Find the vertical stress increase at 4 m below A, B, and C.
Answer to Problem 8.27CTP
The increase in the vertical stress
The increase in the vertical stress
The increase in the vertical stress
Explanation of Solution
Given information:
The depth of the point from the ground level,
The intensity of the uniform pressure,
Calculation:
Vertical stress increase at point A:
Show the free-body diagram of the L-shaped raft as in Figure 1.
Rectangle 1:
Find the value of
Substitute 4 m for
Find the value of
Substitute 6 m for
Refer Figure 8.16 “Variation of
For
The value of variation
Find the increase in vertical stress
Substitute
Rectangle 2:
Find the value of
Substitute 8 m for
Find the value of
Substitute 6 m for
Refer Figure 8.16 “Variation of
For
The value of variation
Find the increase in vertical stress
Substitute
Rectangle 3:
Find the value of
Substitute 8 m for
Find the value of
Substitute 8 m for
Refer Figure 8.16 “Variation of
For
The value of variation
Find the increase in vertical stress
Substitute
Find the increase in vertical stress
Substitute
Therefore, the increase in the vertical stress
The vertical stress increase at point B:
Show the free-body diagram of the L-shaped raft as in Figure 2.
Rectangle 1:
Find the value of
Substitute 12 m for
Find the value of
Substitute 6 m for
Refer Figure 8.16 “Variation of
For
The value of variation
Find the increase in vertical stress
Substitute
Rectangle 2:
Find the value of
Substitute 8 m for
Find the value of
Substitute 14 m for
Refer Figure 8.16 “Variation of
For
The value of variation
Find the increase in vertical stress
Substitute
Rectangle 3:
Find the value of
Substitute 8 m for
Find the value of
Substitute 6 m for
Refer Figure 8.16 “Variation of
For
The value of variation
Find the increase in vertical stress
Substitute
Find the increase in vertical stress
Substitute
Therefore, the increase in the vertical stress
The vertical stress increase at point C:
Show the free-body diagram of the L-shaped raft as in Figure 3.
Rectangle 1:
Find the value of
Substitute 12 m for
Find the value of
Substitute 14 m for
Refer Figure 8.16 “Variation of
For
The value of variation
Find the increase in vertical stress
Substitute
Rectangle 2:
Find the value of
Substitute 12 m for
Find the value of
Substitute 8 m for
Refer Figure 8.16 “Variation of
For
The value of variation
Find the increase in vertical stress
Substitute
Rectangle 3:
Find the value of
Substitute 8 m for
Find the value of
Substitute 8 m for
Refer Figure 8.16 “Variation of
For
The value of variation
Find the increase in vertical stress
Substitute
Find the increase in vertical stress
Substitute
Therefore, the increase in the vertical stress
Want to see more full solutions like this?
Chapter 8 Solutions
Fundamentals of Geotechnical Engineering (MindTap Course List)
- P2: A flexible L-shaped raft shown in Figure applies a uniform pressure of 60 kN/m2 to the underlying ground. Find the vertical stress increase at 4 m below A, B, and C - 6 m 8 m 4 m A 8 m В Carrow_forwardRepeat Problem 10.12 for q = 700 kN/m2, B = 8 m, and z = 4 m. In this case, point A is located below the centerline under the strip load. 10.12 Refer to Figure 10.43. A strip load of q = 1450 lb/ft2 is applied over a width with B = 48 ft. Determine the increase in vertical stress at point A located z = 21 ft below the surface. Given x = 28.8 ft. Figure 10.43arrow_forwardA point load of 500 kN is applied at the ground level. Plot the lateral variation of the vertical stress increase at depths of 2 m, 3 m, and 4 m below the ground level.arrow_forward
- A 10 ft diameter flexible loaded area is subjected to a uniform pressure of 1200 lb/ft2. Plot the variation of the vertical stress increase beneath the center with depth z = 0 to 20 ft. In the same plot, show the variation beneath the edge of the loaded area.arrow_forwardRefer to Figure 8.24. Determine the vertical stress increase, , at point A with the following values: q1 = 100 kN/m x1 = 3 m z = 2 m q2 = 200 kN/m x2 = 2 m FIG. 8.24 Stress at a point due to two line loadsarrow_forwardFor 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 10.41arrow_forward
- 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 10.48arrow_forwardA point load of 1000 kN is applied at the ground level. Plot the variation of the vertical stress increase z with depth at horizontal distances of 1 m, 2 m, and 4 m from the load.arrow_forwardA 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.arrow_forward
- 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 areaarrow_forwardThe Infinite line load as shown in figure has an Intensity of 600 kN/m. Determine the vertical stress at a point A with coordinates x = 5 m and Z = 4 m. | q = 600 kN/m Z=4marrow_forward3.9 Figure P3.3 shows the plan of a loaded area on the surface of a clay layer. The uniformly distributed vertical loads on the area are also shown. Determine the vertical stress increase at A and B due to the loaded area. A and B are located at a depth of 3m below the ground surface. Uniformly distributed vertical load 4₂ = 200 kN/m² ר 2 m 3 m PLAN Uniformly 3 m distributed load on a flexible arca a.~100 kN/m²arrow_forward
- Fundamentals of Geotechnical Engineering (MindTap...Civil EngineeringISBN:9781305635180Author:Braja M. Das, Nagaratnam SivakuganPublisher:Cengage LearningPrinciples of Foundation Engineering (MindTap Cou...Civil EngineeringISBN:9781337705028Author:Braja M. Das, Nagaratnam SivakuganPublisher:Cengage LearningPrinciples of Geotechnical Engineering (MindTap C...Civil EngineeringISBN:9781305970939Author:Braja M. Das, Khaled SobhanPublisher:Cengage Learning
- Principles of Foundation Engineering (MindTap Cou...Civil EngineeringISBN:9781305081550Author:Braja M. DasPublisher:Cengage Learning