The initial principal stresses at a certain depth in a clay soil are 100 kPa on the horizontal plane and 50 kPa on the vertical plane (Figure No. 1). Construction of a surface foundation induces additional stresses (Figure No. 2) consisting of a vertical stress of 45 kPa, a lateral stress of 20 kPa and a counter clockwise (with respect to the horizontal plane) shear stress of 40 kPa. a. Plot Mohr's circle for the initial state of the soil b. Plot Mohr's circle for the final state of the soil c. Determine the change in magnitude of the principal stresses d. Determine the change in maximum shear stress e. Determine the change in the orientation of the principal stress plane

N B 0 Horizontal The stresses shown in the figure are applied at a point in a dry clayey sand soil mass. A= 50 kPa and B= 125 kPa The shear strength parameters of the clayey sand are: c'= 9kPa and p'=29° 0=30° a) The value of the shear stress, T, is slowly increased. What value would cause shear failure at this point (in kPa)? b) At failure, what angle does the failure plane make with the horizontal (in degrees)?

1. The bar has a cross-sectional area of 400*106 m². If it is subjected to a uniform axial distributed loading along its length and to two concentrated loads, determine the average normal stress in the bar as a function of x, for 0.5 m < x≤ 1.25 m. -X 0.5 m w = 8 kN/m -6 kN 0.75 m 3 kN

Two foundations are located next to each other as follows. Determine the stress increase on a horizontal plane (i.e. - the increase in vertical stress) beneath Point A at a depth of 3 m below the ground surface. The foundations are bearing on the ground surface. 3 m- +2.5 m -6 m 5 m A O= 90 kPa = 120 kPa 6 m