Deformation of Concrete

Deformation of Concrete

Fall 2010

Dept of Architecture

Seoul National University

12

^th

week

Stress and strain of

cracked sections

7. Stress and Strain of Cracked

Section

Bounds between uncracked and fully cracked stages

Chapter 2, 3, 4, 5

Chapter 7

Chap. 8 Uncracked section

Fully cracked section

Intermediate stage

7.5 RC Section w/o prestress

Uncracked section

Fully cracked section

?

7.6 Partial prestressed sections

7.6 Partial prestressed sections

8.1 Introduction

1. Reduction in stiffness due to cracking 2. Elongation and curvature

3. Stiffness varies from minimum to

maximum (crack to midway between cracks)

4. Two extreme states

5. Interpolation :extent of cracking

8.2 Basic assumptions

1. Free from crack: state 1 2. Fully crack : state 2

3. Bernoulli’s hypothesis

4. Contribution of concrete in the tension zone : tension stiffening

8.3 Strain due to axial tension

1. Free from crack

2. Section in state 2

 

₁

r ct c s ct

N  f A  nA  f A

1) N before cracking lower than the following value

s c

n E

 E

r sr

s

N

  A

Stress in steel

N  N

r

2) After cracking

2 s

s

N

  A

Stress in steel at a crack

2

1

s

s s

N

  A E

 

1 1

1

s c

c c s c

N N

E A nA E A

    



Axial force

N Nr

(state 1)

(state 2)

2

1

s

s s

N

  A E

1

1

1

s

c

N

  A E

max

s



s



sm

Stress in steel in state 2

s2

sr

Strain in steel

l  l sml

N

N

2

s s sm

  

  

Fully cracked Mean steel strain

Assume strain difference has hyperbolic variation with stress in steel

max

2 sr

s s

s

  

   

 

max 2 1

2 sr

s s s

s

   

   

m 2

s s s

    

2 max

2 sr

s s

s

  

   

 

2

2 2 1

2 sr

s s s

s

   



 

    

 

2 2

1 2

2 2

sr 1 sr

s s

s s

   

 

 

   

 

     

 

     

Let

 ¹ 

_{1 2}

sm s s

      

2

2

1 ^sr

s

 



 

   

 

2 1 2

2

1 ^sr

s

   



 

   

 

1 : bond effect



2

: loading characteristics



8.4 Curvature due to bending

8.5 Curvature due to bending and

axial force

Summary

Torsional deformation