Chapter 10, Problem 10.10P

### 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

# Refer to Figure 10.41. Given: q2 = 3800 lb/ft, x1 = 18 ft, x2 = 8 ft, and z = 7 ft. If the vertical stress increase at point A due to the loading is 77 lb/ft2, determine the magnitude of q1.Figure 10.41

To determine

Calculate the magnitude of line load q1.

Explanation

Given information:

The line load (q2) is 3,800lb/ft.

The horizontal distance between two line loads (x1) is 18ft.

The horizontal distance between line load q2 to point A (x2) is 8ft.

The depth of the stress from ground surface (z) is 7ft.

The vertical stress increase at point A (Δσz) is 77lb/ft2.

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 7ft for z, 18ft for x1, and 8ft for x2.

Δσz(1)=2q1×73π[(18+8)2+72]2=686q1525,625π=4.15×104q1

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.

Δσz(2)=2q2z3π[x22+z2]2

Substitute 3,800lb/ft for q1, 7ft for z, and 8ft for x2

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