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

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Discussion Overview

The discussion focuses on the relationship between beam length and bending stress, particularly how the length of a beam affects the stresses generated when a moment is applied at one end while the other end is anchored. The scope includes theoretical considerations of bending stress and moments in structural engineering.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant states that bending stress is calculated using the formula M*y / I, questioning how beam length impacts stress when the moment is applied at the end.
  • Another participant emphasizes the definition of a moment and its relation to bending stress, suggesting a need for clarity in understanding the concepts involved.
  • A participant acknowledges that while the moment of inertia and distance from the neutral axis remain constant, the resultant moment at the anchor increases with beam length, indicating a potential misunderstanding of the relationship between moment and beam length.
  • One participant asserts that a higher moment results in higher stress and notes that longer beams produce higher moments.
  • Another participant clarifies that if a moment is applied, it remains constant along the beam's length, while shear forces create bending moments that depend on beam length.

Areas of Agreement / Disagreement

Participants express differing views on how beam length affects bending stress and moments, indicating that the discussion remains unresolved with multiple competing perspectives on the relationship between these factors.

Contextual Notes

Participants have not fully resolved the implications of applying a moment versus a shear force, leading to potential misunderstandings regarding how these forces interact with beam length and stress calculations.

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

Thanks
Matt
 
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?
 
The higher the moment the higher the stress. The longer the beam, the higher the moment.

Thanks
Matt
 
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
 
Your welcome.

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

CFDFEAGURU said:
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.
 
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
 

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