Grasshopper

algorithmic modeling for Rhino

bending moment changes according to the size of cross-section?

Hello all,

I made a simple vertical structure, and set supports at the top and bottom points.

bottom : rigid connection; all blocked

top : pin connection; Tx, Ty, Ry, Rz blocked.

Direction of linear load is y.

When I change the size of the cross-section(in this case, diameter of circle),

bending moments changed and also maximun bending moment from "beam resultant component" changes.

In my opinion, the bending moment should not change if I change the inertia, under any support conditions.

I attached the screenshots and gh file. 

I'll wait for your comments. 

Thanks!

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Hello Jamparc,

you are right, the bending moment should not depend on the cross section in this example. Thank you for your bug report. I will look into it and give you notice as soon as I have located the problem.

Best,

Clemens

Thanks for your reply.

I found that when the diameter is 0.1cm, it shows correct maximum bending moment.

Hello Kirk,

you are right, the shear deformations cause the change in the maximum bending moment.

In the attached example the shear area in Y-direction Ay is set in a fixed relation to the moment of inertia  Izz about the beams z-axis (Ay = Izz). Then the moment distribution is also fixed.

Clemens

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Hello Clemens,

Your explanation seems logical but it gives rise to another question. In case the issue was really the effect shear deformations, then why doesn't the Maximum bending moment change with the diameter, when both ends are fixed? This variation is happening only when one end is fixed.

And in your test file, is it possible to force the shear effect on Bending Moment to be zero? In that case the maximum bending moment would be exactly 0.5 instead of 0.4999003 as calculated in Karamba.

regards,

Prashanth

Hello Prashanth,

a statically indeterminate system - like a beam fixed comletely on both ends - can be thought of as the sum of a statically determinate system with the original loads and the same system with sets of self equilibrating loads which ensure displacement compatibility (see also the principle of virtual forces). In case of a beam with both ends fixed, the statically determinate base system can be chosen as a simply supported beam where the shear deformation has no influence on the maximum bending moment. The set of self equilibrating loads would be two equal moments at the ends where the beam is fixed. This causes a constant bending moment along the beam - thus there is no shear force which could influence the bending moment either.

In order to get 0.5 for the maximum bending moment set the property 'Ay' to a very large number (see attached definition).

regards,

Clemens

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Hello , 

I am also trying to verify my hand calculations with Karamba and I have the same problem. The bending moment is depended on the cross-section. I followed the advices of the previous examples, but they are still dependend.  Any solutions?

regards, 

Popi

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Kirk thank you for your response. I thought that the suggestions above where eliminating the shear effect on the bending moments, so I should not have different values for the bending moments.

Popi, in case of shear forces in local z-direction you have to increase Az in order to reduce shear deformations (see attached definition).

Clemens

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Thank you for explaining!

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