[ANSWERED] 1. Use Eqs. (4.1.7) to plot the shape functions N 1 and N 3 and the derivatives (dN 2 =dx) and (dN 4

1. Use Eqs. (4.1.7) to plot the shape functions N
1
and N
3
and the derivatives (dN
2
=dx) and (dN
4
=dx),
which represent the shapes (variations) of the slopes
1
and
2
over the length of the
beam element.
2. Derive the element stiffness matrix for the beam element
in Figure 4–1 if the rotational degrees of freedom are assumed positive
clockwise instead of counter clockwise. Compare the two different nodal sign
conventions and discuss. Compare the resulting stiffness matrix to Eq.
(4.1.14).