Slabs jointing (theory behind maximum length to width ratio)?

[drile007]

Hi to all,

I'm wondering why each ground slab-panel shall be kept as square as possible? Maximum length to width ratio should be less than 1.5:1.
What's the theory behind this rule of thumb?

Thank you for all comments

 

[MotorCity]

Can't say for sure, but I suspect its because as the shape becomes more rectangular, it becomes more like a beam instead of a plate. Since the slab will "span" in the shorter direction, there will be more load sharing in one direction than the other.

 

[charliealphabravo]

Per ACI 224.3 squares are preferred but slab geometry may dictate otherwise. ACI 302.1 says that cracks may become excessive for ratios greater than 1.5 so it is simply an empirical value based on observation. There is a caution in 224.3 that even 1.5 may be too great.

I don't see much in ACI about the theory per se. I think PCI and CRSI might have more. Joist placement is a bit of a black art based on variables including thickness, reinforcement, base friction, w/c ratio, loading, restraint, and environmental effects. I think the 1.5 spacing basically falls out of the physics of the problem which is that stiffness attracts force. If the aspect ratio becomes too large then the crack tendency switches from longitudinal to transverse even though the maximum joist spacing is observed everywhere.

Edit: Imagine a point at the center of mass of a slab with lines radiating outward. The lines represent the direction of tension and strain in an infinite free slab due to shrinkage. Then crop the lines lines with a square or rectangle of control joints where the center of mass is still in the middle. As the aspect ratio increases, the ratio of force lines in the longitudinal direction increases and the tensile strength decreases since the transverse cross sectional area is decreasing. Beyond an aspect ratio of about 1.5 there is no longer adequate strength to resist the tensile forces and drag so the concrete cracks even though the maximum joist spacing was not exceeded.