Neutral Axis 6

[struggle66]

Hi
Recently I attended a two days course on RC design. The speaker who is a quite famous professor here used the centroidal axis(center of the mass) Y=(Summation AY/ Summation A)as neutral axis and find the stresses for both uncracked and cracked section. I am really really confused since I remember that during my university, I used C=T & strain compatibility to find neutral axis and stresses for cracked section. And for uncracked section I used MY/I to find stresses. Without any axial force, if y=0 in My/I, the stress will be zero @y=0. Does it mean centroidal axis = neutral axis for uncracked section?Neutral axis should vary according to the moment. Isn't it? I know this is really basis in engineering but can somebody help me?
Thanks

 

[IDS]

Should read through properly before clicking submit:

so if we transform the stress in proportion to E

should be:

so if we transform the area in proportion to E

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[RFreund]

Multiple layers of reinforcement, post-tensioning, and non-zero axial load can all be dealt with easily with a closed form solution

Where can I research more about a closed form solution. I thought you've posted before about this but can't seem to find it. Currently I have setup calcs which use iteration or draw a P-M interaction but I'd be nice if I could use a closed form equation as long as it is easy enough to adapt to different rebar layouts, etc. Thanks.

EIT

http://www.HowToEngineer.com

 

[Denial]

My website (

http://rmniall.com)

offers a spreadsheet that will calculate the neutral axis location (and a heap of other stuff) for any shape of concrete section, any concrete stress-strain relationship, any steel stress-strain relationship, and any loading that comprises a combination of axial force and bi-directional bending moment.[ ] The only assumption it makes is the old warhorse that "plane sections remain plane".

 

[IDS]

RFreund: Did you look about six posts up?

Open source spreadsheets with examples can be found at:
Using RC Design Functions
SLS Design of Reinforced Concrete Sections
ULS Design of Reinforced Concrete Sections

I also have a spreadsheet that does biaxial bending. It is nowhere near as flexible as the work by Denial, but it does use the closed form solutions for the NA position for any given angle. An iterative solution is the only option for finding the angle under biaxial bending:
Faster Biaxial Bending

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[RFreund]

oops.

EIT

http://www.HowToEngineer.com

 

[struggle66]

Thanks Everyone For your replies, suggestions and spreadsheets.

Attached is the example that the professor used.

So can I say

For RC cracked section,if material properties are linear(triangular stress block), N.A is at centriodal axis of the cracked section which is what the professor assumed in his example.Which can also be found from C,T and M like Rapt mentioned above.

Should it be wrong to use the iterative approach since it is also a way of finding zero strain.

In case of multiple layers of reinforcement, PT & non-linear material properties, iterative approach is required.

Regret that I didn't study all these basic thing during university.

 

[IDS]

Should it be wrong to use the iterative approach since it is also a way of finding zero strain.

No, There is nothing wrong with it, it just takes longer.

In case of multiple layers of reinforcement, PT & non-linear material properties, iterative approach is required.

Not necessarily, or only partially.
- PT (or combined axial load and bending) can be solved without any iteration.
- With multiple layers of reinforcement you need to find which layers are in the compression zone to adjust the modular ratio. The calculation is than the same as for one layer.
- With a bi-linear stress strain diagram you may need to iterate to find which layers have yielded, the exact NA location can then be found without iteration.
- An Ultimate Limit State analysis with a rectangular, linear-rectangular, or parabolic-rectangular stress block (or any other stress block that is easily integrated) can be solved without iteration for a rectangular or trapezoidal section.
- Non rectangular sections can be divided into trapezoidal sections. You then need to iterate to find the layer which contains the NA, and find the exact position within the layer in a single step.


Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/