Beam Bending: Centroidal Axis Rotation

[chandran]

how do we say that in a beam bending problem the bean cross section bends(rotates)around the centroidal axis. Why not about any other axis?

 

[haynewp]

The beam has to satisfy statics. A moment is generated in the beam due to externally applied forces, and this moment results in internal forces which also have to be in equilibrium for the beam to be stable.

Looking at the cross sectional internal forces, there will be forces causing compression on the cross section with equal and opposite tension forces on the section in order to balance an external moment (all compression (or tension) stresses will be above the neutral axis and the opposite will be below the neutral axis).

The centroidal axis is not always the axis bending is about. But this assumption does apply for a symmetrical, homogeneous beams. In this case, the sum of all the areas above an axis passing through the section multiplied by the stress in each area has to equal the sum of all the areas below the same axis passing through the section multiplied by the stress on all these elements. You will find the location of this axis to be the centroidal axis.

 

[fdm44241]

Hello,

If you have a tube under load and bending with concave say downward, would you have a tension stress on the outer top surface, then compression on the top inner surface then tension on the lower inner surface and finally compression on the lower outer surface?

Thank you.