Shrinkage Forrnula

[JohnRwals]

Hello!

I saw these two formula about internal stress of concrete/reinforcement from Dr. Moehle's
Seismic Design of Reinforced Buildings.
I could figure out (5.4), but I do not know how to derive (5.5).
Can anybody explain how to obtain (5.5) expression?

Thanks!

 

[HTURKAK]

@JohnRwals ,

With visual inspection i would say that , your approach to find fc ( the expressions ,n red frame ) is correct. In order to find the steel stress , just write the equilibrium of internal forces ,

In this case the developing comp. force at rebar will be equal to tension force at conc.

fs* As= fc *Ac ⇒ fs = fc*(Ac/As ) then put the fc expression and make some simplification.



Use it up, wear it out;
Make it do, or do without.

NEW ENGLAND MAXIM

 

[JohnRwals]

This is unrestrained reinforced concrete column model


Thanks, HTURKAK!
These formula were assumed P=T as you suggested...

BTW, do these formula make sense?
Let's assume no reinforcement is used, like in the plain concrete column.
A_st=rho_l=0 ---> f_c=0 and f_s=***(Not zero), which means only steel takes the axial load.
This does not make sense! (Because I assume there is no reinforcement.)

I was searching for any paper or book referring to these formula.
But, I could not find out any.
These simple formula are good and convenient to use
as the author shows as an example with the specific condition in the book.

Are these formula and their derivation right?

-JRW

 

[HTURKAK]

Mr JohnRwals ,

Pls find my answers ;


-Q =BTW, do these formula make sense?
- A=It make sense but just gives an idea to estimate the effect of drying shrinkage on internal stresses of an unloaded, unrestrained reinforced concrete cross section ,

- Q= Let's assume no reinforcement is used, like in the plain concrete column. A_st=rho_l=0 ---> f_c=0 and f_s=***(Not zero), which means only steel takes the axial load. This does not make sense! (Because I assume there is no reinforcement.)
- A= This formula derived and valid for unrestrained , symmetrical reinforced concrete cross section. If you keep the long expression without simplification, ( The expression with As , ) when As is zero, fs will also be zero. A similar situation , if y=(x**3)/x , and when you simplfy you will get y= X**2 . However , y=(x**3)/x is not equal to y= X**2 for X=0.
****
-Q= Are these formula and their derivation right?
- A= IMO , Yes right and valid for practical steel percentages ..




Use it up, wear it out;
Make it do, or do without.

NEW ENGLAND MAXIM

 

[JohnRwals]

For As=0, fs of (5.5) is not zero...