Von Misses stress in Beam element are higher than hand calculation

[felixjr11]

Hi All,

I would like to ask for help in what I'm doing wrong for this simple I beam stress analysis.

(as I learn the Nastran software I started to a simple problem for varication)

I have I beam HE 100A , simply supported and loaded with uniform distributed beam of 100N/mm.

when I run analysis, result in moments are correct however the Von misses gives higher stress.

hand calculation = 174.56Mpa

Inventor Vonmises = 306.4 Mpa max

what did I do wrong please help me so I could better understand the Nastran. 

Thank you all in advance

[John_Holtz]

Hi @felixjr11 

I see two potential differences:

1. The image of the deformed shape shows that it is not simply supported.
2. Most hand calculations are for the bending stress in one plane, not the von Mises stress (which includes three normal stresses and 3 shear stresses).

Are you sure that your hand calculations and model are for the same thing?

[felixjr11]

Hi @John_Holtz ,

Thank you for quick reply, for my support I use symmetry at one end at Y direction and on the other end I release rotation at z axis. Am I getting it correct? and for my calculation I use max Mo = wL2/8, then Bstress is = Mo/Sx which I got a 174.57MPa or (180.75Mpa w/o radius bet flange and web).

I notice that Beam equivalent stress are similar with hand calculation, which means that its use a one plane?

[felixjr11]

@John_Holtz,

Regarding Von Misses, I try to model it as shell element, same constraint and loading (but convert to force), what I am getting as a result are similar to calculation. 181.4Mpa. why they have big difference with beam element? 

Please correct me where I am wrong.

Thank you very much

[John_Holtz]

Hi @felixjr11 

Can you provide your hand calculations? That would show us what you are trying to model.

• The beam model is obviously not behaving like a half-symmetry model (if I understood your description).
• The shell model is supported at the bottom flange. That constraint does not match the hand calculation which is based on supporting the beam at the neutral axis.

[John_Holtz · Accepted solution]

Hi @felixjr11 

Sorry, I missed the calculation that you provided in one of your replies. For the convenience of other readers, here are the complete hand calculations (extracted from the model provided):

• arrangement: simply supported I-beam.
• length L = 1000 mm
• uniform distributed load w = 100 N/mm
• area moment of inertia I = 3.319E6 mm^4 (calculated by Nastran, let's assume it is correct)
• depth of section h = 96 mm
• Maximum moment Mmax=w*L^2/8 = 1.25E6 mm*N
• maximum stress = Mmax*(h/2)/I = 180.78 N/mm^2

With the corrected constraint (see analysis 2 in the attached), Nastran is calculating 180.75 N/mm^2 for the maximum stress. Therefore, the results are identical.

The von Mises stress at the center of the beam is also 180.75 MPa, so it is correct. This is somewhat of a coincidence because the shear force is 0 at the center of the beam. Otherwise, the von Mises stress is generally different than your hand-calculated bending stress. (The maximum von Mises stress is shown at the supports because the calculated shear stress is high.)

Does this make sense?

[felixjr11]

Hi @John_Holtz  Thank you for correcting my support definitely this is correct answer .

Kind Regards

[radek_pytlik]

Hello, Von Mises stress is calculated: =Sqrt[(Equivalent Stress)^2 + 3*(Total Shear Stress)^2)], but for Beam element doesn´t make sense to use it because it has higher values, than Equivalent stress. It can be verified by simple bended beam supported at one end and force on opposite end. And it corrsponds always to hand calculations.