Question

Explain degrees of freedom with example in structural analysis

Answer 1

Degrees of Freedom :

it is the mininum no. of independent coordinates required to describe the state of a system or particle in a phase space with constraints. it is given by

f = 3n-m

n= no. of particles

m=no. of constraints

in simple language

consider the example of a particle doing circular motion in a plane say x-y plane

then the phase space will be obviously the 3d cartisian coordinate space. we need only two coordinates to describe the motion of particle i.e x and y but circular motion means radius remains constt. so this constancy of radius is the constraint to motion i.e we have x^2+y^2 = r^2 i.e. r = contt. so we need only the angle theeta to differentiate between two positions of particle so its degree of freedom will be one. i.e only theeta coordinate is sufficient to mark the particle .