Someone cut enormous holes through my floor joists for plumbing — how do I strengthen them?

The realistic repair options, roughly in increasing order of intervention:

Sistering. Fixing a new full-length member alongside the damaged one, bearing on the same supports at both ends. This is the standard repair and it works because the new member takes the load rather than reinforcing the old one. The critical detail is that it must reach the supports — a sister that stops short of the bearing points is decoration.

Flitch plates. Steel or engineered plate sandwiched to the joist, bolted through. Useful where a full-depth sister will not fit past the pipes, since the plate can be shaped around them.

Adding a support underneath. A beam and posts halving the span. Often the cheapest and most effective option if the space below allows it, because halving the span dramatically reduces the load on the damaged section.

Rerouting the plumbing. Frequently the right answer and the one people resist. Running a pipe below the joists in a dropped ceiling, or in a different direction, may cost less than structural work.

Plywood sisters glued and screwed on one side are sometimes proposed. They add stiffness and they are not equivalent to a full-depth member on both sides.

The first thing to establish is where the holes are, because position matters more than size.

A joist in bending has tension along the bottom edge and compression along the top, with a neutral zone in the middle. That means:

• A hole in the middle third of the depth, near the middle of the span, removes material that was doing relatively little.
• A notch or hole near the top or bottom edge is far more serious, because it cuts the parts carrying the most stress. A notch in the bottom edge is the worst case of all, and it is what most improvised plumbing produces.
• Holes close to the supports are affected differently again — shear dominates there rather than bending.

So before anything else, note for each joist: how far along the span, how far from the top and bottom edges, and how big relative to the joist depth. That set of numbers is what any answer depends on, and it is what an engineer will ask for first.

On when to get an engineer, and the answer is more often than people like: now, in your case.

The signals that it is not a do-it-yourself decision:

• Holes or notches that look large relative to the joist depth, which yours do.
• Anything cut into the top or bottom edge.
• Multiple joists affected, which yours are.
• A long span, or a floor that already deflects or bounces.
• A bathroom, which means a wet room and possibly a heavy fixture.

A structural engineer's visit for a domestic floor is not an enormous expense and you get a specified repair rather than a guess. That specification is also what a building inspector will want, and what a future buyer's surveyor will want to see.

Worth adding: a joist that has been like this for decades without visible problems is not evidence it is adequate. It is evidence it has not yet been loaded enough.

One thing to check while the floor is open, since you will not have this access again: whether anything else was cut for cables or ducts in the same joists.

It is common to find that whoever ran the plumbing was followed by somebody running wires who made their own holes in the same members. Two moderate holes in one joist are worse than one, and finding the second one after you have completed a repair is annoying.

Photograph everything with a tape measure in shot before you close it up.