Question

CIVL310 Geotechnical Engineering Problem Set 1: Review of Solid Mechanics and Fluid Mechanics 1. Stresses on a soil element are as follows: σ

x

=400kPa,σ
x

=700kPaτ
z

=−200kPa. Assume compressive normal stresses to be positive, and shear stresses causing counter clockwise rotation to be positive. For this soil element, (a) Draw the element and show the stresses on the element (b) Draw the Mohr Circle (c) Determine the magnitude of major and minor principal stresses (d) Determine the direction of the major and minor principal stresses (with respect to principal planes) (e) Determine the magnitude of the maximum shear stress (f) Determine the direction of the maximum shear stress (with respect to principal planes)

Answer 1

To solve this problem, we need to draw the stress element and calculate the major and minor principal stresses, the direction of the principal stresses, the maximum shear stress, and its direction. The given stresses are σx = 400 kPa, σy = 700 kPa, and τxy = -200 kPa. We assume compressive normal stresses as positive and shear stresses causing counter-clockwise rotation as positive.

Step-by-step explanation:

To solve this problem, we need to draw the stress element and calculate the major and minor principal stresses, the direction of the principal stresses, the maximum shear stress, and its direction. The given stresses are σx = 400 kPa, σy = 700 kPa, and τxy = -200 kPa. We assume compressive normal stresses as positive and shear stresses causing counter-clockwise rotation as positive.

(a) Drawing the element and labeling the stresses:

(b) Drawing the Mohr Circle:

(c) Calculating the magnitude of major and minor principal stresses: The major principal stress (σ1) is located at the topmost point of the Mohr circle, which is 700 kPa. The minor principal stress (σ2) is located at the bottommost point of the Mohr circle, which is 400 kPa.

(d) Determining the direction of the major and minor principal stresses: The direction of the major principal stress is perpendicular to the line connecting the center of the Mohr circle to the topmost point of the circle. The direction of the minor principal stress is perpendicular to the line connecting the center of the Mohr circle to the bottommost point of the circle.

(e) Calculating the magnitude of the maximum shear stress: The maximum shear stress (τmax) is equal to half the difference between the major and minor principal stresses, which is (700 - 400)/2 = 150 kPa.

(f) Determining the direction of the maximum shear stress: The direction of the maximum shear stress is at a 45-degree angle to the line connecting the center of the Mohr circle to the topmost or bottommost point of the circle.