MT-1620 Fall 2002 C. Structure is overrestrained reactions > of d o f) → STATICALLY INDETERMINATE must solve for reactions simultaneously with stresses, strains etc in this case, you must employ the stress-strain equations Overall, this yields for elasticity 15 unknowns and 15 equations 6 strains=Emn 3 equilibrium (o) 6 stresses = 6fF Um 6 strain-displacements(E 3 displacements 6 stress-strain(o-e MPORTANT POINT The first two sets of equations are "universal(independent of the material)as they depend on geometry(strain-displacement)and equilibrium equilibrium). Only the stress-strain equations are dependent on the material Paul A Lagace @2001 Unit 4-p. 6MIT - 16.20 Fall, 2002 c. Structure is overrestrained (# reactions > # of d.o.f.) ⇒STATICALLY INDETERMINATE …must solve for reactions simultaneously with stresses, strains, etc. in this case, you must employ the stress-strain equations --> Overall, this yields for elasticity: 15 unknowns and 15 equations 6 strains = εmn 3 equilibrium (σ) 6 stresses = σmn 6 strain-displacements (ε) 3 displacements = um 6 stress-strain (σ - ε) IMPORTANT POINT: The first two sets of equations are “universal” (independent of the material) as they depend on geometry (strain-displacement) and equilibrium (equilibrium). Only the stress-strain equations are dependent on the material. Paul A. Lagace © 2001 Unit 4 - p. 6