If there are ‘m’ unknown number forces, ‘r’ unknown reaction components and ‘j’ number of joints, then the degree of static indeterminacy of pin-jointed plane frame is given by
Concept: Static indeterminacy is defined as the difference of total number of unknowns (Total member forces+ reactions) and the total number of available equations from the conditions of equilibrium. So for a pin-jointed frame total number of equations available at a joint = 2 So for j number of joints, equations available = 2j So the degree of static indeterminacy of pin-jointed plane frame = m + r - 2j If the degree of static indeterminacy = 0, it is known as a statically determinate structure. If the degree of static indeterminacy > 0, it is known as a statically indeterminate structure. Other Important Points: If the joint is rigid then the total number of available equations available at joint = 3 So for j number of joints, equations available = 3j So degree of static indeterminacy of pin-jointed plane frame = m + r - 2j