## Main Question or Discussion Point

I'm a student taking a non-calculus strength of materials course, and I believe I have what is probably a very simple misconception.

I'm wondering why in the "eccentrically loaded column" b), which has two point loads placed at distances of equal magnitude from a centroidal axis, the moments will cancel each other out, and the cross section will be under uniform compression of a single value, but an element on beam a), which is in a state of plane stress, is not considered to be in compression in the y direction (at least in my textbook).

These seem completely analogous to me, besides the material's dimensions. I've got this sneaking suspicion that compression must exist in the y direction but is "negligible" (would it be negligible in an I-beam?), and also not uniformly distributed.

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mfb
Mentor
What is the y direction?

I'm wondering why in the "eccentrically loaded column" b), which has two point loads placed at distances of equal magnitude from a centroidal axis, the moments will cancel each other out, and the cross section will be under uniform compression of a single value
That is an approximation for beams that are much taller than wide (using the orientation of (b) for those words).

What is the y direction?

That is an approximation for beams that are much taller than wide (using the orientation of (b) for those words).
By the y direction, I meant the vertical direction on element c, which has no stress indicated.

And what I'm really interested in hearing is a response to that part of the question, about the state of stress in the horizontal beam.

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mfb
Mentor
This is again an approximation. Close to the contact points of the forces there will be compression, but you do not have an opposing force on the other side of the beam that would give the usual way of compression. You get shear stress instead.

And what I'm really interested in hearing is a response to that part of the question, about the state of stress in the horizontal beam.
I think I see where your misconception is. You're thinking of the beam as a static whole.
I've got this sneaking suspicion that compression must exist in the y direction but is "negligible" (would it be negligible in an I-beam?), and also not uniformly distributed.
Notice how there is particular attention paid to element c. This is an attempt to show you that stress/strain is not necessarily uniform throughout an object. Precisely as you surmised.

I think I see where your misconception is. You're thinking of the beam as a static whole.

Notice how there is particular attention paid to element c. This is an attempt to show you that stress/strain is not necessarily uniform throughout an object. Precisely as you surmised.