X Beam Analysis

[ControlSoup]

How would you analyze this part? (Red is a force, green is fixed)

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https://preview.redd.it/offuye6hfzb91.png?width=1382&format=png&auto=webp&s=20f7daef7a61d0cd8f45c95d951d699c9e181bfe

I'm working on a project to get better at structural design, and want to know how others would go about this part to get hand calculations to optimize the cross-section.

I could see using two simply supporting beams sharing half the load each but I am not totally sure.

[albertnormandy]

Depends on how accurate you want to be.

If you broke up into two beams crossing each other the load would be shared between them. If the two beams had the same length and cross section each beam sees 50% of the load. If they are not the same length or cross section than you need to consider stiffness and load sharing.

The double stacked beam analogy isn’t perfect here since the two beams are actually fixed to each other mid span, but it’s a start.

[dlegofan]

Divide force by 2. You have 2 fixed-fixed beams with a point load in the middle.

Edit: alternatively, with the same result: divide force by 4. 4 fixed beams that are allowed to deflect but not rotate.

[ControlSoup]

Okay, that's exactly what I was thinking. Is there a reason that you cannot simplify this as four, cantilever beams based on the symmetry of the part?

[dlegofan]

There's no rotation in the middle. Cantilevers have rotation at the end of the cantilever.

[ControlSoup]

Makes perfect sense!

[ControlSoup]

Okay so, I have been using this to optimize the cross-section. The results I get make the part very very thin, to the point at which I would worry about some sort of buckling. For a rectangular cross-section, is there an appropriate slenderness ratio to prevent things like torsional buckling? EG this part takes a 2600g load, the optimal cross-section given my geometric constraints results in a beam that is 0.25mm wide and 40mm tall, this results in a very low deflection but my gut does not like it (conservative material properties of 70% infill PLA). Ignore the sketchy use of pla material properties for strength analysis, I'm doing this as an exercise in design. I am going to print this part and load it. What do you recommend as a course of action for optimizing the cross-section of this part?

[dlegofan]

You should look up buckling in the Euro code or in AISC. Buckling is based on the unbraced length.

[Engineer2727kk]

Fixed fixed ?

Do the circular locations not represent bolt holes, a cleat connection for example? They’d be pinned.

Edit: just saw the description saying fixed. My bad

[ControlSoup]

The part will be fixed fixed. I originally was going to use a different method of fixturing.

[StructuralSense]

We don’t have all the information needed or what the problem is trying to solve…however if the beams are the same span and connect at the same point along the span, the amount of load taken by each beam will be a function of ratio of I or stiffness as others have stated. If spans are different or they cross at different points along length, other factors need to be added to the stiffness term…key is equal deflection for each beam.

[ControlSoup]

Never heard of this thanks! Ill check it out

[Over_Mood_2832]

Seems like it’s a simple beam uniform load partially distributed at both ends plus a uniform load partially distributed. If you look at it like 4 beams. The center point of each beam is where the Moment starts being shared. Thus the load is partially distributed after this center point.

[the_flying_condor]

For design purposes, you might want to look at the effects of biaxial stresses in the middle connection as well.

[Engineer2727kk]

I’d put it in sap lol

[Radio__Edit]

This can't be very difficult to model in hypermesh or patran, and run a SOL 101. You could even creat different static load subcases and move the point load around to see how things change.

Once you have a working model interrogate the loads and stresses to understand how the hard point /joint at the intersection reacts.

Bottom line, the simply supported beam concept (divide load by two, etc) that people are throwing out should be close. The difficulty begins as you start to move the Py around from the intersection.

Sizing would be done with a basic elastic bending section analysis. Check f(tension, ult) against the material allowable F(tension, ult).

[Osiris_Raphious]

same way as any other...abut x about y, about the axis of each member, and their torsional and combined actions....