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Estimation of restraint

Introduction

C660 - Estimation of restraint This calculator estimates restraint in a wall cast onto a rigid based. The method is based of the ACI approach in which the restraint at the joint is determined by the relative stiffness of the new section and the section against which it is cast. The variation in restraint with height is determined by the length to height ratio. The method is described in detail in Appendix A5 PAGE 2 RESTRAINT Wall geometry Base geometry

Relative areas

Relative modulus of elasticity

Restraint at the joint R j

CIRIA C660

The wall geometry is define by the length L , the height H and the thickness, h The base geometry is define by the width W and the thickness, h . The length is assumed to be the same as the length of wall being cast The ratio of the cross sectional area (c.s.a.) of the wall A n and the base A o is calculated. The relative areas of influence A o and A n may be difficult to define. For example, when a wall is cast onto a slab, what width of slab should be considered as providing effective restraint? In such circumstances it is recommended that the relative area is assumed to be in proportion to the relative thicknesses, h n and h o , of the wall and slab. The following simple rules may be applied. • For a high wall cast at the edge of a slab assume A n /A o = h n /h o • For a wall cast remote from the edge of a slab assume A n /A o = h n /2h o • For a slab cast against an existing slab assume A n /A o = h n /h o CIRIA 135 recommends that the ratio E n /E o is assume to be in the range 0.7 to 0.8 at early-age. The lower value gives most conservative result and should be used for conditions in which cool-down is most rapid. When estimating restraint to long term deformations, should there be any differential strains, it should be assumed that E n /E o = 1

Rj

1 An En 1 Ao Eo

PAGE 1

Estimation of restraint

Calculator

Estimation of restraint Wall on a rigid base Cells for input data Dimensions Length Height Thickness c.s.a. A n

Wall 12 4 0.5 2

Base m m m 2

m

Width Thickness c.s.a A o

Ratio of areas

A n /A o

0.83

Ratio of moduli

E n /E o

1.00

Restraint factor at joint R j

0.55

2.85 m 0.85 m 2.42 m2

4.5 4.0

Height (m)

3.5 3.0 2.5 2.0 1.5 1.0 0.5

0.0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Restraint

CIRIA C660

PAGE 2

Introduction

C660 - Estimation of restraint This calculator estimates restraint in a wall cast onto a rigid based. The method is based of the ACI approach in which the restraint at the joint is determined by the relative stiffness of the new section and the section against which it is cast. The variation in restraint with height is determined by the length to height ratio. The method is described in detail in Appendix A5 PAGE 2 RESTRAINT Wall geometry Base geometry

Relative areas

Relative modulus of elasticity

Restraint at the joint R j

CIRIA C660

The wall geometry is define by the length L , the height H and the thickness, h The base geometry is define by the width W and the thickness, h . The length is assumed to be the same as the length of wall being cast The ratio of the cross sectional area (c.s.a.) of the wall A n and the base A o is calculated. The relative areas of influence A o and A n may be difficult to define. For example, when a wall is cast onto a slab, what width of slab should be considered as providing effective restraint? In such circumstances it is recommended that the relative area is assumed to be in proportion to the relative thicknesses, h n and h o , of the wall and slab. The following simple rules may be applied. • For a high wall cast at the edge of a slab assume A n /A o = h n /h o • For a wall cast remote from the edge of a slab assume A n /A o = h n /2h o • For a slab cast against an existing slab assume A n /A o = h n /h o CIRIA 135 recommends that the ratio E n /E o is assume to be in the range 0.7 to 0.8 at early-age. The lower value gives most conservative result and should be used for conditions in which cool-down is most rapid. When estimating restraint to long term deformations, should there be any differential strains, it should be assumed that E n /E o = 1

Rj

1 An En 1 Ao Eo

PAGE 1

Estimation of restraint

Calculator

Estimation of restraint Wall on a rigid base Cells for input data Dimensions Length Height Thickness c.s.a. A n

Wall 12 4 0.5 2

Base m m m 2

m

Width Thickness c.s.a A o

Ratio of areas

A n /A o

0.83

Ratio of moduli

E n /E o

1.00

Restraint factor at joint R j

0.55

2.85 m 0.85 m 2.42 m2

4.5 4.0

Height (m)

3.5 3.0 2.5 2.0 1.5 1.0 0.5

0.0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Restraint

CIRIA C660

PAGE 2