beam overhanging two supports

[swmn]

I am roofing a wood shed.  Nominal 4x8 foot floor, with six 4x4 vertical posts each bearing directly on a cinderblock.  

So the snow load on the roof goes straight to ground via the cinderblock and the floor only needs to support the cordwood.

I am space constrained by the project, and need to put three of these side by side by side.  They need to be relatively portable for both the tax assessor, and in case the young children in the home choose to play behind them; they may need to be moved for the kids if they are playing behind the wood pile next to the road and should be mobile for the tax assessor.

The roofing metal selected by the client comes in three foot section width.

Viewed from the front 8 foot wide aspect I have one  2x6 rafter at each end, with a doubled 2x6 rafter on the middle posts.  Rafters are 6 feet long, centered, on 2:12 pitch, about 7 degrees, so nominal one foot overhang on the front and back.  I am good on snow load there (55 psf) with plenty of head room.

Perpendicular to the rafters I have 2x4 (#2 SPF) purlins, 5 of them @ 14.4 inches on center.  Oriented 3.5" tall and 1.5" width.  

If I am using the 'beam overhanging one support' tool correctly I should be good to put a one foot overhang to the right on the right hand unit and a one foot overhang to the left on the left hand unit.

What about the center unit?  If I raise the center unit roof say 8"or so can I overhang it 6" at both ends or do I need to use a different tool?  

Thanks

[Don P]

Usual disclaimers but I think you should be fine. You could check the impact on the center span compared to a simple beam. In this case I suspect the overhangs are helping that. If the center span moment is potentially getting into trouble or if the positive moment over the support is high I'd call in more help. I'm thinking that would take a good deal more overhang. Do block solid between purlins over the rafters.

[swmn]

Ok, thanks for that.  I think it looks good then.

The simple beam shows 0.11 inches max deflection, the hanging end shows 0.02" max center span and -0.02" max at the overhanging end.

My section modulus is almost double what is required at M1, 3.06 v- 1.59 and golden at M2, section required 0.45 and I have the same 3.06

I seem to be golden at R1,  section required is 1.7 and I have 5.25.

So really the weight hanging off the edge is helping keep the middle more flat it seems like.

I tried it again with a six inch overhang and see what happens to M1 and M2.  M1 goes up to 127 ft lb, my required section modulus goes up to 1.76 and I have 3.06 available.  If I do six inch overhang at both ends of a shed would M1 for the full span (9 foot purlin on an 8 foot shed) double? If so my section modulus comes up a little short, would be looking for 3.5 and I only have 3.06.

[Don P]

We're getting above my schooling as far as giving you an exact answer but here is how I'm looking at it.
Run a sample calc using the simple beam and the overhanging beam. Notice the overhanging beam lowers the bending moment. The overhang up to a point is indeed "helping" the main span by lowering the bending moment. An overhang at the other end is going to give about the same amount of help again. You are in that range. As the overhang relative to the main span becomes considerably greater then it would be bowing the center span up and you get into a different problem, you are nowhere near that. So short answer after all that, the second overhand reduces the main span moment more which decreases needed beam size. I would not reduce beam size but no you don't need to double the moment.

[swmn]

I feel a lot better about committing reasonable overkill if I put a sixth purlin up on the rafters of the shed unit with 6" overhang at both ends.  It drops the maximum M1 moment down under 100 ft lbs.  I guess I don't really know how many foot pounds I can exert on a 36" crowbar, but my last few vehicles all required 100 ft lbs second pass torque on the lugnuts.  I don't think I could shift a 2x4 held down with 3 or 4 well placed timberlocks using my torque wrench as the lever.

I concede if snow load is uniform five purlins is likely adequate; even with severe wind sculpting it seems unlikely to overbalance a 6" strip against an adjacent 48" span.  But the homeowner has only been there less than six months and isn't the sort of individual to notice where snow drifts up and gets blown from.  He wants the wood shed to outlast his mortgage, one and done.  He is willing to keep it level as the cinderblocks press into the ground.

Is Doug Fir strong enough to bother putting it into the tools for dimensional lumber 2-4" thick?  I am getting to have a lot of respect for Doug Fir over on the beams and stringers tools compared to SPF.  And I have pulled some beauties lately.  In the last 6-8 months I have pulled 4 quartersawn beauties out of the #2 grade 2x4x96 stacks, 2 of them had no visible sapwood, one of those was no sapwood and zero knots, end to end.  Given my advancing age it might be the best 2x4 I see in my life, but I did bring it home.

[Don P]

Sure, I'll double check it tonite but DF-L is 4th item down, I think I chose the weaker combination but I'll check. I realized last night I need to stick red pine in there as well.

[Don P]

I found some equations and had to take off my shoes. This is as much as I could get to produce what seems to be good output so far. I'm still scratching my head on the rest. Feel free to bang on it and tell me where it breaks;
http://timbertoolbox.com/Calcs/beamover2posts.htm


Edit;
Reactions aren't adding up  :-\

[Don P]

Try again
http://timbertoolbox.com/Calcs/beamover2posts.htm

At the bottom I added "Distance from left support to max moment, X"
Look at the moment diagram above and you'll see that if the overhangs are different lengths the point of max moment moves, so its giving you that point. That might need better labeling, it is quite possible that the point of maximum bending moment is right over a post depending on overhang  proportion to span. 

A couple of other things to think about. Notice that the inflection point in that moment diagram, the point where the bending moment passes through zero also moves in relation to overhang lengths.

Anyway, attempt 2.

[swmn]

I will make a point to play with it ASAP.  I just came off 13 days in a row with 130 hours clocked, had one day off and started 12 more days in a row on 06-29 with 14 hours.

I don't expect lateral assymetrical snow loading to be much of a problem on my current project, and I think I have enough pitch on the roof for the snow to slide off longitudinally all at once when it happens, but now I am curious.