Why use different moment of inertia in deflection calc in ACI and PCI? 1

[StructLin]

ACI and PCI basiclly deal with same material, i.e. concrete, why in ACI, Ie=0.35Ig or 0.25Ig is used in calculating the member or slab deflection. While in PCI, the gross Ig is used in calculating the member or slab deflection? That makes no sense.

 

[cooperDBM]

An effective inertia, Ie, accounts for cracking of the slab. PCI generally concerns themselves with prestressed slabs. Assuming the slab doesn't crack due to the prestressing the full section inertia, Ig, can be used to check deflections.

 

[Lion06]

cooper is exactly right. If, however, your prestressed section is cracked (typically if the bottom stress exceeds 12 * sqrt f'c) then you should use the same Ie calc that is in ACI. That calc should be checked after all losses.

 

[rapt]

StructuralEIT,

Agreed, PCI is definitely wrong.

However, your 12 * sqrt f'c limit is not correct.

Even ACI318 says 7.5 * sqrt f'c and this is only correct if you take into account restraint effects (shrinkage restraint due to internal reinforcement as well as external effects with shrinkage and temperature movement).

And this is still wrong for flat slabs due to the complete illogic of ignoring column strip moment concentrations in ACI318.

 

[Lion06]

ACI gives 3 classes for prestressed concrete:
uncracked (bottom stress < 7.5*rootf'c
transition (7.5*rootf'c<bottom stress<12*rootf'c
cracked (bottom stress>12*rootf'c)

The 7.5*rootf'c is the modulus of rupture for traditional (non-prestressed) C.I.P concrete.

 

[StructLin]

Now I need to calculate the deflection of a building floor. The floor is a 9" thick slab, sitting on 20' spacing column in one direction and 22' spacing column in other direction, all column is 20" square. Total factored load are given as "w" (psf). My question is:

1. Should I Add column strip deflection in one direction, say 20' spacing direction to middle strip deflection in 22' spacing direction?

2. will following approximation method to get the slab deflection be justified:

first, calculate 22' direction middle strip deflection by delta1=(w*22'*22'*20'/2)/(384*Ec*Ie), where 20'/2 is the middle strip width. Then considering that the end point of 22' direction middle strip is sitting on mid span of column strip in 20' direction, the end point itself has deflection, so I need also add 20' direction column strip deflection delta2=(w*20'*20'*22'/2)/(384*Ec*Ie).

3. If I put W12x65 beam across 22' direction cloumns, can I now consider the slab as one way slab and consider the 20' span length slab as fixed boundary condition at both ends. So the deflection is: delta=(w*20'*20'*1')?(384*Ec*Ie_at_1_foot_width)?

 

[frv]

rapt-

I don't think you should make sweeping assertions like "PCI is definitely wrong".

As StrEIT mentioned, they deal with prestressed concrete (precast is very frequently presetressed) and cracking is usually avoided. In that context, it makes sense for them to focus on what they do, and using Ig is reasonable to them.

 

[rapt]

frv

UUUALLY avoided is not a good excuse. If always avoided and that is stated then ok, but USUALLY avoided means there are cases where it is allowed and must be designed for so the book should say that.

Structlin,

Yes adding the column strip deflection in one direction (allowing for any cracking in that strip) to the middle strip deflection (allowing for any cracking in that strip) in the other direction is an appropriate method. tests I saw the results of a few weeks ago showed it to be remarkebably accurate.

But the load on each strip has to be determined logically. The column strip will have 75% of the moment at the support reducing to about 60% at midspan and the middle strip will have the rest. RAPT does all of this for you automatically.

 

[Lion06]

I don't know anywhere in PCI that says you must use Ig, it just gets used because members are designed not to crack (at service loads). You obviously have to use some judgment and if the member will crack at service loads, then of course you need to use Ie.
That being said, I interned at a very large precaster for over a year and they would always design every flexural member to remain uncracked (or in transition).

 

[cooperDBM]

In the PCI Handbook, section 4.8.2 covers elastic (Ig) deflections when the service tensile stress is below rupture. Section 4.8.3 covers bilinear deflection when the tensile stress exceeds rupture.

The slab load tables (section 2.5) are limited to Class U members (2.3.2) and therefore use gross section properties to determine an elastic deflection.

 

[frv]

rapt-

There is a lengthy thread on this forum precisely about using engineering judgment.

Codes aren't meant to substitute common sense or engineering knowledge.

Personally, I don't want the codes to hold my hand every step of the way.

Designers with even a cursory knowledge of concrete design know that cracked concrete has significantly lower stiffness. I don't think it's necessary for PCI to spell this out.

 

[rapt]

frv,

Agreed, and PCI manual is NOT a code unless I am mistaken. But any design advice in print should not be misleading. I have not read the PCI manual for about 30 years, I was just commenting on StructLin's comments. Unfortunately a lot of designers depend on books such as this as well as forums such as this one for design guidance. And some people do need to have their hand held. The problem comes when they do not realise it.

StructuralEIT,
In Transition (if you are referring to the ACI definition of it) means it is cracked for deflection calculations according to both ACI and also to logical design. The member needs to be considered cracked at all points where it is IN Transition. Ig can be used elsewhere.

 

[cooperDBM]

The PCI Handbook is not misleading on this issue (see my previous post on section references). I think the original poster was just looking at the slab load tables which are explicitly limited to class U (uncracked) behavior (prestressed precast slabs). That doesn't mean that PCI assumes all slabs to be uncracked, even if prestressed. They provide the guidelines to deal with cracked slabs (class T and C). PCI recommends a more generalized bilinear deflection analysis (using cracked section properties) instead of using an effective moment of inertia as you would with a non-prestressed slab.