**

To find the effective normal stress where both shear strengths are equal, set $SS_1$ equal to $SS_2$:

\[ 8 + \sigma' \tan 34^\circ = 31 + \sigma' \tan 20^\circ \]

This equation can be solved to find the value of $\sigma'$.

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