Plate Allowable Deflection vs Beam Allowable Deflection 1

[Sam Low]

Hi all,

Could please tell me why the plate allowable deflection is considered from the nominal thickness/2 ; whereas the I-Beam allowable deflection is considered from the overall length/200 (depends on code/requirements)?

Is it related with the shape design of the material ?

Thanks in advance!

 

[Ussuri]

Its because of the assumptions on which linear elastic plate bending theory is based. Plate bending (linear elastic) is often based on work by Timoshenko et al, such as his book 'The theory of plates and shells'.

The formulations are based on some assumptions, namely the thickness of the plate is small in comparison to its radius of curvature, and deflections of the plate must be small when compared to thickness. This assumption is that the bending strain in the middle of the plate is small when compared to the outer surface such that the strain in central plane is ignored. The deflection limit of 0.5h has been adopted because errors at this limit are acceptable, after this the errors increase and the mid point strain needs to be considered. Then you get into large deflection theory.

 

[JStephen]

The I-beam deflection limits may be based on floor vibration when walking, or supporting ceilings without cracking plaster or ponding due to rainwater on a flat roof,etc, but usually relates to conditions beyond the beam itself.
The plate deflection as described by Ussuri is due to limitations in the derivations. It doesn't mean you can't have larger deflections, just that the analysis may no longer be valid. But note, for example, that Formulas for Stress and Strain includes some large-deflection solutions for round plates. If you have a plate bending in one direction only and ends are not restrained, the allowable deflection could be increased considerably. You may have cases also where bending is neglected.

 

[saplanti]

It depends on the what you are trying to do. In certain applications you may need to use 1/100, 1/250, 1/500 or 1/1000 for the limit of the beam deflection. As the design engineer, you need to use the specific limits for the purpose. Codes give the certain limitation as best practice.

For the plates it is different issue. The Theory of Plates and Shells by Timeshenko has proper explanation on the issue. Plate or large deflection theory is mainly used. When you use the large deflection theory you basically consider the plastic hinges at some locations and you additionally consider a safety factor for the plasticity for the purpose if needed. For the plate action you want the plate stays in the elastic range. So consult Timeshenko's book for details.