beams

Douglas P. Holmes, P.-T. Brun, Anupam Pandey, and Suzie Protière, Soft Matter, 12, 4886-4890, (2016).

In this paper, a closed-form solution is presented for bending analysis of shape memory alloy (SMA) beams.

I have tested steel pipe (as a beam) under lateral distributed loads. Longitudenal strain gages are on the top and bottom lines of the pipe. Could any one suggest to me how can I derive the bending moment distribution along the pipe. I have E, I , t (thickness, and r(radius) for the pipe.

 I have found a formula from litrature as follows : M = K.E.I

Where K = curvature = 0.5 * (ε_tension side - ε_compression side) / C (i.e the Half Section Depth, or pipe radius)

After having taught graduate structural mechanics for several years, I am finally
able to write down my lecture notes (attached) for teaching the beam theory. In
the notes, we formulated the complete classical beam model
(extension/torsion/bending in two directions), which is also called
Euler-Bernoulli-Saint beam theory, in three ways: Newtonian method, variational
method, and variational asymptotic method, using 3D elasticity theory as the
starting point. Many self-contradictions of the various assumptions used in both
Newtonian method and variational method are clearly pointed out. The

I have implemented a 2D co-rotational truss formulation in matlab.  I get identical results to OpenSEES.

Now I'm trying to implement a 2D co-rotational beam formulation.  I have followed the simple formulation in Crisfield's book volume 1.  It seems like this should be a fairly straight forward extension of the truss formulation.  I have rederived everything Crisfield has done and obtained the same results, yet something is still incorrect.