Emad Gad

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1/34Swinburne University of Technology

Fundamentals of Design of

Residential Slabs Complying to

AS2870-2011

Emad GadSeptember 2015

Content Basic assumptions

Design requirements

Recommended methods of design

Design examples

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Assumptions3

Assumptions

4

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Assumptions5

Assumptions Control, but not prevention, of shrinkage cracking

Control, but not prevention, of cracking due to footing

movement

Design life is 50 years

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Design Actions

Design actions to be considered for serviceability andsafety against structural & bearing failures are:

Permanent action (G)

Imposed action (Q)(in acc. to AS/NZS 1170.1)

Foundation movement(characteristic movement with less than 5% chance of being exceeded in 50 years in acc.

to AS 2870.11)

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Load Combinations For slab failure, reactive soil movements & settlement

G+0.5Q

Design bearing strength

0.33*ultimate bearing capacity of soil

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Causes of Movement

Foundation movement happens if reactive soil issubjected to changes in moisture content which could

be due to:

Seasonal and regular climatic effects

Irregular climate effects such as droughts

Trees

Unusual moisture conditions caused by leaks, drains,

channel, ponds, swimming pools & etc.

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Moisture changes and foundation movement

Modelled idealised ground heave

Idealised moisture content profile

50% VMC50% VMC Cover

Cover

10

37% VMC

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Idealised Edge Heave & Edge Settlement Condi tions11

EDGE HEAVE

EDGE SETTLEMENT

Lytton Model

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Lytton Model13

Mitchell Centre Heave ModelEdge settlement

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Mitchell Edge Heave Model15

Effects of Movements

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Excessive slab deformation results in wall cracking, door/window jamming and other damages

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Slab Strength Requirements

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Slab Ductil ity Requirement

To ensure the ductility of cross section: 1.2

Where Z .

As per the recommendation by AS2870-2011

. 2.7 ( for sagging) & 1.8 (for hogging)

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Sagging (edge heave)Hogging (edge settlement)

Serviceabil ity Requirements Max design differential deflection of slabs has to be

limited as per Table 4.1, AS2870-11 for different types

of construction

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Slab Differential Deflection (interpretation)21

Acceptable Slab Design Methods

DEEMED-TO COMPLY (Chapter 3)

DESIGN BY ENGINEERING PRINCIPLES

(Chapter 4, simplified / graphical method)

WALSH METHOD

MITCHELL METHOD

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Deemed to Comply

Design of waffle slab based on the deemed to comply is done with reference toFigure 3.4 of AS2870-2011

Example 1: Work out the minimum section depth & reinforcement requirements

for a waffle slab supporting an articulated masonry veneer building of the

dimensions of 12m*15.6m on a Class H2 site

Min required depth: 385mm. Required rebar: 3N16 (Edge beam, bottom), 1N16

(Internal beam, bottom), SL82 (slab mesh, top)

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Design by Eng. Principles Simplified or graphical method is done by reference to

the relevant design graph (Figure 4.1, AS2870-2011)

and limited to:

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Figure 4.1

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movement vs. unit

stiffness ratio

Design by Eng. Principles

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Design Graph- Development Background

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Design Graph- Development Background

Process of Slab Design Using Design Graph1) Find given the site class (refer Table 2.3, AS2870-2011)

2) Work out allowable slab differential deflection ()

given the type of construction and slab length (refer Table4.1, AS2870-2011

3) Read off the required unit stiffness corresponding to

(from Figure 4.1, AS2870-2011)

4) Work out the required section depth (D) for slab

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Example: Design by Eng. Principles

Example 1 (by Eng. Principles): Work out the minimum section depth &reinforcement requirements for a waffle slab supporting an articulated masonry

veneer building of the dimensions of 12m*15.6m on a Class H2 site

For H2 site class:

(from Table 2.3, AS2870-2011)

(from Table 4.1, AS2870-2011)

2.5 (if there is no further in formation we take 2.5 conservatively)

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30

/ =8.90

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number of beams running in long (15.6m) direction, : 10 1 & corresponding 12

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/ =8.90

11

/12 =8.90

8.4 =8.90

8.4=10.

~460

Use the same process to check

the adequacy of the slab depth for

the other direction of slab; userelevant parameters , i.e.

14 & 15.6

Walsh Method - Background & Assumptions It followed the Lytton model

Mound is based on Winkler springs

Mound shape is primarily flat with the edges modelled

as parabolic over the edge distance e (mound height

)

Edge Heave 0.5

Edge Settlement 0.7

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Walsh Method- Background & Assumptions33

Edge distance e

For edge settlement in (m)

For edge heave in (m)

0.2 0.6

where is in (mm) and e is in meters in both

equations

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Walsh Method- Theoretical background35

Edge distance &

Factor for Walsh Mound36

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Mound shape & factor fo r Walsh Method

The is 0.67 for 120 on normal soilprofiles (from Figure F2, AS2870-2011)

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Edge Distance Estimation- Example Work out the edge distance given the following design

parameters:

Slab Length: L=14m, 20, & 2.3

foredgesettlement:

.

+

= 0.84m

foredgeheave:

0.2 14 0.6

1.4m

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Mound Shape-Walsh method

Plot of mound shape for edge heave condition based on Walshmethod for a range of from 10 to 90 mm ( 2.3

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-10

0

10

20

30

40

50

60

70

80

90

100

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Ym(

mm)

Edge distance (m)

Heave profiles -Walsh Method

Ym=10mm

Ym=20mm

Ym=30mm

Ym=40mm

Ym=50mm

Ym=60mm

Ym=70mm

Ym=80mm

Ym=90mm

Process of Analysis - Employed in Walsh Method

Analyse trial raft to determine stiffness properties

Perform an iterative analysis of the edge effects to find the limit

of the support provided

Carry out structural analysis of the raft slab based upon the

support conditions which were derived from the earlier analysis

Check if the section has cracked. If so, then analyse as cracked

section

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Moment M and Stiffness EI-Walsh

Simplified equations for analysis of rafts to be usedtogether with tabulated support indices by Walsh

(CSIRO-1978)

Walsh produced tabulated values for C1 and C2 which

are function of footing geometry and soil properties.

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CORDhttp://www.fmgengineering.com.au/our-services/design-software.html

Code Oriented Raft Design by Walsh method

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Mitchel Method (Assumptions)

Mound is based on static equilibrium Weight of house must equal stiffness forces provided by the foundation as the

ground soil system settles under the house load

In Mitchell method free shape of mound caused by moisture changes is

required (i.e. unloaded mound shape, similar to Walsh s method)

Gravity forces (house & raft slab loads) are equal & opposite to the soil forces

after equilibrium is reached

Bending moments from house & slab forces are equated to bending moments

corresponding to assumed raft slab curvature (

Mound shape is exponential over a distance X from raft centreline

Footing displacement=soil displacement at all points of contact

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Mitchel Method Process

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Notes by P Uno

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Notes by P Uno

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Notes by P Uno

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Mitchel Method

Notes by P Uno

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Notes by P Uno

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Notes by P Uno

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Notes by P Uno

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Notes by P Uno

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Notes by P Uno

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Notes by P Uno

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Notes by P Uno

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Notes by P Uno

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Notes by P Uno

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Example: Design a waffle slab supporting a full masonry

building on a Class H2 in Melbourne

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12 Foundation Length

B 8.4m Foundation width

1 /m (i.e. 1 KPa produces 1mm of soil settlement)

70 mm (Table 2.3, AS 2870-2011)

0.7 49 (Appendix F, AS 2870-2011)

2.3 (Table 2.4, AS 2870-2011)

10mm (Table 4.1, AS 2870-2011)

0.2

0.122 (say 0.1 conservatively)

2.29 Critical depth & 0 embed. Depth

.

= 7.86 [~8 approximately]

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Example cont.

0.2,

0.1, 8

For hogging condition 0.85

For sagging condition ~0.79

Since the smaller value of would produce greater bending

moment and stiffness requirements, the sagging condition in this

example (edge heave) would govern the design (i.e. 0.79 is

employed)

1- ;

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Example cont.

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Example cont.

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Bending moment and stiffness

1-

.

1-0.79 190.5 (Say 200 )

Divided between 8 beams running in long direction 25KNm is the required bending

moment to be carried by each internal/edge beam of the waffle slab

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L=12m

B=8.4m 1090mm

110mm

Required Moment of Inertia

25 10

30 10 30 10

15000 (as per AS2870 for 20MPa)

. 2000 10 (required)

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Design-Internal Beam for Sagging Try 460

50 (cover to bottom steel)

50 410

201 (1N16)

13.33

0.0044

0.0594

)+ 2

0.0594)+ 0.0594 20.0594 0.290

0.29 410 119 depth to neutral axis

n

13.33 201410 119

. 900 10 2000 10

evised the section depth up

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16

8 SL82 Mesh Reo 8

5

375

110

1200

E = 15000 MPa (AS2870)

20MPa Concrete

Design-Internal Beam for Sagging Try

50 (cover to bottom steel)

50 700

201 (1N16)

13.33

0.0026

0.0348

)+ 2

0.0348)+ 0.0348 20.0348 0.231

0.231 700 162 depth to neutral axis

n

13.33 201700 162

. 2476 10 2000 10

64

16

8 SL82 Mesh Reo 8

5

665

110

1200

E = 15000 MPa (AS2870)

20MPa Concrete

you may refine

the depth

slightly down

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Use the same process to check the trial design for theedge beam under sagging with:

600

Repeat the same process to check the adequacy of the

design under hogging

for this case the required & are to be obtained

based on the relevant moment correction factor (in

this example 0.85 )

110 (effective width of beam)

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Example cont.

SLOG http://www.slog.net.au/ For design of slabs and residential footings (developed by Peter Mitchell)

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Thank you

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