Is max bending stress always at the location of max moment?

[JeffZ]

Hello guys,

I have a simple question about the max bending stress in a beam.

We know that in a cantilever beam, the biggest moment occurs at the wall. This is also the location of the max stress with equation stress= M*y/I
,

However, in a simple supported beam, we have

This time, the max moment occurs at the middle of the beam. But I doubt this is the location of the max stress. I think the max stress location should still be at the wall.

So we have a problem here: Is the max bending stress located at the location of the moment?

 

[SteamKing]

Hello guys,

I have a simple question about the max bending stress in a beam.

We know that in a cantilever beam, the biggest moment occurs at the wall. This is also the location of the max stress with equation stress= M*y/I
,

However, in a simple supported beam, we have

This time, the max moment occurs at the middle of the beam. But I doubt this is the location of the max stress. I think the max stress location should still be at the wall.

In a simply supported beam, there is no 'wall' like there is for a cantilever beam.

So we have a problem here: Is the max bending stress located at the location of the moment?

There's no problem here. Since σ = My / I, the location of max. bending stress is going to be where the max. bending moment is located.

You have to pay attention to the support conditions for a beam because a simple support is not the same as a fixed support.

 

[Chestermiller]

Also, since a simply supported beam has zero slope at its center, from the center to each edge, each half of the beam looks like a cantilever beam.

Chet