Three examples of equilibrium problems are presented where concentrated contact interactions arise to guarantee partwise equilibrium. In the first example, a concentrated force is applied at the boundary of a half plane, and the stress field has an integrable singularity at the point where the force is applied. Suturing two such stress fields so as to have a mirror-symmetric stress field in the whole plane produces a second example of concentrated contact interactions. For a third example, a concentrated couple is applied at the boundary of a half plane, and the standard stress field has a nonintegrable singularity at the point where the couple is applied, whereas the associated hyperstress field, although still singular, is integrable.