CONDITIONS OF EQUILIBRIUM
According to Newton s law, a particle or body can have no acceleration it there s no restultant force acting on it. Such a body is said to be in a state of equilibrium.
A Single particle or mass point will obviously be in equilibrium if the resultant of all forces acting on it is zero0.
A stucture as a whole 1S in a state of static equilibrium when the resuitant o1 al Cxtetid forces actng on it is zero.
In structral analySis, the use of equilibrium equations which states that the structure or parts of it remain in the stationary position. Hence, if the entire structure is considered, the reacton
rom tne Support and the loads on the structure should be in static equnoruill.
1ne equations of static equilibrium are as folows:
i) The summation of all the forces along any axis (x, y and z) 1s zero.
ii) the summation of all the moments about any axis (x, y and 2) 1S also Zc0
Or 2D(Iwo dimensional)system with x and y-axis the equations of equilibrium are
summation of
Fx=0 fy =0 and mz,=0
H=0 v=0 and M=0
fOr Dhree dimensional) system withx, y and z-axis the equations of equilibrium are
Conditions of equlibrium of summation of
Fx=0 Fy= 0 and Fz=0 which must always be
My =0 Mx=0 and Mz=0 obey by the complete set
oI forces acting on a structure.
where, Fx 2, and are algebraic sum of the components of all external forces
(applied loads and reactive forces) alongX, y and z-axis respectively.
Fx and Fy are shear forces (tangential forces)
FzAxial forces
Similarly, 2Mx.2 My and 2 Mz
forces are the algebraic
(applied sum
loads of the
and moments
reactive forces) of all
about externa
x, y and z-axis
My and respectively.
My are bending moments
M>Torsional moment
