CIE 3008 lecture 04 stresses in a soil mass 1

lecture 04stress in a soil mass

CIE 3008 lecture 04 stresses in a soil mass 2

Why do we need to know the stress (strain)?

Stress < StrengthRecall structural engineering (Allowable stress design)

Settlement (deformation) < Allowable

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Outline

• Stress and strain – a review• Components of stress and strain• Calculating stress (strain) on an arbitrary plane –

Mohr circle• Stress – strain relationship

• Distribution of vertical stresses under external loading• Point load• Line load• Circular load• Rectangular load• Empirical stress distribution estimation

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Stress Components

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Calculating stress – strain on an arbitrary plane – Mohr circle

σvσh

σv σy σ1

σh σx σ3

Sign Convention:Normal Stress+ Compression

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Normal and shear stresses – Mohr circle

CIE 3008 lecture 04 stresses in a soil mass 7

Normal and shear stresses – Mohr circle

Sign Convention:Normal Stress+ Compression

Shear Stress+ Clock-wise

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Normal and shear stresses – Mohr circle

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Mohr Circle – Change in shape

σvσh

σv

σh

∆σv

∆σv

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Mohr Circle – Change in shape

σ1σ3

σv

σh

If σv > σh

σv,

σh,

Sign Convention:Normal Stress+ Compression

Shear Stress+ Clock-wise

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Mohr Circle - Example

The soil sample is subjected to equal pressure of 10 kPa. Draw the Mohr circle.

The axial stress is increased to 50 kPa. Draw the Mohr circle.

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A shear stress of 10 kPa is applied at the vertical and horizontal boundaries. Plot the Mohr circle.

Mohr Circle - Example

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State of Stress – Mohr Circle - Pole Method

σ kPa)

kPa)

계산순서:1. 기준면선택2. Pole (극점) 계산3. 구하고자하는면도시응력계산

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State of Stress – Mohr Circle - Pole Method

CIE 3008 lecture 04 stresses in a soil mass 15

State of Stress – Mohr Circle - Pole Method