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Principles of Geotechnical Enginee...

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

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BuyFindarrow_forward

Principles of Geotechnical Enginee...

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

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.

images

Figure 10.42

To determine

Calculate the magnitude of line load q2.

Explanation

Given information:

The magnitude of line load (q1) is 375kN/m.

The horizontal distance between two line loads (x1) is 7.5m.

The horizontal distance between line load q2 to point A (x2) is 5m.

The depth of the stress from ground surface (z) is 5m.

The vertical stress increase at point A (Δσz) is 58kN/m2.

The angle of line load q2 with horizontal (θ) is 63°.

Calculation:

The line load q2 inclined at an angle of 63° with horizontal surface.

Calculate the horizontal component of line load q2 as shown below.

q2(H)=q2cos63°=0.454q2

Calculate the vertical component of line load q2 as shown below.

q2(V)=q2sin63°=0.891q2

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[x22+z2]2

Substitute 375kN/m for q1, 5m for z, and 5m for x2.

Δσz(1)=2×375×53π[52+52]2=93,7502,500π=11.94kN/m2

Calculate the vertical stress increase at point A (Δσz(2)) due to the vertical component of line load q2 as shown below.

Δσz(2)=2q2(V)z3π[(x1+x2)2+z2]2

Substitute 0.891q2 for q2(V), 5m for z, 7.5m for x1, and 5m for x2.

Δσz(2)=2×0

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