Homogenization of a plate to an equivalent rod .

[perfectz]

Homogenization of a plate to an equivalent rod...

Folks, I have a doubt... Sorry if it is a really stupid one...

Imagine you have a steel plate say 200mm by 200mm in dimension, with a stiffness of say some "k" N/mm...

Is there any formula to convert that plate into an equivalent steel rod with the same stiffness of "k" N/mm?...

Waiting for your answers.....

 

[nvn]

First, compute the plate deflection under the applied load. Then divide the applied load by the plate deflection to obtain the plate stiffness, kp. Now set kp equal to the rod stiffness, kr, where kr = E*A/L, E = rod modulus of elasticity, A = rod cross-sectional area, and L = rod length. For the three parameters E, A, and L, arbitrarily set any two of these parameters, and solve for the third.

 

[perfectz]

Ok thanks buddy... Thank you very much...

 

[perfectz]

will the plate and rod have the same mass after homogenization? It won't right?

 

[nvn]

The plate and rod generally will not have the same mass. You could design them to concurrently have the same mass by introducing an additional constraint equation, rhor*Vr = mp, where rhor = rod density, Vr = rod volume, and mp = plate mass.