You can increase the order of the lagrange element, but this step still leads to C0 continuity because the functions space is higher order inside element but C0 between elements.

Technically you can enforce high order continuity by usinghigh order elements (Hermite polynomials for beams) or by isogeometric formulation or by discontinous galerking with weakly enforced continuity.

I support the above answer. In real life, there is no C1 continuity between trussses as they hinge about each other hence I believe there is not right to enforce C1 continuity in the computational model.

So to make this clear for me. There is no need to increase my continuity in a plane or truss problem for example? This increase will not give me better results, regarding the smoothness?

Spyros Asrva. My comments were only regarding trusses. By plane problems do you mean plane stress and plane strain?