Teaching Mechanics: Inequalities in Statically Indeterminate Static Friction Problems

In this contribution, we provide a mathematical treatment of the inequality systems arising from two toy examples of statically indeterminate, static friction problems with multiple contact planes. Both examples illustrate general phenomena that are not covered by introductory textbooks. The first one illustrates that a certain inequality might restrict the solution set for a certain choice of a parameter, while being not restrictive for another choice of the parameter. The example also illustrates why it is not suffcient to investigate only the limit case of impending motion (H = μ 0 N ) for more complex problems.