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Lecture 9 Advance Design of RC Structure

1Advance Design of RC Structure

Lecture 9

Design of Raft Foundation

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2Raft Foundations

Raft foundations

A raft is essentially a very large spread footing that usually encompassesthe entire footprint of the structure. They are also known as mat

foundation.

Foundation engineers often consider mats when

The structure loads are so high or the soil conditions so poor that the

spread footings would be exceptionally large. If spread footings wouldcover more than about one third of the building area, a mat will be more

economical.

The soil is very erratic & prone to excessive differential settlements. The

continuity & rigidity of the mat foundation helps in reducing differential

settlement of individual columns relative to each other. Lateral loads are not uniformly distributed through the structure & thus

may cause differential horizontal movements in spread footing. The

continuity & rigidity of the mat will resist such movements.

The uplift loads are larger than spread footing can accommodate.

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3Raft Foundations The bottom of the structure is located below the groundwater table, so

waterproofing is an important concern. The weight of the mat also helps

resist hydrostatic uplift forces from the groundwater.

Types of raft foundation

Cellular raft foundation

Used on site where, poor ground must

resist high bending momentsCrust raft foundation or blanket mat

Slab with thickening under the columns

& walls

Plane raft foundation

Piled rafts

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4Raft Foundations

Methods of designing raft foundation

The conventional rigid methodThis method is easy to apply & the computations can be carried out

using hand calculations.

The application of this is limited to rafts with relative regular

arrangement of columns.

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5Raft Foundations The finite element method

This method can be used for the analysis of raft regardless of the

column arrangements, loading conditions, & existence of cores &

shear walls.

Commercially available computer programs like SAP2000 & SAFE

can be used.

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6Geotechnical Design

Bearing capacity

The allowable bearing capacity of a raft footing is given by

21 0.33

1 10.08 3.28 25.4

fall

N D sq

B B

For B < 1.2m

0.08 25.4allN s

q

Where

qall is allowable bearing capacity in kilopascals

N is standard penetration test (SPT) blow count

B is the width of the footings is the settlement in millimeters

Dfis the depth of the footing in meters

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7/16Lecture 9 Advance Design of RC Structure

7Geotechnical Design

Settlement of raft foundation

The settlement of raft footing can be estimated in a manner similar to

that of spread footings.

Immediate Settlement; based on the theory of elasticity can be used to

estimate the corner settlement of a rectangular footing with dimensions

of L' and B',

2

1 21 1 2'

1

s si F

s s

v vs qB I I I E v

Where

q is the contact stress

B is the least dimension of the footing

vs is the Poisson ratio of the soil

Es is the elastic modulus of the soil

I1 , I2 & IF are obtained from, the table & the figure attached, in terms

of the rations N = H/B (H = layer thickness), M = L/B & D/B

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8Structural Design of Raft Foundation Conventional rigid method

Step 1: Check soil pressure

The resultant of columns working loads

equals:

1 2 3...

total iP P P P P

The soil pressure at any point can be

obtained;

ytotal xallowable

x y

MP Mq y x q

A I I

Where;

A = area of the raft (BL)

Ix = moment of inertia of the raft about

x-axis = BL3/12

Iy = moment of inertia of the raft about

y-axis = LB3/12

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9Structural Design of Raft Foundation

The ex & ey are the eccentricities of the resultant from the C.G. of the raft.

The coordinate of the eccentricities are given by:

1 1 2 2 3 3...

'

total

P x P x P xX

P

'2

x

Be X

1 1 2 2 3 3...

'total

P y P y P yY

P

'2

yLe Y

Compare the maximum soil pressures with net allowable soil pressure

max ,n allq q

Mx = moment of applied loads about the x-axis = Ptotal ex + Mx

My = moment of applied loads about the x-axis = Ptotal ey + My

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Step 2: Draw the shear force & bending moment diagrams

Divide the raft into several strips in the X-direction (B1, B2, B3)

& in the Y-direction (B4, B5, B6, B7)

The soil pressure at the center-line of the strip is

assumed constant along the width of the strip.

( ) ( )

( )2

u total u x

u B

x

P M Lq

A I

( ) ( )

( )2

u total u x

u E

x

P M Lq

A I

The average pressure equals:

( ) ( )

( )

2

u B u E

u avg

q qq

This value shall be used in

the analysis of the strip

The total soil reaction (RB-E) for the strip B-E is equal to:

( ) 2B E u avgR q B L

The total soil reaction (RB-E) for the strip B-E is equal to:

( )5 ( )6 ( )7 ( )8B E u u u uP P P P P

All the loads has

to be factored

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11Structural Design of Raft FoundationThe achieve equilibrium, columns loads & soil reaction must be

modified such that the sum of the forces is equal to zero

( )2

B E B Eu avg

R PP

The modified soil pressure equals:

( )

mod

u avgPq

L

The modified columns loads are obtained by multiplying each of theapplied loads by the factor given by;

( )u avg

B E

P

P

The shear & bending moment can be

computed using regular structure analysis

The same process should be carried out

for all the strips in the raft foundation

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Step 3: Design for flexure

The maximum positive & negative moments can be obtained.

The negative moments need top reinforcement & positive

moment needs bottom reinforcement.

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13Discussions

Any Question?

Notes

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14I1 and I2 for Settlement Equation

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15I1 and I2 for Settlement Equation

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16IF For Settlement Equation

ECCS5105.101_29042009

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