Chapter # 3Equilibrium In Two Dimension

Ms. Sana YahyaLecture # 10

ME 101: BASIC MECHANICAL ENGINEERING

Equilibrium Conditions

• The equations relating force and acceleration for rigid body motion are developed in dynamics from Newton’s second law of motion.

• There equations show that the acceleration of the mass centre of a body is proportional to the resultant force ΣF acting on the body. Therefore if body moves with constant velocity (zero acceleration), the resultant force on it must be zero, and the body may be treated as in a state of translational equilibrium.

Categories of Equilibrium

Two and Three –Force MembersThis example is of equilibrium of a under the action of two forces only.

For such two force membr to be in eqilibrium, the forces must be equal, opposite and collinear.

REMEMBER: the shape of the member doesnot affect this simple requirement.

Also here weight is considered negligible as compare to forces applied.

Here is a three force member, equilibrium will be attain if the line of action of all forces to be concurrent.

Q. What if they were not concurrent?

ANSWER

• If they were not concurrent then one of the forces would exert a resultant moment about the point of intersection of the other two, which will violate the requirement of zero moment about every point.

• NOTE: the only exception occurs when the three forces are parallel. In this case we may consider the point of concurrency to be infinity.

• A body in equilibrium under the action of more than three forces may be reduced to a three-force member by a combination of two or more of the known forces.

• In this case the polygon of forces is drawn and made to close, as shown in fig below

Quiz 3