A beam is said to be in static equilibrium when the beam is initially at rest and remains at rest when subjected to a system of forces and couples.
Generally, there are 3 equilibrium equations for a planer structure.
The conditions of zero resultant force and zero resultant couple can be expressed as:
where F
x represents forces along the horizontal or x-axis, F
y represents forces along the vertical or y-axis, and M
z represents the sum of moments taken around any point on the beam.
Degree of indeterminacy = Total number of unknown forces - Total number of equilibrium equations
Eg. Statically indeterminate structure
Here, the total number of unknown forces = 7
total number of equilibrium equations = 3
So, the degree of indeterminacy = 7 - 3 = 4, which is greater than zero so it is a statically indeterminate structure.
Eg. Statically determinate structure
Here, the total number of unknown forces = 3
Total number of equilibrium equations = 3
So, the degree of indeterminacy = 3 - 3 = 0, so it is a statically determinate structure.