deflection due to water

huangyhg

deflection due to water
i have an open top,rectangular water container.  it is constructed with a bottom and four sides.  the containter is 40" deep x 110" wide x 440" long.  the walls are 1/4" thick.
i need to know how to figure what the deflection will be on the sides of the tank.
thanks
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is the container completely full of water?
you could do a static analysis of it to get a "rough" estimate.  however, a finitie element analysis will yield far batter results.
as sperlingpe says, the depth of water fill is important. (your view seems to show holes in the walls near the top of the side plates.) also important is the dimensions of the flange around the top edge.
if you ignore the contribution of the top flange, and assuming the box is full of water to the brim, you will find a maximum deflection at the mid-point of the longer top edge of approximately 110 mm (approx. 4 1/2"). bending stresses in the bottom of the wall are close to yield for mild steel, so this is probably an unacceptable solution.
if you have a suitably proportioned stiffener flange at the top edge, this will act as a ring beam, and will greatly reduce stresses and deflections in the wall plates.
i believe "formulas for stress and strain" has some rectangular-tank formulas; check there.
if not, you can use the rectangular plate equations.  assume simply supported on three (or four) sides and fixed on three (or four) sides and your case should be in between those two cases.
julian hardy,
thanks for your answer.
as you assumed, the water level will be 40in deep. i felt the deflection would be high, so i added a 4inx4inx1/4 wall square tube around the top.  how much will this "rim beam" reduce the stress and deflection in the side plates?
from what i calculated, the force on the side walls are given by f=wl*d^2 where w=62.4lb/ft^3, l=440in(36.7ft), d=depth of water 40in(3.3ft).  i get this to be 12,697lb
i am still looking for a rectangular simply supported equation.
thanks again.
a finite element analysis may not be totally useful here...depending on your software.  many do not include in their formulae the aspect of tensile straightening.
if you have a cable, and is spans from a to b - and you hang a load on it at midspan, it will deflect into a "v" shape.  if you add tension, it will draw upward, eventually almost straight.
in your box problem, the water will tend to bow the walls outward, but the orthogonal forces at each end will tend to straighten out the top edges of the tank....a typical finite element analysis may not include this effect and your stresses will be somewhat inaccurate.
another simplification that may help- treat the sides as vertical slats, design them as simply supported beams; then design the top stiffener to carry the reactions from the top.  the flat-plate equations approach this approximation as the width becomes much larger than the height.
>another simplification that may help- treat the sides as >vertical slats, design them as simply supported beams then >design the top stiffener to carry the reactions from the >top.  the flat-plate equations approach this approximation >as the width becomes much larger than the height.
how do i determine what the reaction is at the top?  do i just design the top stiffener to carry this full load or would that be too much of a s.f.?
i calculated the loading on the side is around 13,000 lbs.
karthur,
if you don't already have it, get yourself a copy of design of welded structures by omer blodgett.  it can be found at the lincoln arc welding society website and is relatively cheap.  section 6.5 is on the design of tanks, bins and hoppers.  it will have the information you need.  
aggman,
thanks for the suggestion.  i read his column in welding design and fabrication every month.  i just ordered both the design of welded structures and design of weldments.
got both of them new for about $45.
can't wait to get them now.
thanks
the load on the top stiffener would just be the beam reaction from the vertical strips of plate.  isolate a vertical strip of plate, sum moments about each end of it to find reactions.