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

Replies to This Discussion

Permalink Reply by Karamba3D on December 16, 2015 at 11:54pm

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

Permalink Reply by Jaeman PARK on December 17, 2015 at 5:19am

Thanks for your reply.

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

Permalink Reply by Karamba3D on December 17, 2015 at 11:30am

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

Attachments:

• bending_moment_test_CP.gh, 28 KB

Permalink Reply by prashanth raghunath on December 22, 2015 at 8:24pm

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

Permalink Reply by Karamba3D on December 23, 2015 at 2:11am

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

Attachments:

• bending_moment_test_CP_II.gh, 35 KB

Permalink Reply by popi papa on December 8, 2017 at 9:35am

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

Attachments:

• ScreenHunter_11 Dec. 08 17.32.jpg, 16 KB
• ScreenHunter_10 Dec. 08 17.31.jpg, 96 KB
• FRAMES-TEST.gh, 41 KB

Permalink Reply by popi papa on December 8, 2017 at 10:42am

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.

Permalink Reply by Karamba3D on December 11, 2017 at 1:40pm

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

Attachments:

• FRAMESTEST_cp.gh, 30 KB

Permalink Reply by popi papa on December 12, 2017 at 9:09am

Thank you for explaining!