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INPUT   DATA

♥ EXAMPLE Of Input/Output

Title

Depth of point, z		m
Horizontal distance, r		m
Surface load, P		N

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OUTPUT   VARIABLES   &   GRAPHS

Variables	Values	Units
♦  Vertical stress - Boussinesq, σz		N/m2	Graphs:  Stress variation with horizontal distance    Stress variation with depth
♦  Vertical stress - Westergaard, σz		N/m2
♦  Shear stress - Boussinesq, τrz		N/m2

Vertical Stress In A Soil Due To Surface Point Loading

The vertical stress in a soil caused by a concentrated surface load is commonly estimated by two equations based on the elastic theory, and the assumptions that the soil mas is semi-infinite, homogeneous and isotropic. These equations are the Boussinesq and the Westergaard equations given below:

where
     σ_z = vertical stress at a point
     P = total conentrated surface load
     z = depth of point
     r = horizontal distance from vertical projection of load point

The tangential shearing stress at the point acting normal to the rz plane is given by:
     τ_rz = σ_z[r/z]

Tips

    ◊ Use link EXAMPLE Of Input/Output  to demo data entry expectations and results; you may edit & use it as starting point

BIBLIOGRAPHY

• Hicks TG; Civil Engineering Formulas, Pocket Guide; McGraw Hill, New York, 2002.
• Mikhelson I; Structural Engineering Formulas; McGraw Hill, New York, 2004, Chapter 4.
• Young WC & Budynas RG; Roark's Formulas for Stress and Strain; 7th Edition, McGraw Hill, New York, 2002.