Flitch beam / joist

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Hello,
have to repair an undersized and badly notched joist 38x175mm sitting in an intermediate floor connected to the ceiling below.

The joist is sagging but also has a slope resulting in a lower level support in the middle of the flat (double span joists).

A metal plate 8x150mm would be bolted but the question is, how to manage the installation? Would the metal plate be leveled with the new sistered joist or aligned to the sagging sloping one? In the ideal world. Flitch beam would have elements connected perfectly matching their sides.

See the attachment. Yellow rectangle representing the new straight timber joist. Red rectangle the existing joist. How would you install the metal plate considering 1) timbers not matching their shape 2) support on the right warped leaving a gap between the new straight joist underside and the old joist directly sitting on the bearer.
 

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Just use a slightly deeper steel and timber to pick it all up, notching the ends onto the bearing if necessary.
 
I would think you'd probably need to prop up the sagging joist to bring it ~level, then drill and install the steel plate / bolt it up so when you release the prop, the load is shared properly.
 
I would think you'd probably need to prop up the sagging joist to bring it ~level, then drill and install the steel plate / bolt it up so when you release the prop, the load is shared properly.
Normally I would but below, the flat belongs to another owner, so no feasible. I'm wondering I should just install the metal plate aligned with the sagged sloped joist and then attach a levelled new joist with a spacer at the girder bearing?
 
Just use a slightly deeper steel and timber to pick it all up, notching the ends onto the bearing if necessary.

I was thinking something similar. What about the solution in that picture attached? Thin black lines represent the deformed uneven girder support.
 

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As you cannot prop it up from below there may be a away to pull it up from your side.
Two stretcher bearers across your floor at right angles to the joists. On top of the bearers lay a sheet of steel thick enough not to bow. Drill through the steel a series of holes in line with the affected joist. Using the longest screws you can get your hands on screw into the joist through the holes in the steel. This MAY raise the joist enough to bring it almost parallel.
However, (there's always a however), if you do manage to raise the joist by any method, there is a good chance your neighbours ceiling may crack in the process.
 
As you cannot prop it up from below there may be a away to pull it up from your side.
Two stretcher bearers across your floor at right angles to the joists. On top of the bearers lay a sheet of steel thick enough not to bow. Drill through the steel a series of holes in line with the affected joist. Using the longest screws you can get your hands on screw into the joist through the holes in the steel. This MAY raise the joist enough to bring it almost parallel.
However, (there's always a however), if you do manage to raise the joist by any method, there is a good chance your neighbours ceiling may crack in the process.

The method described is clever, but I would still have the deflected girder bearer (support in the middle of the flat), so I think that trying to straighten the joists in my case is by default not possible. Let alone, as you said, cracks below that are unwelcome by others understandably.

I'm just wondering if from a mechanical/physics perspective, forces are spread in the best possible manner (considering constraints) as shown in the sketch above.
 
When a timber deflects, and its part of a floor or roof, its unlikely to be able to go back to how it was.

Any plate should be fitted level, and if the floor needs to be levelled, new joists added to the correct level - and if new timbers are added, they should be on they own supports, and so a plate and a timber is normally unnecessary.
 
When a timber deflects, and its part of a floor or roof, its unlikely to be able to go back to how it was.

Any plate should be fitted level, and if the floor needs to be levelled, new joists added to the correct level - and if new timbers are added, they should be on they own supports, and so a plate and a timber is normally unnecessary.

So, double up new joists attached to old ones ensuring new ones have their own levelled bearing surface?
 
Yes, and if you are bolting the new to the existing to form a single unit, then the new joists don't need to be the same size as the existing.

In short, you need to decide if the deflection is the whole floor or a single joist, and if so is the cause the notching or undersized joists generally?
 
Yes, and if you are bolting the new to the existing to form a single unit, then the new joists don't need to be the same size as the existing.

In short, you need to decide if the deflection is the whole floor or a single joist, and if so is the cause the notching or undersized joists generally?

The whole floor is sagging, the ventral girder is at lower level with respect to the wall will plate. Joists alternative correct size with undersized ones that are also badly notched. I don't mind to add new joists of the same length and correct size.
 
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