Static

Statically determinate
r=3n
b+r=2j
b+r<2j (Internal unstable)

Statically indeterminate
r>3n
b+r>2j (Internal unstable if reactions are parallel)

Advantages in Indeterminate
Light, more rigid, increase factor of safety with redundant supports

Failure case
a) Fracture
b) Instability: plastic buckling

Failure criteria:
Maximum shear and stress
Tensile strain
Total energy strain U=(σy)^2/2E
Strain energy of distortion U=(1+v)(σy)^2/2E
Octahedral shear stress τ=0.47σy

Factors:
Stress
Material
Condition
Temperature