max stress deformation of flat plate under triangular pres

huangyhg

max stress & deformation of flat plate under triangular pres
hi everyone,
just found this great forum. i'm looking for a formula that will give the maximum stress and deformation of a thin plate under a triangular pressure load.
pounder's formulae only seems to cover uniform pressure load, i've looked for a solid week on the internet & in books for a suitable formula, but cant find anything. does it exist?
it seems very rare to find any formula dealing with triangular pressure loads at all.
look in the first site below.
if you are dealing with a circular plate and a linearly increasing load over a diameter, then roark has it, as well as many other loading conditions and plate shapes.
prex
rourk's formulas for stress and strain, table 26.
blodgett's design of welded structures.
pca's rectangular concrete tanks.
moody's moments and reactions for rectangular plates
a reasonable estimate is to use the average pressure as a uniform load.  then add an extra 5% and that will get you pretty close.  i've compared the results to accurate solutions and it works fairly well if you have no other resources to work with.
joe tank
thanks for the tips guys the xcalcs software managed to give a reasonable deflection profile, i'll order roark's book today for the stress calc & see if that helps.
i swear by roark, this should be compulsory purchase for structural engineers.
i second rtmotes comments, roarks is one of those handfull of texts that no structural office should be without.
csd
while the roark book is excellent for general engineering usage, some of the other references may be better for your application.  blodgett has an example of a stiffened steel tank.  the pca book tabulates moments and shears for various tank geometries.  moody's tables are hard to find, but also very useful.
i suspect that this problem is not so readily solved by roark.  i'm thinking about the panel supported on three sides.  sure the top (and the bulk of the panel) could reasonably be represented as a simply supported beam, possibly a beam with intermediate elastic supports (representing the angles) but the lower portion is well supported by the lower edge support which would be a complex geometry for roark.  what makes this more significant is the loading is increasing towards the lower edge.
it would seem that the top edge is undeflected, that the out-of-plane deflection increases with depth, untill the effect of the lower edge is felt by the panel 'cause the bottom edge is also undeflected ... this is probably where the maximum bending happens in the angle stiffeners  
interesting comments, i got round the problem in the end by a thin plate bending formula from prex's suggestion. luckily the membrane and bending stresses weren't too huge on the bottom edge lip so the weld should hold.
i'm resurrecting a fe thin plate analysis code (from phd) at the moment for any future unusual plate bending problems. roark and moody's books will hopefully enlighten the triangular pressure input load for it.
interesting topic, just today i worked on a similar problem.
my load is an triangular pressure on a circular plate which is highest on the inner radius and 0 at outer radius.
i tried roark to find a formula but there isn't one for the  case i had. my workaround: i figured out an average pressure and verified that via fea.
the roark formula gave a slightly higher value, so i am on the safe side in this case.