Tetsuaiga":2b7aqrfm said:
Beams under force are meant to compress on their top section and have tension on the opposite side.
Something I'm wondering is that the shortest distance between two points, for instance the end of a beam is a straight line. When the beam bends, does the top section get shorter while bending, because I imagine for it to compress that's what has to happen. I suppose the flexing must bring the ends at the top closer to the centre but further apart than originally on the bottom?
The top curve and the bottom are not idential replicas of one another, if you imposed one on top of the other?
An awful lot of very complicated books with a lot of maths in them have been written on this subject, and an awful lot of experimental work done in many, many laboratories - mainly because a lot of the built environment depends on being able to predict what beams will do!
The simple answer is "it depends". On lots of things. The material the beam is made of - especially whether that material behaves as an elastic or as a plastic, it's dimensions, and how it's loaded. A great deal of time and money are spent analysing such things to ensure that things will do what they're supposed to - aircraft wings, for example, are not much good if they break off at 30,000 feet. Hence lots of hard sums to see that they don't. Normally.
For something like a shelf in a bookcase, made of wood, and supported at both ends, with a full load of books, the wood will deflect - you can usually see it! If the shelf returns to it's straight original form when the books are removed, that deflection is referred to as 'elastic', and in that case, the top fibre will compress a little, and the bottom fibre will stretch a bit. (Same thing happens with most metals, but not with concrete, unless someone puts some steel wire reinforcement in it.) The shape of the curve the shelf takes up will not be the same if the load were just a heavy lump in the middle, and will be different again if the lump were nearer one end. If the shelf is fairly thin relative to it's length (which most are!) the curve of the top fibre will be very close to the same shape as that of the bottom fibre - but that may not hold good in a beam that's thick relative to it's length, or of changing section (aircraft wing again!).
So - yes, in a simply-supported beam with a point load or a distributed load, the top fibre is in compression and shortens, and the bottom fibre is in tension and stretches; thus, the ends of the top are (very slightly) closer together, and the ends of the bottom further apart - you're quite right. In most 'normal' situations, those changes of size are not great, however.
Hope that helps - for more information, any good book on Strength of Materials will do; but don't blame me if you end up scratching your head - this stuff can get seriously complicated!
