PSAD Civil Engineering Licensure Examination (CELE) Practice Test

For planar trusses, determinacy hinges on matching the number of unknowns to the number of independent equilibrium equations. Each joint must be in equilibrium in two directions, giving 2j independent equations in total. The unknowns you solve for are the axial forces in all members plus the reactions at the supports, totaling m + r unknowns. When these two counts are equal, you can fully determine all member forces from static equilibrium alone, without extra compatibility conditions; this is statically determinate, expressed as m + r = 2j. If there are more unknowns than equations (m + r > 2j), the structure is statically indeterminate; if fewer (m + r < 2j), the structure lacks enough constraints and becomes a mechanism. So the relation m + r = 2j is the correct reflection of determinacy. For example, a simple triangle with three joints, three members, and three reactions (r = 3) satisfies m + r = 6 and 2j = 6, making it determinate.