Force and momentum diagram for an isosceles trapezoid

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Hello

I am trying to figure out the effect of stacking molds of hot liquid material on top of other molds.

I know there needs to be a moment analysis but my statics knowledge has been lost.

We are seeing cracks develop in the center of the molds and I'm looking to see what is the actual resulting force within this area.

I've included a drawing that should have all the data necessary for this problem.

Thank you

 

[ishvaaag]

I think more data is required. The material of the mold, its strength in the temperature range, knowledge about intital stresses from fabrication if relevant, its thickness everywhere, the exact way in which the load of (just one?) mold above are passed to the mold below, the temperature at the liquid, the configuration of the cracks. With this at least a 3d model with some input of temperature effects can be made and judged against strengths. Since it takes more time than mere advice, this is some kind of a job, so better look in-company or outsourced engineering help. The mold seller company if any may help itself.

 

[ad911001]

Thank you for the reply.

The thickness of the mold is three inches, everywhere. I don't see how the material is relevant, I'm just looking for the internal stress at the middle of the top lip section. This will be the same for any material. Also, disregard the temperature, assume it is room temperature. Initial casting stresses are negligible. I've included another picture showing the stacking pattern. The bottom row of molds in fully supported on the bottom with another row of molds on top (rectangles molds used for simplicity). The top row of molds is supported by the two different bottom molds, one for each side. Bad explanation, see picture.

Thanks

 

[ishvaaag]

The first thing I notice is that your dimension don't square, a 43" wide bottom and side faces 15º from the vertical gives only a square of 58" sides at 28" height. Yours', except misinterpretation, have there 72", hence your angle separates more from the vertical than 15º, you have bigger dimensions maybe than understood, projected or wanted, maybe some fabrication failure causing bigger stresses? Also the load, except weighed, could be more, out of the bigger volume implied.

Will elaborate more, hope soon.

 

[ishvaaag]

Have modeled the thing with 58" and 72" top sides.

I think a conservative model, not knowing more, is with loads of 1.5 ton (have taken 1.5 tonne) at corners of the bottom of the topping molds.

Unconservatively, the weight of the mold itself and the pressure of the molten material is for now omitted in all these quoted models that follow.

On this asummption and P-Delta included, we get a maximum VonMises stress result of 2.6 MPa in the lesser dimensions' model and of 11 MPa in the second bigger. Flexural behaviour of course is involved. This is with the actual loads without any safety factor. The maximum stresses occur under the applied loads of 1.5 ton.

At the center of the faces, atop, the VonMises stresses stand in the range of somewhat over 1.1 MPa in these models with 1.6 ton point loads.

Have, also, modeled the loads applied uniformly to each side, 3 tons in the loaded length. Then the maximum stresses occur at the center of the side faces, atop, at values of around 1.8 MPa in the lesser model and 3.75 MPa in the bigger.

Modeling the same thing with brick or tetrahedral elements may lead to somewhat lesser stresses.

Other load conditions may be causing the cracks. How the molds are being hung and then at what impact factor laid, and the quality of the wanted uniform support at the rim have a say in the results. As well including the omitted factors. The temperature effects in the production cycle will impact stresses and maybe standing strengths.

More detailed studies of the cracks, loadings, temperature effects would help to a more accurate adjudication of the cause of the failures.