Finding the bending moment for maximum stress

Click For Summary

Discussion Overview

The discussion revolves around determining the maximum bending stress in a beam using the formula My/I, with a focus on how to find the appropriate bending moment in a scenario involving multiple loads on a pin joint cantilever beam. The conversation includes technical explanations and clarifications regarding the bending moment diagram (BMD) and its relationship to shear forces.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • One participant expresses uncertainty about how to find the bending moment due to multiple loads on the beam.
  • Another participant suggests that internal moments can be determined from the shear diagram, which can be constructed from the reactions of the beam.
  • A later reply clarifies that the maximum bending moment corresponds to the values that lie furthest from the zero axis on the bending moment diagram.
  • There is a discussion about whether the maximum bending moment should be considered as the absolute value from the x-axis.

Areas of Agreement / Disagreement

Participants generally agree on the method of using the bending moment diagram to find the maximum bending moment, but there is some uncertainty regarding the interpretation of values and the relationship between shear force and bending moment.

Contextual Notes

The discussion does not resolve the initial participant's confusion about identifying the correct bending moment in the presence of multiple loads, and assumptions regarding the beam's loading conditions are not fully explored.

Who May Find This Useful

This discussion may be useful for students or professionals dealing with structural analysis, particularly those working with cantilever beams and seeking to understand the relationship between shear forces and bending moments.

Jameseyboy
Messages
25
Reaction score
1
Hi,

I am looking to use My/I to find the maximum bending stress for a beam

My problem is I don't know how to find the bending moment- the reason why:

The beam has more than one point of load, aside from the reaction points. (Pin joint cantilever beam)

The sum of all moments equal 0 so I don't know how or which bending moment to use.
 
Physics news on Phys.org
Your problem is not clear. Perhaps there is a diagram showing the beam and loading which you can post?

In any event, if the beam is in equilibrium, the sum of all moments will equal zero. However, you are looking for the moments which are internal to the beam. If you have the reactions of the beam, construct the shear diagram, and from this, you can construct the bending moment diagram. Once you have done this, the max. BM should be clear.
 
Ahh ok, so I can physically get the answer from the BMD? Is this typically when it crossed the x axis? Then the actual value is THAT particular moment on the beam disregarding the other ones?

Sorry to be so vague
 
The maximum BM is just that: it's the value which lies the furthest above or below the zero axis. The points where the shear force is zero are also points where the BM is a maximum or minimum, since dM(x)/dx = V(x), according to Euler beam theory.
 
Right. So it's not the value I.e. Going from +2 to -2 meaning 4 ---> it's actually the absolute value from the x axis- so '2'?
 
Correct.
 
Fantastic. Cheers
 

Similar threads

  • · Replies 4 ·
Replies
4
Views
4K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 11 ·
Replies
11
Views
3K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 9 ·
Replies
9
Views
4K
  • · Replies 2 ·
Replies
2
Views
4K
  • · Replies 1 ·
Replies
1
Views
3K
Replies
6
Views
2K
  • · Replies 7 ·
Replies
7
Views
3K
Replies
2
Views
8K