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

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SUMMARY

The discussion focuses on the relationship between beam length and bending stress, specifically using the formula for bending stress, σ = M*y / I. It is established that while the moment of inertia (I) and the distance from the neutral axis (y) remain constant, the bending moment (M) at the anchor increases with beam length. This indicates that longer beams experience higher bending moments, which in turn affects the resultant stresses. The distinction between applied moments and shear forces is clarified, emphasizing that shear forces create bending moments that depend on beam length.

PREREQUISITES
  • Understanding of bending stress and its formula (σ = M*y / I)
  • Knowledge of moment of inertia in structural engineering
  • Familiarity with concepts of shear force and bending moment
  • Basic principles of static equilibrium in beams
NEXT STEPS
  • Study the effects of varying moment of inertia on beam performance
  • Learn about shear force diagrams and their relation to bending moments
  • Explore the impact of different beam materials on bending stress
  • Investigate advanced topics in structural analysis, such as finite element methods
USEFUL FOR

Structural engineers, civil engineering students, and professionals involved in beam design and analysis will benefit from this discussion.

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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