Question 37 of 50

In a two-dimensional soil element, what are the planes on which the shear stress is zero called?

A soil element has the following stresses: σy = 2500 lb/ft^2, σx = 2000 lb/ft^2, and τ = 800 lb/ft^2. Using the formulas from the chapter, calculate the major principal stress (σ1).

What is the sign convention for shear stresses used in plotting Mohr's circles as described in the chapter?

For the stressed soil element in Figure 10.6a, the normal stress on plane AB is 150 lb/in.^2 and the shear stress is 60 lb/in.^2. On plane AD, the normal stress is 90 lb/in.^2 and the shear stress is -60 lb/in.^2. Using these values from the text, what is the major principal stress?

In the pole method of finding stresses, how is the pole (or origin of planes) located on the Mohr's circle?

Once the pole is found on a Mohr's circle, how are the stresses on any other plane, such as plane EF, determined?

Using the pole method for the soil element in Figure 10.6a, where the pole P is found from point N (150, 60), what are the normal and shear stresses on plane AE which is inclined at 45 degrees?

Boussinesq's solution for the vertical normal stress increase (Δσz) caused by a point load is independent of which material property?

A point load P = 5 kN is applied to the ground. According to Example 10.3, what is the vertical stress increase (Δσz) at a depth z = 4 m and a radial distance r = 5 m? The influence factor I1 for r/z = 1.25 is 0.0424.

For calculating the vertical stress caused by a point load P, what is the value of the influence factor I1 when the point of interest is directly below the load (r/z = 0)?

What is the key principle used to determine the total stress increase at a point due to multiple loads, as demonstrated in Example 10.4 for two line loads?

Two line loads, q1 = 500 lb/ft and q2 = 1000 lb/ft, are applied to the ground. A point A is located at a depth of 4 ft. The horizontal distance from q1 to A is 5 ft, and from q2 to A is 10 ft. According to Example 10.4, what is the total stress increase at point A?

To determine the vertical stress increase at a point A due to an inclined line load, as in Example 10.5, what is the first step in the solution process?

For a vertical line load q, the vertical stress increase is given by Δσz = 2qz^3 / (π(x^2 + z^2)^2). How can this equation be rewritten in a nondimensional form involving the ratio x/z?

An inclined line load of 1000 lb/ft acts at an angle of 20 degrees to the vertical. At a point A where x=5 ft and z=4 ft, what is the vertical stress increase due to the horizontal component of the load? Use an influence value of 0.125 for Δσz(H)/(qH/z) at x/z = 1.25.

What are the two nondimensional parameters used to find the influence factor for vertical stress caused by a vertical strip load of finite width B?

A flexible strip load of width B=6 m carries a uniform load q=200 kN/m^2. Determine the vertical stress increase at a depth z=3 m and a horizontal distance x=6 m from the centerline. The influence factor from Table 10.4 for 2x/B=2 and 2z/B=1 is 0.084.

The formula for vertical stress due to embankment loading can be simplified to Δσz = qo * I2, where I2 is an influence factor. According to the text, what source provides a chart for determining this influence factor I2?

An embankment load is analyzed by splitting it into a rectangular section and two triangular sections. For the analysis in Example 10.7, for the right side of the embankment (Figure 10.16c), what are the values of B1 and B2 used?

For a uniformly loaded circular area of radius R, at what depth z (as a multiple of R) does the vertical stress increase at the center (Δσz) drop to about 6 percent of the surface pressure q?

For a uniformly loaded flexible circular area with radius R=3m and load q=100 kN/m^2, calculate the vertical stress increase at a depth z=3m and a radial distance r=4.5m. The influence factors are A' = 0.098 and B' = 0.028.

When calculating the vertical stress increase below the corner of a rectangularly loaded area, the formula Δσz = qI3 is used. What are the parameters 'm' and 'n' used to find the influence factor I3?

How can the vertical stress increase at a point that is not under the corner of a rectangular loaded area be determined using the corner formula?

A rectangular loaded area measures 4m by 2m. A point A' is located under a point that is 1m from the 4m side and 3m from the 2m side. To find the stress at a depth z=4m, the area is divided into two rectangles. For the smaller rectangle (1m x 2m), what are the values of m and n?

What are stress isobars in the context of soil mechanics?

According to Newmark's influence chart method, the increase in pressure (Δσz) at a point is calculated by which formula?

What is the first step in using Newmark's influence chart to find the vertical stress increase at a certain depth z below a loaded area?

In Example 10.10, a square footing plan is replotted to a scale where the unit length AB equals 3 m. The footing load results in a uniform pressure q = 660 / (3x3) kN/m^2. If the influence value (IV) is 0.005 and the number of elements (M) counted is 48.5, what is the stress increase?

What is a major limitation of applying the elasticity-based stress calculation methods presented in this chapter to real soil deposits?

Based on field observations mentioned in the chapter summary, what is the typical range of difference one could expect between theoretical stress estimates and actual field values?

The vertical stress increase below the center of a rectangular loaded area of L by B is given by Δσz = qI4. What are the definitions of the parameters m1 and n1 used to find the influence factor I4?

For a vertical line load q=1000 kN/m at a horizontal distance x=3m and depth z=6m, what is the vertical stress increase Δσz? The influence value Δσz/(q/z) for x/z = 0.5 is 0.407.

For a uniformly loaded circular area, what is the vertical stress increase Δσz/q directly under the load at the surface (z/R = 0)?

A soil element has major and minor principal stresses of σ1=300 and σ3=100, respectively. What is the normal stress (σn) on a plane inclined at an angle θ=30 degrees to the major principal plane?

A soil element has major and minor principal stresses of σ1=300 and σ3=100, respectively. What is the shear stress (τn) on a plane inclined at an angle θ=30 degrees to the major principal plane?

What is the primary purpose of constructing a stress isobar plot?

For a uniformly loaded rectangular area of 8m by 12m, what is the vertical stress increase at a depth of 10m below the center? For m1=1.5 and n1=2.0, the value of I4 is approximately 0.54.

A rectangular loaded area is 6m by 9m (L=9m, B=6m) and carries a load of 150 kN/m^2. What is the vertical stress increase at a depth of 3m below its center? The parameters are m1=L/B=1.5 and n1=z/b=3/(6/2)=1.0. The influence factor I4 from Table 10.9 for these parameters is approximately 0.80.

In Boussinesq's solution for stresses caused by a point load, what does the term 'r' represent in the equation for vertical stress increase, Δσz = (3P / 2π) * (z^3 / (r^2 + z^2)^(5/2))?

A rectangular area of 3m by 6m is loaded with q=100 kN/m^2. Find the vertical stress increase at a depth of 3m below one of its corners. Use the influence factor I3 from Table 10.8 where for m=B/z=3/3=1 and n=L/z=6/3=2, I3 = 0.1999.

The theories of stress distribution discussed in the chapter, such as Boussinesq's and Westergaard's, are based on principles from which field of study?

For a horizontal line load q on the surface, the vertical stress increase is given by Δσz = (2q/π) * (xz^2 / (x^2 + z^2)^2). Directly under the load (x=0), what is the vertical stress increase?

In Example 10.9, the vertical stress increase from a rectangular load is found by subtracting the stress of a smaller fictitious rectangle from a larger one (Δσz = Δσz(1) - Δσz(2)). What is the justification for this subtraction?

What is the relationship between the angle 2θ on the Mohr's circle and the angle θ of the plane in the soil element?

If a uniformly loaded circular area has a radius R=4m, what is the vertical stress increase as a fraction of q (Δσz/q) at a depth z=4m directly below the center?

If the influence value (IV) of a Newmark's chart is 0.005, how many elements (N) is the chart divided into?

The solutions for stress increase from various loads presented in the chapter are derived by integrating the solution for what fundamental load case?

In the general formula for vertical stress Δσz = (P/z^2) * I1, the influence factor I1 is a function of what single nondimensional parameter?

For a vertical line load, at what value of x/z does the influence factor Δσz/(q/z) have its maximum value?