PT slab: effective width? 1

[seattlemike]

Hello fellow engineers,

I have not designed a post-tensioned slab before although I do have several design examples and some office help.

For Post-Tensioned concrete slabs with banded tendons, what is the effective width for the slab design? My slab is 10' thick, and the trib load is 20' wide.

I am using the PTData & PTPlus software.
Thanks guys & gals!

Mike

 

[AUCE98]

I assume you mean 10" thick for the slab. Is your slab you are designing one-way or two-way? One-way slabs can be designed based on a 1' trib width, whereas a two-way system requires the entire slab tributary width attributed to you design strip. The boundaries of the design strips are typically 1/2 of the perpendicular span to the adjacent column lines on either side of the column. For additional design information a good reference is "Design Fundamentals of Post-Tensioned Concrete Floors" by Bijan Aalami. It is published by PTI.

Good Luck,

AUCE98

 

[seattlemike]

Oops, yes, it is 10" thick, and it is a 2-way slab.

Yes, I am using the 20' width (1/2 perp ea side) for the tributary load, but it is my understanding that the effective width for the design of the concrete is considerable less for banded tendons, much like the tributary width vs. effective width on a T-beam.

 

[AUCE98]

seattlemike,

Regardless if you are looking at the design strip in the uniform direction or banded direction, the prestress due to the tendons distributes uniformly into the slab trib width. The disposition of tendons does not have any effect on design. Tendons are placed in the banded/uniform manner for ease of construction. The banded/uniform method does not require interweaving of tendons in different directions. Additionally, both directions can be designed for maximum permissible tendon drape. Banded and uniform tendons generally do not cross at their high or low points at the same location, aside from a couple of uniform tendons at the column. These uniform tendons are placed below the banded tendons allowing the bulk of uniform and all the banded tendons placed at the maximum high point.


Regards,

AUCE98


AUCE98

 

[haynewp]

That the force will get uniformly distributed across the width is the assumption used often in banded-distributed slab design. But it is not always the best assumption if you are dealling with wide widths between the bands. And there are regions that may not feel this force at all at each slab edge toward the middle. Sometimes a few additional tendons are placed between the bands to keep the average slab stress decently high. I am sure rapt will have plenty of comments if he sees this thread, I know he does not care for some of the assumptions commonly used in U.S. PT design.

 

[rapt]

Seems I am getting a reputation. You could have put in my answer for me haynewp and saved me the time.

Yes the P/A distributes evenly if you assume plate action of a homogeneous elsatic material. Concrete is not and concrete slabs are not. Shell action would show there are membrane stresses which cause te P/A to distribute differently depending on the relative deflections across the slab and on the cracking and long term effects also if allowed for. Unfortunately the FEM software does not use shells and does not allow for the rest.

But this is not the main problem. The moments and stresses due to vertical loads do not distribute evenly across the slab and they do not care that the slab is reinforced or prestressed or a sheet of plate metal. In fact, at the column the ratio is between 4 to 1 and 3 to 1 between the "column strip" and the "middle strip" as usually defined for 2 way slabs.

The ACI code says you can ignore this. The ACI code is "WRONG". You get a very unconservative design by ignoring this distribution of the moments and stresses. The concrete cracks at a point due to the stresses at that point, not due to the average of the stresses over a 30' width.

Crack control and deflection calculations must be based on the real distribution of stresses amd moments, not an average.

Ultimate strength calculations will not be affected by this to the same extend as long as
1 the section is very ductile
2 there are no changes in section such as drop panels
3 the loading is uniform
4 the tendons are arranged in a proper "load balancing" configuration (AUCE98 is wrong here, "any distribution" will not work)
5 extra reinforcement is added over the columns to make sure that moment transfer to the column is satisfied

Also, a lot of designers using FEM software are ignoring the Mxy moments and designing simply for Mx and My, because that is what the programs do. This is also wrong.

 

[seattlemike]

Hi Rapt,

Coincidentally, I recently ran some simple FEM concrete slab analysis using SAP 2000 at the University of Washington under the direction of Dr. Laura Lowes. From those results, I was under the impression SAP did use shell elements, and did have some uneven distribution of stresses due to real stiffnesses, although we were only running linear elastic analysis.

Any thoughts? I am only a begineer with FEM and Non-linear Analyis.

Mike

 

[rapt]

seattlrmike

I was referring to the specialist FEM concrete design programs. Thye do not give control over the element type.

In programs like SAP 2000 you can specify plate or shell elements and control the analysis the way you want. In the specialist programs you get what is offered. Unfortunately many designers do not understand that there is a difference and that FEM is not as super accurate as they think. It is the old problem, thinking software will do it all for you without having to put ypur brain into gear. Unfortunately, the reverse is true: You have to have a better understanding of design as the software gets more complex.