GEO-MECHANICSGEO-MECHANICS(CE2204)(CE2204)

Stresses Under Applied Load Stresses Under Applied Load

Lecture Week No 4

Mdm Nur Syazwani Noor RodiMdm Nur Syazwani Noor Rodi

LINTON UNIVERSITY COLLEGELINTON UNIVERSITY COLLEGESCHOOL OF CIVIL ENGINEERINGSCHOOL OF CIVIL ENGINEERING

INTRODUCTION

The distribution of stress depends on:a)Stiffness of foundation b)Compressibility or stiffness of soilc)Loading conditions – uniform or point.

STIFFNESS OF FOUNDATION

Type Comment Example

FlexibleHas no resistance todeformation and will

bend into a dish shape

Earth embankment/silo

Stiff Some resistance to

bending, forms a flatter dish shape

Raft foundation

RigidWill not bend, moves

down uniformlySmall thick r.c. pad

foundation

STIFFNESS OF FOUNDATION

Contact pressures beneath foundations under uniform loading

DETERMINATION OF SOIL STRESSES DUE TO APPLIED LAODS

In civil engineering, increases in vertical stresses are usually considered and Boussinesq in 1885 developed expressions for various loading conditions, based on the following soil conditions:

a) Semi-infinite in both lateral and vertical directions

b) Isotropic (same in all directions)

c) Homogeneous (uniform, i.e. not layered)

d) Elastic (Hooke’s law of stress and strain)

BOUSSINESQ EQUATION (1885)

Applicable only for point loads, Q

pv Iz

Q

2

25

2

5

1

1

2

3

2

3

zrR

zI p

Where Ip = the point load influence factor

Variation of Δσ vertically with depth,

Variation of Δσ horizontally offset from point load,

EXAMPLE 1

A foundation carrying a point load of 500kN will be place on the site at ground level. Determine the variation of Δσ vertically to the depth of 10m for the following:

a) 1m offset from the point loadb) 3m offset from the point loadc) 5m offset from the point load

FADUM’S CHART (1948)

qkv

Only applicable to: a) Rectangles structureb) Increase beneath a corner

of the foundation

EXAMPLE 1

Figure below show the plan of a rectangular foundation which transmit a uniform contact pressure of 180kPa. Determine the vertical stress induced by this loading at a depth of 3m, 5m &10m below point A, B, C & D

20m

12m

A

B

6m

10m

C2m

3m

D2m

4m

NEWMARK’S CHART (1942)

N = Number of segment

Iq = Influence value/factor

q = Vertical stress

qIN qv

Applicable to any shaped foundation

EXAMPLE 1

Consider a circularly loaded area on the ground surface. Given diameter of circular area of 1500mm and uniform pressure of 200 kN/m2, Determined the vertical stress induced by this loading at

a) a depth of 3m below the centre of the foundationb) a depth of 5m below the circumference of the

foundationc) a depth of 3m below the point of 4.5m offset from

the centre of the foundation

TUTORIAL 1Figure below shows the plan of a large circular raft foundation (d = 20m); the centre area (d = 10m) transmits a contact pressure of 60kPa and the outer annular area transmits a contact pressure of 150 kPa. Using the Newmark’s chart provided, calculate the intensity of vertical stress induced at point in the soil mass 6m below A, B and C.

A B C