Refering to a pdf I uploaded at here. Why does these stiffness matrix displacement do not need to consider the inertia (determines the shape of cross-sectional area of each element) ? I have always thought that the inertia will affect the displacement too. Thank you for reading and have a nice day :)
Indeed the stiffness matrix for problems with bending is dependent on the area moment $I$ as well as the elastic modulus $E$_.
Take the example of a cantilever beam.
Page 2 of this pdf lecture for example, shows the following
As you can see the stiffness matrix depends on $E I$ (shown outside the matrix as a common factor) where $E$ is the modulus of elasticity and $I$ is are second moment of area of the beam.
For example a rectangular beam has $ I = b h^3/12$.
But for problems with only axial deflection (like the truss made of rods the question describes), then the stiffness matrix only depends on the axial stiffness of the rod which is $ k = \frac{E A}{L}$