PDF Deformation of Concrete - Seoul National University

Deformation of Concrete

Fall 2010

Dept of Architecture

Seoul National University

5 th week

Time-dependent stress and

strain in composite sections

2.5 Time dependent s-s in composite section

2.5.1 Instantaneous stress and strain 2.5.2 Change in s-s during period

2.5.1 Instantaneous stress and strain

1)Equivalent Forces= load + prestressing force 2) 

^O

  t

0

and    t

0

concrete

Normal reinforcing bars

prestressing

 

 

₀

c

t

o

y

     

_c

 E t

_c

   

_o

  

_o

t

_o

    t

_o

y  

     

ns

t

o o

t

o

t

o

y

ns

     

ns

  t

0

 E

s

  

o

  t

0

    t

0

y

ns

 

 

0

 

0

 

0

ps

t

o

t t y

ps

    

^ps

 

^{t0 }

 

^ps _initial ^{Eps }_^o

   

^{t0  t y0 ps}_

2.5.2 Change in s-s

The change of strain due to creep and shrinkage of concrete and relaxation of prestressed steel is first artificially restrained by application of axial force and bending moment.

 

o

2

1

c

I B N B A M E AI B





    

   

            

   

The restraining forces

creep shrinkage relaxation

N N N N

M M M M

   

       

  

           

       

   

o 0

1 0

m

c c

c

i c c

creep i

A B t

N E

B I t

M

 

 

  

  

      

      

 



    

1 0

m

c c cs

c

i c c

shrinkage i

A B

N E

B I M





 

  

      

     

 



   

prestressing

ps pr

ps ps pr i

N A M A y





   

 

     

 



 

   

 

⁰

0

0

, 1 ,

c c

E t t E t

 t t

 

Change of strains due to creep and shrinkage and relaxation

Restrained stress in concrete

Change in stresses in concrete, reinforcing bars and prestressing

steel

Restrained forces due to creep, shrinkage and

relaxation

Think about free strain due to temperature

     

, , 0 , 0 0

c restrained

E t t

c

t t

c

t

cs

          

  ,

0

 

c restrained

E t t

c o

y

   

     

 

ns

E

ns o

y

ns

  

    

ps pr

E

ps o

y

ps

     

        