Bending of Plates 1

[ZeroStress]

I'd be grateful if anyone can guide me in the right direction.

A flat plate 2m x 2m with a thickness of 20mm (Stainless steel with fy = 220 N/mm2) is supported on two of its parallel sides and a its acting as a wall inside a chamber. The loading on this plate is a hydro static load.

Am I correct in assuming that the lateral torsional buckling isn't relevant to this case as the plate is not in pure compression. The plate experiences stress variation going from tensile to compressive through its thickness. As the entire thickness of the plate isn't in compression, the lateral torsional buckling is not valid which would mean the plate can't undergo LTB under this load, hence it would always be a compact section. So in order to design the plate (i.e. check to see if the thickness is adequate), I'd just compare its extreme fibre stresses with fy = 220 MPa (divided by material factor for ULS).

Is this approach correct?

Thanks.

 

[phamENG]

If your plate is experiencing a hydrostatic pressure load - load over the surface of the plate - then no, LTB isn't a design check. LTB is a failure mode for beams, not plates.

 

[RPMG]

phamENG is correct, but just to clarify a concept:
Lateral torsional buckling is relevant to members not in pure compression, just not members that can't buckle laterally and torsionally, such as the described plate. The plate compression zone can't twist.

 

[Blackstar123]

If the plate is laterally loaded by hydrostatic pressure, then there will also be a torsional load due to the difference in centroid of load and plate.

Am I correct in assuming that the lateral torsional buckling isn't relevant to this case as the plate is not in pure compression. The plate experiences stress variation going from tensile to compressive through its thickness. As the entire thickness of the plate isn't in compression, the lateral torsional buckling is not valid 

You are partly correct. Since plate is bending about its in-plane axis, it will yeild way way before it can lateraly buckle. So it's not even a possibility.
That part about which you're not correct is that, for lateral torsional buckling it's not a condition that members be in a state of pure compression. On the contrary, for lateral totsional buckling indeed its a condition that members be in bending, that is, in part compression part tension. Otherwise it will simply be called buckling.

so in order to design the plate (i.e. check to see if the thickness is adequate), I'd just compare its extreme fibre stresses with fy = 220 MPa (divided by material factor for ULS).

If you are calculating elastic capacity divided by Safety Factor (and not ULS), then yes. Otherwise, at ultimate load capacity, stresses will not be more than Fy and you cannot calculate flexural stresses using M/S.

Euphoria is when you learn something new.

 

[klaus.]

correct ...no LTB

 

[JoelTXCive]

If the plate is free on 2 sides and simply supported on the other, then isn't it just flat plate bending on the weak axis. The nominal moment is the full plastic moment. So you actually get to use the plastic section modulus and not elastic section modulus.

AISC Steel Manual Equation F2-1

M_n = M_p = Fy * Z

The plastic section modulus for a rectangle is 1/4 b * h^2 versus the elastic section modulus of 1/6 b * h^2. (the shape factor is 1.5)