How to get the place of max bending moment ?

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Discussion Overview

The discussion revolves around the location of the maximum bending moment (BM) in cantilever beams compared to simply supported beams. Participants explore the conditions under which the maximum BM occurs, particularly in relation to shear force and support reactions.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants assert that the maximum bending moment in a cantilever beam occurs at the fixed support, questioning how this aligns with the concept that maximum BM occurs at zero shear.
  • Others clarify that the rule about maximum BM at zero shear applies primarily to simply supported spans, suggesting that cantilevers have different conditions due to their single support.
  • One participant notes that the maximum BM condition only holds where shear force is a continuous function, indicating that discontinuities in shear load can affect this relationship.
  • There is a suggestion to draw bending moment (BM) and shear force (SF) diagrams to better understand the differences between cantilever and simply supported beams.

Areas of Agreement / Disagreement

Participants express differing views on the application of the maximum BM at zero shear concept, indicating that multiple competing perspectives remain unresolved regarding its applicability to cantilever beams versus simply supported beams.

Contextual Notes

Participants mention the importance of understanding the conditions under which maximum bending moments occur, particularly in relation to shear force continuity and the nature of support reactions in different beam configurations.

hadeel
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what i know is the the max BM at zero shear
but it is said that max BM in the cantileaver beam is at the fixation
how?
is the shear there )0) ??
there is reastion so how?
 
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Yes the max bending moment in a cantilver occurs at the root or fixed support.

A cantilever has only one support so there must be a moment at that support to stop it toppling over.

what i know is the the max BM at zero shear

Check again with your notes or textbook.
This only applies to simply supported spans. These must have two supports and there is a maximum in the BM curve at the same point as the vertical shear curve crosses the horizontal axis.


Have you tried drawing some BM and SF diagrams?
You should do this for both cantilevers and simply supported beams.

Try also beam with an overhang at one or both ends
 
Studiot said:
This only applies to simply supported spans.

Not quite. It only applies where the shear force is a continuous function, for example a distributed load along the beam. It doesn't apply at points on the beam where the shear load is discontinuous.
 
thanks a lot

but please when the max BM at zero shear is applied
 
thanks a lot

but please when the max BM at zero shear is applied

It is not clear whom you were thanking for what.

I suggested you draw some diagrams.

Did you do this?

I have attached a very simple comparison of a simply supported beam with a cantilever.

Do you understand the diagrams I have drawn and how to obtain them?
 

Attachments

  • beams5.jpg
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