Given below is a sequence that might properly address the question of what to teach in the first (and the only) UG couse on strength of materials or solid mechanics.
0. Note: It's a mistake to believe that the contents for such a course can be covered in a linear fashion. Apply the spiral theory of knowledge and revisit certain concepts again and again: e.g., the concepts of stress, strain, fields, BV problems, theoretical structure, etc.
The range of (stress/strain/displacement analysis) problems to address.
Qualitative and empirical characterization of materials response under tension, compression, shear, fatigue, creep, impact, etc.