Straightening my roof

A guy came by to give a solar estimate and noticed that my roof was sagging just a little. You can just barely tell in the photo. Anyhow I wanted to fix it now since I'm planning to add solar panels here and I wanted to fix any structural problems before I added them.

The Problem
Turns out my roof is built with 2x6 rafters 2 ft on center. If you lookup the structural engineering span table for roofs with this type of construction, it will say that the maximum span between supported sections is a little less than 12 feet. Unfortunately this section of the house has a slight bump out which causes the span to exceed the span limit whereas the rest of the house doesn't.

Purlins
This section of my roof is actually over 24 ft long. To allow such a long span, with these rafters, the builder supported the roof with a 2x6 placed perpendicularly to the rafters (still horizontal). This is known as a purlin or underpurlin. Of course a purlin hanging from the rafters would do no good, so the purlin needs to be supported. By code, (California at least) a 2x6 purlin needs to be supported every 6 feet. This can be done with a vertical piece of wood under the purlin which would be called a "strut". The bottom of this strut also needs to be supported by something like a post or an interior wall (which turns it into a load bearing wall). It wouldn't be a good idea to use your ceiling joists unless you want a big dip in your ceiling. In cases, where the interior walls are not perfectly under the purlin, code allows you to angle the struts up to 45 degrees from vertical.

Compounding the Problem
It just so happens, that the purlin for this section is directly over a 14 foot wide room. To support the purlin  every 6' over this room, the builder added angled struts from the purlin to the outside walls of this room. Unfortunately, there was not enough height in the attic for these angled struts to maintain a 45 deg angle. Inevitably, you could see that the purlin was bending due to the insufficient support. So when you combine the bending purlin and the overspanned rafters there's no wonder that a slight dip would form.

The rafter had dipped 1.5". The bottom of the wedge should be flush with the laser.

The Fix
The easiest solution I came up with, was to install a second purlin further down the rafters so that there would only be an 11' span. This meant, that I would have even less vertical room for struts than the first purlin did. There would be no way for me to use angled struts to the room's outer walls. I had to instead, install a 14' beam from wall to wall directly under the purlin. This type of beam is called a "strutting beam". The strutting beam would allow me to add vertical struts where ever needed. It would also provide a good place for me to place jacks to jack the roof into a flat plane.

The Strutting Beam
I used an online calculator to size the beam according to my roof span, room span, the number of point loads bearing down on the beam, and the required design specs required in my area (20 psf live load, 10 psf dead load, L/180 deflection). I then upsized the beam to the next lightest beam with a 4x dimension (3.5" wide) so I would have a nice platform for the 2x4 struts. This turned out to be a 14' long 4x6.

Installing the Beam
Getting anything 14' long into an enclosed attic is a feat by itself not to mention that its also close to 90lbs. Luckily, my garage loft provide the perfect access to maneuver the beam and the purlin in without cutting any new holes. Before getting the beam up there though, I did manage to install some solid blocking between the outside wall studs to attach a 4x6 hanger to and a 2x4 spacer that would elevate the beam by 1.5" from the ceiling. The spacing is provided so the beam can bend under the weight of the roof. If you put the strutting beam right against the ceiling drywall, you may find several ceiling drywall panels pushed into the room below. I also had to notch what seemed to be an unnecessary hanging beam for the ceiling so that the strutting beam could go under it. I then nailed down the beam into the hanger and installed blocking at the other end to keep the beam from rotating under load.

Installing the Purlin
The purlin is probably trickier to install than the strutting beam. This is because the roof already has a dip and I'm trying to attach a straight 2x6 to rafters that are not in line with each other. Also when you try to mate a square edged purlin to angled rafters, the bearing point between the two won't be flat. In most construction books, they recommend that you cut a birds-mouth (ie a little stair step) into the rafter. I didn't think cutting into an overloaded rafter was such a good idea, especially since I would be under it. Instead, I cut wedges that matched the roof slope and glued and screwed them in place. Then to attach the purlin to the rafters, I used hurricane ties wrapped around the wedges. I recommend using a plumb vertical laser to align all the hurricane straps when installing them.
 You can see all this in the photo below. I started attaching the purlin in the middle at the lowest part of the dip and worked my way towards either side. For each rafter, I was able to bend the purlin with a bottle jack until it was flush with the wedge and then nailed it together.

Jacking the Roof

Now came the fun yet nerve racking part. I used a level laser line to establish how far I wanted the purlin to be raised. I then proceeded to carefully jack up the roof next to each strut location. I could see the strutting beam bending as well as the roof straightening out. Luckily, I got to the laser line just as the beam bottomed out at the ceiling. In hindsight I probably would have added a half inch more space, but that would have meant that I needed to make my notch in that hanging beam even bigger.

Tricks of the Trade
If you decide to do this by yourself, there are lots of little things I did to make things easier.

• To lift and hold the purlin in place by yourself so you can attach it to the rafters, use some hanging wire and some screws attached to the rafters to support both ends. The wire should go from the screw, under the purlin, and back to the screw like a loop. When you're at one end, lift the purlin as high as you can, then twist the wire together under the purlin to remove all the slack and keep the purlin lifted. Repeat on each end until you get the purlin close enough for you to hold it in position with your hands.
• To position the beam under that notched hanging beam, I used 2 strands of hanging wire twisted together with a piece of metal conduit sleeved over it. I then attached the wire between the ceiling joists so that the strutting beam could rest on the conduit/wire without pressing on the ceiling drywall. This gave me a place to rest the strutting beam while I threaded it through the ceiling joist bay and the hanging beam. Be sure to remove this conduit/wire from under the beam before you put any load on the beam or else you'll flex the ceiling joists they are attached to.
• Cut and notch your struts on the ground not in the attic. Just leave them extra long to account for the strutting beam flexing too. You then only need to trim them to length in the cramped attic space.
• Use a power nailer. I had a pneumatic palm nailer which works, but if you can spring for those hanger nailers that let you precisely place the nail tip, that would be ideal.
• Self-leveling lasers are awesome, but trying to line up a laser beam with a pencil mark 14' away in a dark attic cramped attic is nearly impossible. I stood up my speed square (looks like a triangle) on the mark and that gives me a nice large plumb target to aim for.

Finally Done
Here you can see my finished work and how the purlin matches the laser now. I think the total cost of materials was less than $100 even if you had to buy the items I already had. I splurged on a new Makita cordless jigsaw which made the notch cutting in the attic much easier.

Bill of Materials

• 4x6x16' #2 Doug Fir - $36
• 2x6x16' #2 Doug Fir - $12
• Box of 1.5" 8d Common Nails - $5
• 7 Hurricane Rafter ties - $6
• 4x6 Hanger - $2
• 2x4x8' #2 Doug Fir - Already had
• 16d 3.5"Common Nails - Already had
• 10d 3" Common Nails - Already had
• (Optional) Scrap hanging wire, conduit - Already had 

Total - $61

Tools used

• Ridgid Pneumatic Palm Nailer
• DEWALT D55146 4-1/2-Gallon 200-PSI Hand Carry Compressor
• Amflo 577-50A Green 300 PSI Rubber/PVC Air Hose 3/8" x 50'
• Milwaukee 6955-20 12-Inch Sliding Dual Bevel Miter Saw
• Speed Square
• Makita BSS610Z 18-Volt LXT Lithium-Ion Cordless 6-1/2-Inch Circular Saw
• Makita XVJ03Z 18-Volt LXT Lithium-Ion Jig Saw
• Makita LXDT04Z 18-Volt LXT Lithium-Ion Cordless Impact Driver
• Husky 6-Ton Bottle Jack
• DEWALT DW087K Horizontal and Vertical Self-Leveling Line Laser
• Hammer