Finding Stress Resultant of Cantilevered Beam | James

[recreated]

Can someone please tell me how to find the stress resultant of a section of a cantilevered beam as shown in dia. below? The dashed x, y line is showing the centroid (if that makes a difference for this question)

I know how to find the bending moments and sheer stress, but I am not sure what stress resultant actually means so it makes it 'slightly' hard to find it. If someone manages to just define in simple terms the expression 'stress resultant', or just gives me a bit of advice I should be able to find it easily I think.

Thanks, James.

 

[nvn]

recreated: Are you sure you gave us the whole wording of the question? In the context of an entire cantilever cross section, this is a slightly tricky question. In this context, a stress resultant is the total force acting on the entire cantilever cross section, for each different type of stress. In other words, the stress resultants at a given cross section of your cantilever, on the entire cross section, are shear force F_y, and moment M_x, on the cross section.

 

[Kokuson]

Hi,

You should mention where are you taking the cross section.

If you want to find the stress resultant. You know there are two types of stress : Shear & Normal.

But there are two main types of stress which they are shear and normal stresses.
There are shear stress caused by: A force parallel to the cross section (Average shear), a shear stress caused by Torsion and the real shear stress (not the everage) in which you should find the Area moment, Moment of inertia and you should know a particular deepness on the cross section where you want to find the shear stress.

As for the Normal stress, there are normal stress caused by bending of the beams and you also need to know the deepness of the location you want to find the stress as the stress varies with deepness of cross section. and there are normal stress caused by axial forces (Average normal stresses).

Thus I want to say you should bring more information.

And Total shear stress = Average Shear stress + Shear stress due to torsion + Real shear stress (Note: I do not see any causes of torsion stress in your figure)

Total normal stresses Normal stress (average) + Stress due to bending.

regards

 

[nvn]

It appears Kokuson currently misunderstood the question, and is talking about just stress in post 3 (and additive stresses). But post 1 is asking about stress resultant, not stress. A stress resultant is force, not stress. A stress resultant is stress multiplied by a given thickness, for each different type of stress. Or in the unusual case of post 1, a stress resultant is stress multiplied by a given area (the cantilever cross-sectional area). Therefore, for post 1, the stress resultants are simply the forces acting on the cantilever cross section.

And, some people might be under the misconception that, after you find these force vectors, you then compute a resultant vector. That is generally not the case. You generally cannot describe a stress state with only one vector and orientation. Therefore, combining all stress resultants into a single vector generally would not make sense, or often would not be useful.

 

[Kokuson]

Stress resultant = force ?

This is the first time I hear this in my life. May there are diffrences in terms.
By the way, I studied Hibbler's Mechanics of Materials.

regards