It may seem counterintuitive at first, but this is because there are no bending stresses in the neutral axis.
12.
Here, z is the distance from the neutral axis to a point of interest; and M is the bending moment.
13.
Also, you can test that you have calculated the neutral axis correctly, by seeing if the beam will balance about that axis.
14.
If you have access to a lathe, place the beam on the lathe such that the neutral axis is the axis of rotation.
15.
Z = I / C where I is moment of inertia, C is distance from the neutral axis to the most distant fibre.
16.
In the elastic region of the cross-section, the stress distribution varies linearly from the neutral axis to the beginning of the yielded area.
17.
Denoting \ epsilon _ m as the maximum strain in the beam ( at a distance c from the neutral axis ), it becomes clear that:
18.
The farther a given amount of material is from the neutral axis, the larger is the section modulus and hence a larger bending moment can be resisted.
19.
When a limb is rounded, as in a longbow, some material sticks out farther from the neutral axis, and thus is put under greater stress.
20.
Elementary Elastic Bending theory requires that bending stress varies linearly with distance from the neutral axis, but plastic bending shows a more accurate and complex stress distribution.
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