I have seven 24 x 13.302 glass panels that I want to use to build a greenhouse. I also have a lot of 2x4x14s and 2x4x8s that I can use. I would like for the greenhouse to be as close to 14x14 as I can get.
Can I span 14' with just 2x4x14s for ceiling joists to support the window panels with no supporting beams underneath?
Can I span 14' with just 2x4x14s for ceiling joists
Here's why:
You want a flat roof with 14' 2x4s. They will have a hard time supporting themselves (horizontally) over that distance, let alone also supporting any sort of roofing material, especially something as heavy as glass. If, however, you'd like to use the roof as a (short lived) trampoline, then you've got the makings of great fun! Please be sure to video that event, as you'll earn your 15 minutes of internet fame with the footage!
According to the ceiling joist span table at this site* the maximum ceiling span you can get out of a #2 Douglas Fir 2x4 for a flat span is 12'5". Note that this is a different wood than Southern Yellow Pine (SYP) or Spruce-Pine-Fir (SPF) lumber (which is what most big-box store lumber yard construction lumber is). If you've got SYP or SPF, your maximum span is 11'10". Oh, and that's if you're spacing them every 12 inches on-center!
In order to span 14', you'd need to step up to 2x6" lumber, then you can span at 12", 16" or 24" OC for your flat roof.
If you're actually looking at a pitched roof, then these are rafters, not joists.
Again referring to the same site, but this page**, you can span 7'1" if you have #2 SPF and you space your rafters at 12" OC. That's 7'1" from the ridge beam to the wall which will just get you your 14' wall-to-wall span. However, at 12" OC, I don't think your glass panels will fit between them.
In order to space the rafters 16" OC to enable you to put your glass panels between them, you'll again need to step up to 2x6" lumber. You can use #2 SYP or #2 SPF, spaced 16" OC and span 8'5" or 9' (respectively). That will easily get your 14' clear span from the ridge beam and leave you with enough room to put the glass in between.
*The first site listed in a search for "roof span table". No affiliation, recommendation or endorsement intended or implied. Feel free to look at other tables/calculators to see if they give you different numbers if you'd like.
**Since we don't know where you live, I'm using the more conservative table that includes a 50PSF snow load. You may adapt as necessary to your locale.
24x13.302a dimension in inches? Is the.302portion a typo of some sort? It's quite unusual to quote inch dimensions in decimal fractions and very unusual to go to the thousandth of an inch.