A cantilevered solid shaft with length of 400-mm and diameter of 150-mm is loaded at its free end as shown. If F₁ = 1 kN, F₂ = 2 kN and M₁ = 30 N-m answer or perform the following: 2 a. Which point among a, b, c and d, experiences the greatest number of stress components? Provide the number of nonzero stress components for each point. UN b. Determine the stresses at point a c. Draw the complete state of stress of point a

A 9 ft wide and infinitely long flexible strip load of 800 lb/ft2 is placed on an elastic medium as shown in Figure P8.7. Find the vertical stress increase at points A, B, and C located 3 ft below the surface.

The soil profile at a site is shown Figure P16.3. Find the total horizontal normal stresses at A and B, assuming at-rest conditions.

Use Eq. (6.14) to determine the stress increase () at z = 10 ft below the center of the area described in Problem 6.5. 6.5 Refer to Figure 6.6, which shows a flexible rectangular area. Given: B1 = 4 ft, B2 = 6 ft, L1, = 8 ft, and L2 = 10 ft. If the area is subjected to a uniform load of 3000 lb/ft2, determine the stress increase at a depth of 10 ft located immediately below point O. Figure 6.6 Stress below any point of a loaded flexible rectangular area

Refer to Figure 10.42. Due to application of line loads q1 and q2, the vertical stress increase at point A is 58 kN/m2. Determine the magnitude of q2. Figure 10.42

Refer to Figure 10.48. If R = 4 m and hw = height of water = 5 m, determine the vertical stress increases 2 m below the loaded area at radial distances where r = 0, 2, 4, 6, and 8 m. Circular contact area of radius R on the ground surface Figure 10.48

For the drilled shaft described in Problem 19.7, estimate the total elastic settlement at working load. Use Eqs. (18.45), (18.47), and (18.48). Assume that Ep = 20 106 kN/m2, s = 0.3, Es = 12 103 kN/m2, = 0.65 and Cp = 0.03. Assume 80% mobilization of skin resistance at working load. (See Part c of Problem 19.7) 19.7 Figure 19.16 shows a drilled shaft without a bell. Here, L1 = 6 m, L2 = 7 m, Ds = 1.5 m, cu(1) = 50 kN/m2, and cu(2) = 75 kN/m2. Find these values: a. The net ultimate point bearing capacity. Use Eqs. (19.23) and (19.24) b. The ultimate skin resistance. Use Eqs. (19.26) and (19.28) c. The working load, Qw (FS = 3) FIG. 19.16

For the same line loads given in Problem 10.8, determine the vertical stress increase, z, at a point located 4 m below the line load, q2. Refer to Figure 10.41. Determine the vertical stress increase, z, at point A with the following values: q1 = 110 kN/m, q2 = 440 kN/m, x1 = 6 m, x2 = 3 m, and z = 4 m. Figure 10.41

A soil element beneath a pave ment experiences principal stress rotations when the wheel load, W, passes over it and moves away, as shown in Figure 10.51. In this case, the wheel load has passed over points A and B and is now over point C. The general state of stress at these points is similar to the one shown by a stress block at point D. The phenomenon of principal stress rotation influences the permanent deformation behavior of the pavement layers. Investigate how the magnitude and the orientations of the principal stresses vary with distance from the point of application of the wheel load. Consider the case shown in Figure 10.51. An unpaved aggregate road with a thickness of 610 mm and unit weight of 19.4 kN/m3 is placed over a soil subgrade. A typical single-axle wheel load, W = 40 kN, is applied uniformly over a circular contact area with a radius of R = 150 mm (tire pressure of 565 kN/m2). The horizontal and shear stresses at each point are calculated from a linear elastic finite element analysis for a two-layer pavement and are presented in the following table. a. Use Eq. (10.28) to calculate the vertical stress increases at soil elements A, B, and C that are located at radial distances 0.457,0.267, and 0 m, respectively, from the center of the load. Determine the total vertical stress (y) due to wheel load, the overburden pressure at each point, and enter these values in the table. b. Use the pole method to determine the maximum and minimum principal stresses (1 and 3) for elements A, B, and C. Also determine the orientation (s) of the principal stress with respect to the vertical. Enter these values in the table. c. Plot the variations of 1 and s, with normalized radial distance, r/R, from the center of loading.

A point load of 1000 kN is applied at the ground level. Plot the variation of the vertical stress increase Δσ with depth at horizontal distance of 1 m, 2 m, and 4 m from the load.