Not even close to being an engineer, but got an engineering question

[Razzle-Snout]

Thanks in advance for indulging me. I was on another forum (a woodworkers forum) discussing bed design (I'm not really a carpenter either, sort of a intermediate woodworking hobbyist). My question there, and now here, has to do with figuring out the optimal placement for two posts holding up a beam. The goal is to minimize deflection of the beam when a load is placed on it at any point. The specific context is that I am building an elevated platform bed and trying to decide the optimal positioning of the legs onto the bed rails, so as to minimize any tendency of the rail to deflect downwards when it is supporting the sleeper + bed materials. This tendency to sag would be most acute in the middle obviously.

My initial thought was that if you had a 3 ft beam being held up with a single post, then the best placement is obviously in the middle (so that it forms a T). Therefore, if you had a 6 ft beam (bed rail), you might want to treat it as two 3 ft beams placed side to side, such that the posts would be 1.5 ft in from either end (1.5 ft, leg, 3 ft, leg, 1.5 ft). However, on further reflection, it seems that the situation with a 6 ft beam and two posts is comparable to a (3 ft beam with a single post) X 2, only when a point load is placed outboard of the legs (somewhere in the 1.5 ft sections that extend beyond the legs). If however such a load were placed anywhere in the middle, then the tendency to sag would be counteracted to some degree by both posts (legs). This, in turn, suggests to me that the best post (bed leg) placement would be something LESS than 25% in from the end of the beam (bed rail). I assume that the tendency to sag (or with a perfectly rigid beam, the force which would try to break the beam off the post) is partly a function of the load's distance from the support post, and that perhaps this is not linear. I assume also that this info is important for figuring out the optimal placement. But then again, as I said at the start, I am not even close to being an engineer. It sounds like a very basic engineering question though (like in building bridges or buildings, etc.)

Thanks in advance for any illumination on this issue, and I apologize for any mis-use of terminology (e.g., force, point load, etc.)

 

[jack action]

You can learn about what influences beam deflection here. Once you read that, you can find more cases already solved online, like here, here and even this calculator.

I think this case would best represents half of your single-post design and this case would best represent your 2-post design.