Question:
Can I model a deep beam or plate girder with plate element ? How can we extract the bending moment at required section along the beam length?
Answer: Yes, one can model a beam or a plate girder with the plate element and can obtain the bending moment about any desired axis oat any section.
Following are two models, one modeled with beam entity and another with plate entity.
The dimension of the beam is as mentioned below.
Length 3.048 m
Width 0.152 m
Depth 0.61 m
The plate is meshed and now after performing the analysis, the cantilever end moment is reported as 135 KN-m in the member entity model.
Now let us compare it with the extracted bending moment in the plate entity model.
The bending moment at any section is the total moment developed about the neutral plane due the longitudinal stress exerted by the infinitesimal number of fibers sections at the said location.
Now. in this simple cantilever beam, the upper half of the neutral axis experiences tension and the lower half experiences compression.
These two opposite forces generates the moment due to the bending action.
Although the fiber and their corresponding stress distribution is continuous in reality but here we need to discretize them by the finite element meshing to account for the total force.
So, we need to compute the summation of the all the moments developed about the N/A.
Please see the following calculation.
The total moment here is 132 KN-m.
So, the bending moment in Member entity model = 135 KNm
So, the bending moment in Member entity model = 132 KNm
The more you mesh, the better the result you can expect.
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