After jacking up and sistering the joists, we still had some sag and too much bounce for me to be confident enough that the tile in the tub above would be stable enough. There's never been tile in the bathroom to prove/disprove my thoughts. Couldn't go with taller sistering as the ceiling height is already about 7'7". So we decided to add a beam in the middle of the kitchen to effectively shorten the span of the joists for the bathroom floor. Normally this would require footings in the foundation to support the extra load. But normally, beams carry a lot more weight.
We have approximately an 18 foot span for the worst joists. A beam would take approximately half the load if it's in the middle, meaning it supports 9 feet of joist. The beam in our case only needed to span across a few joists, giving it a 6.4 foot span. 6.4 * 9 is ~58 square feet that said beam is supporting. BUT, it's also supporting a sidewall for a dormer. The sidewall of a shed dormer should carry no load, so it's mostly just dead weight. Anyway, assuming 10 lbs PSF dead load, and 40 lbs PSF live load, (The state building code standard) we come up with 2900 lbs of support needed IF EVERY square foot of the floor above was loaded FULLY. Doing more calculations (accounting for the lack of floor over the stairway, etc) brought the realistic max load to about 2300 lbs, plus the dormer load.
Once again, we turned to LVL lumber. MAX-LAM 2.0 is the strongest LVL I've found. LVL is like plywood in normal lumber form. It's many layers sandwiched together with resin. Stronger than normal lumber and doesn't warp.
The goal was to use the shortest height beam and still be confident that it would handle the load.
Using a table from the LVL manufacturer, we found that the max load on a 6 ft span of a 5.5" tall beam would be VERY close to what we needed. Made some calculations with some help (Thanks Jon!) to make sure.
Local lumberyard had no 5.5" in stock, so they cut some 11 1/4" stock in half for me. I got 4 pieces. (2 pieces of 11.25" cut in half) 2 were used as the columns to support the beam. Since there would be 2 pieces remaining, we decided to double the beam thickness and then we were POSITIVE that the beam would MORE than handle the load. In fact the beam should then be able to handle close to 6000 lbs, which is about twice what we think it would actually be loaded to in a worst case scenario.
Part of the kitchen wall was ripped out to get access to the foundation. Ripped a piece of LVL to about 4" to match the studs in the wall. Ended up the best place to set it was right against another stud.
On the other side of the beam, there's a concrete pad in the floor that supports the chimney, water heater and furnace. We rested the other column on this concrete. This is how we cheated a bit in not having to pour a footing. Had to cut out existing flooring to get access to enough space on this concrete.
We *Again* jacked up the joists as best we could with jack posts, 4X6s and a bottle jack. This held the joists up as much as we could.
The columns were set in place for a mock-up. Then, using a string and a level, ran a line from the lowest hanging joist to each column to create a straight line all the way across. (Since the bottom of the joists were not straight.) With that line, I was able to measure and cut the columns. Set them in place and crossed my fingers. And to my surprise, the beam slid nicely in place the first time! So I nailed a mending plate in to hold the beam to the column on one side. On the other side I secured the beam to the adjoining stud. A mending plate will be added later when more of the kitchen wall is out. Then nailed the 2nd layer of beam on with nails sized and spaced per the LVL manufacturer's instructions.
Then, I used wood shims to make sure ALL of the joists in the span were making good solid contact with the beam. We carefully lowered the jack posts that were providing temporary support and loaded the beam. No noticeable flex, very little noise. But the beam is taught and definitely loaded. Project was a success! And the floor above is more solid than I imagined it could be! Probably more than it ever has been since the house was built.
First picture shows the inside column.
The second picture shows the outside wall side.
The third picture shows the beam. Notice the shims in place between the beam and the joists.
This was the last thing to do before we could make some major progress IN the bathroom. (FINALLY!) The next thing is to frame a wall that will become one side of the tub alcove. Then the current tub will be destroyed and removed so we can build the wall for the other side of the alcove.
But first, I need to go take care of the snow.