Stress Distribution 3

8/17/2019 Stress Distribution 3

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Stress Distribution

in Soil Mass – Part 3

KAEA 3233 - SOIL MECHANICS II

Dr. Tan Chee GhuanDepartment of Civil Engineering

Faculty of Engineering

University of Malaya1


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Vertical Stress Caused by a Rectangular Load

2

Shallow foundation


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3


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4

Table: Variation of I2 with m and n


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5

Table: Variation of I2 with m and n (continued)



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6

Chart gives the stress at a

distance z, beneath a corner

of a rectangular loaded area


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Example 4

7The flexible area shown in the figure is uniform loaded. Given that

q = 150 kN/m2, determine the vertical stress increase at point A.


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Vertical stress beneath loaded areas of

irregular shape

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• The vertical stress at any particular depth in the soil

due to the action of vertical load on the surface of the

ground was given and explained by the famous

Boussinesq’s theory.

• This theory gave formulae to calculate vertical stresses

at a point for different types of vertical loading, taking

into consideration only a few well defined and

standard shape of loading like a point loading, line

loading, strip loading, rectangular loading and circularloading.

• When some complex shape of loading, like a plan of a

structure was given, it became very cumbersome to

calculate the vertical stress using these formulas.


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• Hence, a need for more simpler and faster method of

stress calculation was realized.

•

Newmark formulated a new simple graphical methodto calculate the vertical stress at any particular depth

caused due to any shape of vertical uniformly

distributed loading in the interior of an elastic,

homogeneous and isotropic medium, which is bounded

by horizontal planes (i.e. semi-infinite medium).

Vertical stress beneath loaded areas of

irregular shape


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Newmark’s Influence chart

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How to UseNewmark’s Influence Chart

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How to UseNewmark’s Influence Chart

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Procedures:

1. Draw the plan of the loaded area on a tracing sheet to the same scale asthe scale of the line segment AB on the chart representing the depth, z.

2. Mark the location of the point (P) where the vertical stress is required on

the plan.

3. Place the tracing sheet over the chart, such that P coincide with the center

of the chart.

4. Count the number of mesh (n) covered by the plan.

• In case of partly covered mesh an intelligent judgement of the fraction of mesh

covered is required.

• Let the total number of mesh be equal to ‘n’ . Then the vertical stress at the

desired depth is given by:


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z = 5 m

Example 6

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A raft foundation of dimension 11 m x 6.2 m is subjected to total load of 10000 kN

and placed on the surface of the ground. Determine the vertical stress due to the

raft foundation at a depth of 5 m below the ground level. The raft.

Number of mesh covered = 29 x 4

(n) = 116

σz = 0.005 x 116 x {10000/(11x6.2)}

= 85 kN/m2


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Example 6

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Given:

Determine the vertical stress of soil at 5 m below the point A using Newmark’s

Influence Chart.

A

5 m

5 m

2.5 m

2 mq = 150 kN/m2


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Stress Distribution 3