# How can I calculate the load capacity of a platform?

I'm planning to build a very basic bed frame, but I'm not sure what size lumber to use.

I was thinking of building the entire thing from 2x4s (legs would be 4x4), but I'm not sure if this will be adequate.

Some other ideas:

• 2x6 Perimeter with 2x4 cross members.
• All 2x6.

I'm also not sure how I want to attach the legs. I was thinking of using carriage bolts, but I'm not sure if this is overkill or not in this situation. Maybe notch the 4x4s to receive the frame, then use carriage bolts to secure them.

I'd like to be able to do some calculations with different combinations of materials and fasteners, to figure out the optimal combination. Do I have to go back to school to become a structural engineer, or are there tools/formulas for figuring this stuff out?

Here would be my basic approach (Mechanical Engineer here, Statics TA for 4 semesters):

• For starters, you could figure out the weight of the mattress and box spring plus the weight of two people lying on it (`W`). Add in a safety factor (at a minimum 2, ideally a bit more) - remember, an uneven or dynamic loading will apply significantly higher stresses to your frame.
• If you assume the weight will be evenly distributed it makes things a whole lot easier.
• Figure out which supports your box spring will be resting on. Does it come in contact with the outer skirt on the sides? If not, divide up the weight of the box spring/mattress/people by the number of cross supports (`n`) the entire thing rests on, less 1 (`W/(n-1)`). For the end cross supports, use half of this loading.
• Use the distributed load (or half of it) that you just calculated over the span of each cross support in conjunction with a fixed-fixed cantilever beam equation explained in Figure 23 here.
• Calculate maximum beam stress at the center with `σ=M*c/I` (where `M`=moment,`c`=distance from neutral axis, and `I`=area moment of inertia) and compare to your material (pine? oak? maple?) maximum compressive and tensile strengths.
• Apply the reaction forces for the cross piece ends to the sides of the supports running the length of the bed as point loadings. (If you want to get fancy, you can include the moment as well and add a torsional stress to the beam, but I don't think I can explain how to do that very well over the internet.) Use superposition (multiple P forces) and Figure 25 for this one. Repeat calculating maximum stress.

If you end up with not enough of a safety factor for your chosen design, increase the width (vertically) of the side beams. For the center, you could just add another support and recalculate. I don't think fasteners will be the limiting factor here, and calculating/estimating the stress concentration factors in an anisotropic material such as wood is a bear.

Edit: So that's how an engineer would approach this. However, @rachet freak has a very good point that you could save a lot of time by using a proven design. In that case, take a look at Ana White's website. It's got dozens of plans that people have already built with basically just a circular saw and a drill.

• I am looking for the "Engineer approach", since learning the basic concepts will come in handy in future projects. The question was more than simply "how do I build a bed frame?", and you answered it nicely. Commented Feb 28, 2012 at 17:27
• I'd put the weight of two people in the center of the bed. Two people piled up in the center is not an uncommon scenario. Commented Feb 29, 2012 at 13:58
• Haha, good point guys. Although I did realize if you're using a box spring, most of the weight may be redistributed to the outer edges. Commented Feb 29, 2012 at 14:47
• Just a consideration; most king beds use two XL Twin box springs, and some queens now have split foundations as well (it's an inexpensive way to tweak the firmness of the mattress, and the more rigid box springs are just easier to wrangle when they're split). As a rule, each corner of each box spring must be supported to the ground, so your design would need a center runner. It's just a general good idea, as the slats then have half the "moment" they normally would and can support more weight for it. Commented Feb 29, 2012 at 21:39

putting the legs on the inside will induce a shearing load on the connection. A better connection would be having the wood frame rest on the leg (with a notch). You also need to account for the needed strength in the corners so everything stays square.

or you can do a google search on bed plans and get a tried and tested design the first link even only needs 2x4 lumber

I can't speak as to how to calculate it, but from experience, 2x4s are overkill. For the beds I've seen, 1x3s slats (laid down, not vertical), with a vertical 1x4 perimeter, were sufficient unless both people weigh 300+lbs.

You will want a center rail and possibly a center leg (some mattress warranties actually require one!). Reducing the span length is a huge win in terms of support.

Your design has lots of shearing at all joints. A better design would to be rabbet or dado the edge rails and let the slats in that way. Alternatively you can just place the slats directly on top of the perimeter and center rails. Likewise for the legs, either build a plate for the leg to push on, or use 4x4s and notch two sides. (I actually prefer the design where the 'legs' are bookcases and go the full width.)

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• Welcome and thank you for your answer! Could you perhaps rotate the images clockwise and adjust their colours (make background white) to improve readability? Or would you prefer if somebody else did that? Commented Jun 23, 2021 at 19:35
• My previous first message was deleted. Funny that I asked for help and clarification, felt the forum does not provide either Commented Jun 24, 2021 at 12:40