Question

in a direct shear test on a specimen of cohesionless sand, the vertical normal stress on the specimen is 240 kn/m2 and the horizontal shear stress at failure is 160 kn/m2 . (a) assuming uniform stress distribution within the failure zone and a straight line failure envelope which goes through the origin, determine by means of the mohr circle the magnitude and direction of the principal stresses at failure.

Answer 1

The direct shear test question involves using the Mohr circle to determine the magnitude and direction of the principal stresses in a cohesionless sand specimen, based on given normal and shear stress values.

Step-by-step explanation:

The question involves using the Mohr circle to determine the magnitude and direction of the principal stresses during a direct shear test on cohesionless sand. Given the normal stress (σ) of 240 kN/m² and shear stress (τ) of 160 kN/m² at failure, the Mohr circle can be constructed to find the principal stresses σ1 and σ2. Since the failure envelope is a straight line passing through the origin (implying a frictional material with no cohesion), the radius of the Mohr circle, which equals the maximum shear stress (τmax), will be half the difference between the major and minor principal stresses.

The center of the Mohr circle is at (σaverage, 0) which is (240 kN/m²/2, 0) = (120 kN/m², 0) on the σ-axis. Using the Pythagorean theorem, we can compute the magnitude of the principal stresses. The direction of the principal stresses is perpendicular to each other, with σ1 being aligned with the maximum normal stress and σ2 with the minimum normal stress.