Question $1$

Consider the beam of rectangular section $(3mm1mm)$ under the action of a couple $M$ applied at its center.

a$)$ Determine an equation for the rotation of point C using energy method. Account for bending and shear only.

b$)$ Provide a comparative table between the results from part a$)$ and Abaqus FE simulation.

c$)$ Show a plot of the undeformed and deformed shape $($superimposed on each other$)$

d$)$ What happens to the contribution from the bending part versus the shear part when $L$ increases?

Take $E=207{10}^3\frac{N}{m}{m}^2,v=0\mathrm{.}29,$ beam length $l=28($in mm $),M=6($in KN$-$mm$)$