beam theory or plate theory

[calculor]

I have a plate 5"x5" with a hole in the middle. The plate is simply supported on two sides only. Can I use beam theory to calculate the bending moment as a result of a point load or plate theory?

 

[Qshake]

It depends on what you'd like to know about the plate as a result of your analysis. If the load is being applied via the hole and the hole is large relative to the plate you may wish to use plate theory or at least Roark's formulas for stress and strain. If, however, the hole is small, yet the load is applied at the diameter then perhaps a good estimate will result from beam theory. Also if the plate is loaded by an eccentric point load then plate theory will predict stress and strain much better than beam theory as the plate behind the point load will contribute to the overall stiffness and shouldn't be ignored.

 

[calculor]

Lets consider a case where the supports are spaced 1.75" apart (the supports are 1.5" wide). The hole is centered between these supports and is slotted, 1.7" long and 1" wide. The load is applied as a point load via a bolt. The plate is 3/8" thk and bolted to the supports with 4- 1/2" dia. bolts (one in each corner). The plate is supposed to be rated for a 55 kip point load. However, I have analyzed the plate using plate theory and the results suggest the maximum allowable point load is around 5 kips. My co worker analyzed the plate using beam theory and suggests, if we increase the plate thk to 5/8" this would be adequate to support the 55 kip load. I disagree, any comments?

 

[Ingenuity]

calculor,

Intuitively a 5/8" plate for 55 kips load seems to be pushing it....3/8" seems ridiculous!

I am a bit confused with your dimensions (1.5" bearing x 2 + 1.75" span does not quite equal 5&quot...but close enough!

It seems that if the 55 kip load effectively spans 1.75" and lets say it is fixed at both ends (4 bolt connection may argue it is effectively clamped) then the moments MAY be PL/8 at both negative and positive moments assuming beam theory, or 12,000 lb.in. Lets neglect any stress concentrations and use the mispan section modulus as 5/8 thick plate x 5" less 1.7" slot for a elastic section modulus that equals 0.21 in2. So elastic stress is 12,000/0.21 = 57,000 psi. Does not look good.

Now you did state that a bolt is the means of load application, so it had a hex head and so the load is distributed and not a really point load - you may be able to see what happens with the bolt head bearing. But seems that you need to consider the real situation, including stress concentrations too!

HTH