Non-linear flexural rigidity (EI)

[Jaguar9]

Hi all,

I am trying to find the fexlural rigidity of a bending beam under a load increasing step-by-step till the beam fails. Assuming material is non-linearity, can I use this formula:
Flexural rigidity (EI) = Bending moment (M)/Curvature
to calculate EI for non-linear material?

Could anyone help me in this point.
Thanking you in advance.
regards,
Jaguar9

 

[Denial]

The formula is NOT applicable to non-linear material behaviour, since it assumes that:
(1) Plane sections remain plane;
(2) The longitudinal stress at any point on the cross section is proportional to the strain at that point.

For a non-linear material, condition (2) is violated by definition.

HTH

 

[heitor]

You can't use the formula but you can allways find a relationship between the applied moment and the curvature. Then a curve fit will give you the formula that you are looking for.
Are you doing this experimentally?

 

[Jaguar9]

First of all, many thanks to Denial and Heitor
Can EI be set up for linear inelastic case(?): assuming that moment and curvature can be found from a given stress-strain curve with a linear degradation of tensile stress?
Heitor: I am not doing experiment for this
regards,
Jaguar9

 

[ccw]

Hi Jaguar9,

University and DOE lab research has been trying to calibrate models in nonlinear code such as DYNA (tm) to impact and crash test results for years. I can give you a contact. If you are interested just supply your e-mail address.

From doing some simple experiments I can attest to the observations that published post-yield material behavior varies widely. Piecewise look up is probably more accurate than linear degredation. Cyclic work hardening history and section geometry are also big players for the gross beam behavior.

 

[Jaguar9]

Hi ccw,
Thank you very much. I would be very grateful if you would contact me through this email
jaguar9_do@yahoo.com
Regards,
Jaguar9