Plate simple supported at corners 3

[vlad1981]

Good morning,
I've been trying to find the right formulas, for a plate that is going to be simple supported at the corners.
the only reference I've found online (not even Roark has the condition) is a webpage structX.
see screen shot attached, my question is, to what extent are the Moment formulas correct?

am I missing something, or the moment formulas are missing some units if W = psi and b^2 = inch^2 and alpha = dimensionless then Moment = lb....

 

[jayrod12]

I would bet the W is in plf or lbs/in based on the entire plate width

 

[rb1957]

I agree w is probably psi, but I think their moments are moments/inch

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[vlad1981]

that's the thing, W is in psi or Mpa (

https://structx.com/Plate_Formulas_014.html)

 

[Celt83]

The table seems close I just ran a quick 10ft x 10ft 1" thick ASTM A36 plate with 100 psf loading
a=b=120 in
a[sup]2[/sup]=b[sup]2[/sup]=14400in[sup]2[/sup]
w = 100 lbs/ft[sup]2[/sup] * 1ft[sup]2[/sup]/144 in[sup]2[/sup] = 0.69444... psi

Mo(b) = 0.0947 * 14400 in[sup]2[/sup] * 0.6944... psi = 947 lb*in/in
Mo(b),fem = 1.0949 ft-kip/ft * 1000 lbs/kip * 12 in/ft * 1 ft / 12 in = 1094.9 lb*in/in
approx. error = (1094.9 - 947 / 1094.9) * 100 = 13.5%

M2(b) = 0.1606 * 14400 in[sup]2[/sup] * 0.6944... psi = 1605.9 lb*in/in
M2(b),fem = 1.5065 ft-kip/ft = 1506.5 lb*in/in
approx. error = 6.6%

 

[jayrod12]

And just design the entire plate on a per inch width basis, that actually makes much more sense.

 

[vlad1981]

@rb1957 & @Celt83 Moment, in lb*in/in, does it means, that at X=0 Moment = 0, and @ X=L/2 (Center) Moment = Value Calculated (in lb*in/in) * L/2 (in inch) = Max Moment at center in lb*in?????
BTW thanks all for the responses, this forum is the best ever!!!!!!!!!

 

[Celt83]

Recommend this free lecture series: Link
I believe the associated textbook used to be a free download but I'm not able to locate the link currently.

 

[robyengIT]

 

[rb1957]

moment per inch means your section modulus is 6/t^2 as opposed to 6/(Wt^2) ...

ie stress = 6*M/t^2

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[HTURKAK]

Dear vlad1981 (Civil/Environmental)(OP),

When you look to the bottom of the page , you will see the notation and the units..
Notation
a = shortest span length, in or mm
b = longest span length, in or mm
E = modulus of elasticity, psi or MPa
Mi = maximum bending moment, lbf.in/in or Nmm/mm
t = plate thickness, mm or in
w = load per unit area, psi or MPa
∆i = deflection or deformation, in or mm
αi = length to width ratio coefficient
ηi = length to width ratio coefficient
μ = poisson's ratio of plate material, assumed to be 1/6 for coefficients

http://www.structx.com/Plate_Formulas_014.html

Tim was so learned that he could name a
horse in nine languages: so ignorant that he bought a cow to ride on.
(BENJAMIN FRANKLIN )

 

[centondollar]

Take Navier's solution to the Kirchoff plate bending problem with different number of terms (e.g., 3, 5, 10) until you are satisfied with convergence, and then apply definitions (take derivatives of the deflection field) to find bending moments and twisting moments. Alternatively, solve it by using a suitable trial function (a trial for SSSS plate with uniform load should be found by googling) with the Rayleigh-Ritz or Galerkin method. If that is too cumbersome, use some FE software.

There really is not much reason to trust tables for simple problems, but my suggestions will help you confirm or deny coefficients in that table.

 

[dold]

If that is too cumbersome, use some FE software.

Yes, that sounds much more cumbersome than using some FE software.