sand jack

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Does anyone know how to calculate the allowable load on a sand jack, or sometimes called a sand trap, for falsework design?

couldn't you make the jack out of steel. Use a steel pipe with 20mm steel plate end pieces. You can weld in a couple of 25mm diameter nozzles with threaded end caps to blow the sand out.

As for calculating the capacity I think you could check the steel plate for deflection, and perhaps the design the pipe wall thickness for the pressure. But if you size the jack to suit the formwork support I think you will find it cannot fail. If you use timber then of course it is liable to burst.

Give it to a structural engineer.
I have delt with these before, we call them sand pots. Too hard to explain thru a forum how to do it exactly. But you need determine lateral pressure due to the surcharge of what ever the sand jacks are supporting, then you can determine the tension on the bands. Once you know the tension in the bands you can compare to the allowable tension of the band. You must also check the plywood for shear, flexure should not be an issue. Make sure the corners of the pot are rounded or there is some protection to prevent the pot from cutting into the band.
If you have some and what the capacity, you could just back solve the process I mentioned.

Some specific info on one size of sandjack:

We use 21"x15" out to out sandjacks.
Walls made of 2x6
bottom made of 1/2" ply.
Plunger made of 1/2" ply.
Two 3/4" x.02" bands wrapped around box.
Nailing side walls is optional.
I've load tested numerous jacks with various fill materials.
Concrete or masonry sand works well.
Anything poorly graded will blow out nicely.
I've taken these to well over 210,000 lbs.
I rate them at 70,000 lbs for actual use.
Rating is based more on settlement than on jack capacity.
Bands rarely break. I've only broken one during a test.
Walls will fail. The 2x6 will split between the banding and will continue to open as load is applied.
Plunger averages just under .1" of settlement for every 10,000 lbs. of load.
Obviously if you set the sandjacks at an angle then you reduce the capacity.
Load caculation on the sidewalls is a little tricky but it can be done reasonably accurately.
Hope this helps.