Notching joists

[tony1851]

For the purposes of deflection or bending strength?
I agree for the bending strength, but for deflection presumably the overall deflection would be better than a plain 150 joist, due to the thicker, less elastic parts taking a lot of the total amount of bending.

Or does it not exactly work like that?

Both I would think, though probably more effect on bending strength. Intuition suggests that deflection would not be as bad as with a 150 joist.
Trying to work out the bending strength of beams of varying cross-section is a nightmare, often involving integration - I don't go there because I last did that in the 6th form and have forgotten most of it. Thankfully it's rarely a problem in practice, and if someone cuts into the underside of a joist in the middle, it's easier just to assume the whole joist is the reduced depth and check it on that basis.

 

[tony1851]

a 50mm notch in the middle will be weaker than a simple 150mm joist due to the forces being concentrated at the centre

Good point - you may be right - and what complicates it with timber is that (unlike steel) it is not homogenous. It is stonger in compression parallel to the grain than in tension, so presumably the neutral axis won't necessarily be in the middle of the cross-section - complicating it more.

(Yes, curves at changes of profile help to redistribute stresses more effectively than sharp angles. I saw a vid. on you tube the other day about the ill-fated Comet jet. Apparently the windows were square in the corner (rather than rounded as in modern planes) and stresses built up at the corners, resulting in the aluminium skin eventually tearing at that point).