# Finding My, Mz in Complex/Asymmetrical Beam Bending

So I have done a three point loading test on a piece of bone.

I have been able to obtain the Second Moments of Area $I_{xx}$, $I_{yy}$, $I_{zz}$. As well as the centroid. I also have the data from the experiment that gives load and extension.

However now I would like to obtain the stress for the specimen using complex or asymmetrical bending equation. How though do I find the moments $M_y$ and $M_z$?

Note this was a three point bending experiment so only one load was placed.

• A three point load test usually only creates bending in one direction. And given that bone is (roughly) cylindrical, the second moments of area should all be the same (except the torsional one). In order to get moments around the three axes ($M_x$, $M_y$ and $M_z$), you'll need to apply multiple forces. Am I misunderstanding your setup? Please edit your question with more information. – Wasabi Sep 11 '15 at 13:19
• No you have understood exactly the setup. – ANT1 Sep 11 '15 at 20:43
• Then I don't understand your question. That setup will only generate bending around one axis. What do you mean to obtain for the other axes? – Wasabi Sep 11 '15 at 20:46
• Sorry I was in the middle of writing an edit, and computer turned off. If then load is only placed in y direction then is it safe to assume that $M_z,y$ both equal zero – ANT1 Sep 11 '15 at 21:05
• Yes. For a horizontal beam (or bone) on an XY plane under vertical loads (y direction), the beam will only suffer $M_z$ (rotation around the axis perpendicular to the XY plane). Other moments will be null. – Wasabi Sep 11 '15 at 21:27