ANALILIS STRUKTUR

EQUILIBRIUM OF STRUCTURES

A structure is considered to be in equilibrium if, initially at rest, it remains at rest when subjected to system of forces and couples. If a structure is in equilibrium, then all its members and parts are also in equilibrium. For a space structure, condition of equilibrium can be express :

S Fx = 0

S Fy = 0

S Fz = 0

S My = 0

S Mz = 0

S Fy = 0

S Mz = 0

r < 3 the structure is statically unstable externally 

r = 3 the structure is statically determinate externally

r > 3 the structure is statically indeterminate externally

STATIC DETERMINACY OF INTERNALLY UNSTABLE STRUCTURES-EQUATIONS OF CONDITION

• r < 3 + ec the structure is statically unstable externally 
• r = 3 + ec the structure is statically determinate externally
• r > 3 + ec the structure is statically determinate externally
• ec = equation of condition
• S Mx = 0
• S = Sigma

For a plane structure, condition of equilibrium can be express :

S Fx = 0

STATIC DETERMINACY, INDETERMINACY, AND INSTABILY

• An internally stable structure is considered to be statically determinate externally if all its support reaction can be determinate by solving the equations of equilibrium.
• If a structure is supported by more than three reactions, then all the reactions cannot be determined from the three equations of equilibrium.
• Such structure are termed statically indeterminate externally.
• In reactions in excess of those necessary for equilibrium are called external redundants, and the number of external redundants is referred to as the degree of external indeterminacy.
• If a structure has r reactions (r > 3), the degree of external indeterminacy.

ie = r - 3