Length & Bending Stress: How Does Beam Length Impact Stresses?

[studentoftheg]

if you have a beam or something, anchored at one end and apply a moment at the other end, then the bending stress is given by M*y / I, where I is the moment of inertia of the beam. what affect does the length of the beam (i.e. the distance between the anchor and the end of the beam, where the moment is applied) have on the stresses generated?

 

[CFDFEAGURU]

Look at the definition of a moment and then equation for bending stress.

Thanks
Matt

 

[studentoftheg]

Thanks Matt, OK well maybe I'm not picturing this correctly in my head. I know that a moment = force x distance (from point of interest), but in my example there is an applied moment to the end of the beam (irrespective of the length of the beam). As I stated above, the bending stress is M*y / I. Now the moment of inertia of the beam isn't affected by the length of the beam, and obviously neither is the distance from the neutral axis (y). So, if say a moment of 100kNm is applied to a beam that is anchored at one end, then the stress doesn't appear to be affected by the length of the beam (it is M*Y/I), which I'm thinking has to be wrong?

 

[CFDFEAGURU]

The higher the moment the higher the stress. The longer the beam, the higher the moment.

Thanks
Matt

 

[studentoftheg]

Right, I see now. So the resultant moment at the anchor will increase as you increase the length of the beam. I was picturing it wrong...
Thanks again

 

[CFDFEAGURU]

Your welcome.

Matt

 

[AlephZero]

if you have a beam or something, anchored at one end and apply a moment at the other end...

The longer the beam, the higher the moment.

Be careful about what you really mean here. If you apply a moment (i.e. two forces that produce a couple), the moment is constant along the length of the beam.

If you apply a shear force, that creates a bending moment which does depend on the length of the beam.

 

[CFDFEAGURU]

Yes, that is correct. Due to the length factor, I was figuring a force was being applied to create a moment load at the anchor.

Thanks
Matt