Chapter 10, Problem 10.9P

Principles of Geotechnical Enginee...

9th Edition
Braja M. Das + 1 other
ISBN: 9781305970939

Chapter
Section

Principles of Geotechnical Enginee...

9th Edition
Braja M. Das + 1 other
ISBN: 9781305970939
Textbook Problem

For the same line loads given in Problem 10.8, determine the vertical stress increase, Δσz, at a point located 4 m below the line load, q2.Refer to Figure 10.41. Determine the vertical stress increase, Δσz, 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

To determine

Calculate the vertical stress increase (Δσz) at point A.

Explanation

Given information:

The line load (q1) is 110kN/m.

The line load (q2) is 440kN/m.

The horizontal distance between two line loads (x1) is 6m.

The horizontal distance between line load q2 to point A (x2) is 0.

The depth of the stress from ground surface (z) is 4m.

Calculation:

Calculate the vertical stress increase at point A (Δσz(1)) due to line load q1 by using the principles of the theory of elasticity as follows.

Δσz(1)=2q1z3π[(x1+x2)2+z2]2

Substitute 110kN/m for q1, 4m for z, 6m for x1, and 0 for x2.

Δσz(1)=2×110×43π[(6+0)2+42]2=14,080π×2,704=1.657kN/m2

Calculate the vertical stress increase at point A (Δσz(2)) due to line load q2 by using the principles of the theory of elasticity as follows

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