2D FORCE ANALYSIS : HOW TO FIND REACTIONS IN A CASE OF CONCURRENT FORCE SYSTEM ACTING ON A BODY IS IN EQUILIBRIUM

DEFINITION : CONCURRENT FORCE SYSTEM

If the lines of actions of all the forces in a force system pass through a common point, then the force system is called as Concurrent Force System. The equilibrium conditions for a concurrent force system is

ΣF_x = 0 and   ΣF_y = 0

 

The steps to find out reactions when a coplanar concurrent force system acting on a body in equilibrium condition :

 

 

STEP 1 :

 

(i) Draw the diagram and identify all the contact points the body makes with other bodies including ground.

(ii) Draw a tangent at each contact point with the object. These tangents are called Contact Surfaces.

(iii) Draw a perpendicular to the contact surface at each and every contact points. These perpendiculars will be the directions of reactions at each and every contact point.

(iv) Find the angles made by the reactions with respect to horizontal with the help of Geometry.

 

 

STEP 2 :

 

(i) Draw the Free Body Diagram (FBD) that consists of the external forces acting on the object. (applied forces, forces of gravity and reactions all are external forces)

(ii) Assign reactions by symbols like R₁, R₂ ....... and resolve all the external forces along X-axis and Y-axis.

(iii) Now add all the horizontal component forces as ΣF_x and put ΣF_x = 0 ---- eqn (1)

and add all the vertical component forces as ΣF_y and put ΣF_y = 0 --------eqn (2)

(iv) Solving these two equations we shall get values of  R₁, R_2.