Explaining Bending Stress in Cantilever Beams

[Timisoarian]

Hey everyone,

I was just wondering if someone could explain to me what Bending stress is? Supposed you have a cantilever beam with a point load at the free end, I know that the bending stress will decrease as you move away from the fixed end? but why? and how can you back that up?

Also, as the beam is bending downwards, doesn't that create a hogging moment? tension at the top and compression at the bottom? which mean top is negative bottom is positive? please explain!

Please, any help is appreciated!

 

[PhanthomJay]

Hey everyone,

I was just wondering if someone could explain to me what Bending stress is? Supposed you have a cantilever beam with a point load at the free end, I know that the bending stress will decrease as you move away from the fixed end? but why? and how can you back that up?

Also, as the beam is bending downwards, doesn't that create a hogging moment? tension at the top and compression at the bottom? which mean top is negative bottom is positive? please explain!

Please, any help is appreciated!

You'll need to take a course in mechanics of materials, but basically, the bending moment increases as you approach the fixed end (varies from 0 at free end to maximum PL at fixed end, using moment equation formulae) , and since bending stress is a function of bending moment and beam properties (M(y)/I if you are at all familiar with the formula for bending stress), it too will increase to a maximum at the fixed end topmost or bottom-most fibers. Yes, hogging, tensile bending stress on top fibers, compression bending stress on bottom fibers, no bending stress at neutral axis, etc... what do you mean by negative, that's a loaded word...

 

[SteamKing]

Hey everyone,

I was just wondering if someone could explain to me what Bending stress is? Supposed you have a cantilever beam with a point load at the free end, I know that the bending stress will decrease as you move away from the fixed end? but why? and how can you back that up?

The bending stress is caused by a bending moment applied to a beam. Due to the nature of bending and its effects on a beam, the bending stress at at particular location is partly tensile and partly compressive, unlike stresses produced by other types of loadings:

The bending moment in a cantilever beam which has a point load applied at the free end is a maximum at the fixed end and is zero at the free end; thus, the bending stress is a maximum at the fixed end and zero at the free end.

This is a nifty graphic showing a plot of bending moment magnitudes along a cantilever beam:

Also, as the beam is bending downwards, doesn't that create a hogging moment? tension at the top and compression at the bottom? which mean top is negative bottom is positive? please explain!

Please, any help is appreciated!

In most stress conventions, tensile stresses are considered positive, while compressive stresses have negative magnitudes.

If the force applied at the tip of the cantilever is pointing down, then the bending moment can be called "hogging" [which term is mostly used in nautical circles].

If the force applied at the tip of the cantilever is pointing up, then the bending moment can be called "sagging".