Two Way Slab Stiffness Modifiers 3

[JSMHA]

I am using RAM Concept to design a two way slab with edge beams and supporting columns. Most of the design examples I see seem to run the models with no stiffness reduction factors. Based on my interpretation of ACI 318-19 Section 6.6.3.1 it seems at factored loads the reduction coefficients noted in this section have to be applied. And ACI makes no mention of designing for strength using a moment distribution based on full uncracked member stiffnesses. How do people handle the stiffness factors when determining the moment distribution in two way slabs? Do you just apply the ACI reductions? Does anyone design in RAM Concept based only on full stiffnesses? Is there any code locations i am not aware of that has a further discussion on this?

 

[KootK]

1) I believe that those coefficients are intended for use in global, lateral load design and not for basic, gravity load slab design.

2) For slab gravity loads, I often design the quantity and disposition of my slab reinforcement assuming the concrete to be uncracked. That, for several reasons:

a) I find that the results correspond well to what I know to be conventional slab reinforcing detailing (inflection points etc).

b) Believe that, somewhere, ACI limits how far your assumed load distribution can be from the elastic value. Obviously, you need the elastic value to figure that out.

c) Fundamentally, the elastic load distribution represents stable equilibrium and, in that sense, is as valid as any other distribution for ultimate limit state design.

3) For slab deflections, I do use reduction factors to capture long term effects although I don't recall what those are off hand.

 

[Celt83]

With no modifiers applied you will get the critical negative flexure designs, and possibly the critical punching shear unbalanced moment, at the slab column joints. With the modifiers applied you’ll get higher positive bending results due to the reduced joint stiffnesses. I use the equivalent frame definitions as a basis which allows the use of the gross cross section area to compute moments of inertia and allows a certain percentage of redistribution (concept does not perform redistribution).

If you plan to run the time history deflection analysis you need to use no modifiers as the load step process will progressively crack the design cross sections and reduce their stiffness. If you do the modifiers the time history run will start fully cracked and then experience creep straining which will yield large deflections.

My Personal Open Source Structural Applications:

https://github.com/buddyd16/Structural-Engineering

Open Source Structural GitHub Group:

https://github.com/open-struct-engineer

 

[KootK]

...the modifiers applied you’ll get higher positive bending results due to the reduced joint stiffnesses.

Along similar lines, and at the recommendation of one of my old mentors, I usually provide a basic bottom mat equal to wL^2/20 of the governing span even though elastic FEM will usually indicate less demand than that. His logic was that positive moment capacity is safer than negative because negative moment capacity often relies on the presence of loaded backspan.

 

[Lomarandil]

Celt and KootKs opinions should hold way more weight, but I also do not apply stiffness reduction for gravity load combinations. (Only for lateral load combos).

----
just call me Lo.

 

[rscassar]

Generally no stiffness factors are applied, and the analysis will return moment, shear and reactions based on full stiffness of the slab elements. When either strip-based and load-history deflection plots are viewed these will amplify the deflections based on cracked stiffness, creep and shrinkage. So generally no stiffness reductions are required.

Twisting Moments

It is important to account for twisting moments in slab design. Edge beam you would likely set torsion design to "Beam" For internal slab panels the best torsion design to select would be "wood-armer". To redistribute the twisting forces held in the elements and strips to latitude and longitude moment distributions. For thicker slab around 14"+ thickness (350mm+). I would decrease the Kmrs of these elements, possibly to 0.5. This helps to alleviate the twisting moments the elements hold.

 

[Lomarandil]

RScassar, I recently came across this idea of slab twisting moments in relation to rectangular tank design, but haven't wrapped my head around them yet. Do you (or others) have any suggested resources to help understand that concept?

----
just call me Lo.

 

[centondollar]

Lomarandil:

The twisting moments folllow directly from the definition of a thin plate and the corresponding partial differential equation.

Incorporating them into design of reinforcement in two orthogonal directions (x, y) of the slab can be done by e.g. the wood-armer method. Search the internet for "The reinforcement of slabs in accordance with a pre-determined field of moments" to find the original article (1968) by R.H. Wood.

 

[KootK]

See below for a couple of solid, recent publications on the slab twisting.