1.a. For the circle drawn below, prove that -2a. (r, o) Center of circle b. Find the magnitude and orientation of the principal stresses (from the principal stresses to the pole) for the following stress condition. 10psi 50psi 30 25psi 10 psi Draw stress paths for the following loading conditions (all stresses in psi Path Initial Conditions Final Conditions increases to 60 remains constant remains constant remains constant decreases to 10 20 20 20 20 20 20 20 20 20 20 15 increases to 60 ncreases remains constantdecreases to 7 remains constant increases to 60 3. The surface of an elastic body is loaded by a uniform stress of 2000 psf over an area 30 feet by 60 feet, which has the coordinates (0,0) at the center Determine a. The change in vertical stress at a depth of 10 feet below a corner of the loaded b. the change in vertical stress at a depth of 20 feet below the center of the loaded c. The change in vertical stress at a depth of 30 feet below a point that has area area coordinates 10 feet greater than those of a corner of the loaded area. 4. A uniform load of 2000 psf is applied over a circular area 15 feet in diameter on the surface of an elastic body with -110 pcf and Ko-0.45. Find the following stresses at the centerline at a depth of 10 feet, both before and after loading: Vertical stress horizontal stress and maximum shear stress. 5. A load of 50 MPa is uniformly distributed over a circular area with a radius of 30 m. Determine the magnitude of the major and minor principal stress increments at a point 20 m beneath the right edge of the loaded area. 1.a. For the circle drawn below, prove that -2a. (r, o) Center of circle b. Find the magnitude and orientation of the principal stresses (from the principal stresses to the pole) for the following stress condition. 10psi 50psi 30 25psi 10 psi Draw stress paths for the following loading conditions (all stresses in psi Path Initial Conditions Final Conditions increases to 60 remains constant remains constant remains constant decreases to 10 20 20 20 20 20 20 20 20 20 20 15 increases to 60 ncreases remains constantdecreases to 7 remains constant increases to 60 3. The surface of an elastic body is loaded by a uniform stress of 2000 psf over an area 30 feet by 60 feet, which has the coordinates (0,0) at the center Determine a. The change in vertical stress at a depth of 10 feet below a corner of the loaded b. the change in vertical stress at a depth of 20 feet below the center of the loaded c. The change in vertical stress at a depth of 30 feet below a point that has area area coordinates 10 feet greater than those of a corner of the loaded area. 4. A uniform load of 2000 psf is applied over a circular area 15 feet in diameter on the surface of an elastic body with -110 pcf and Ko-0.45. Find the following stresses at the centerline at a depth of 10 feet, both before and after loading: Vertical stress horizontal stress and maximum shear stress. 5. A load of 50 MPa is uniformly distributed over a circular area with a radius of 30 m. Determine the magnitude of the major and minor principal stress increments at a point 20 m beneath the right edge of the loaded area
