ME101 Lecture05 KD

Rigid Body Equilibrium
Support Reactions
Prevention of
Translation or
Rotation of a body
Restraints

ME101 - Division III

Kaustubh Dasgupta

1

Rigid Body Equilibrium
Various Supports
2-D Force Systems

ME101 - Division III

Kaustubh Dasgupta

2

Rigid Body Equilibrium
Various Supports
3-D Force Systems

ME101 - Division III

Kaustubh Dasgupta

3

Rigid Body
Equilibrium
Categories in 2-D

ME101 - Division III

Kaustubh Dasgupta

4

Rigid Body
Equilibrium
Categories in 3-D

ME101 - Division III

Kaustubh Dasgupta

5

Equilibrium of a Rigid Body in Two Dimensions
• For all forces and moments acting on a twodimensional structure,

Fz  0 M x  M y  0 M z  M O
• Equations of equilibrium become

 Fx  0  Fy  0  M A  0 where A is any point in the plane of the structure.
• The 3 equations can be solved for no more than
3 unknowns.

• The 3 equations can not be augmented with additional equations, but they can be replaced

 Fx  0  M A  0  M B  0
ME101 - Division III

Kaustubh Dasgupta

6

Statically Indeterminate Reactions

• More unknowns than equations:
Statically
Indeterminate
ME101 - Division III

• Equal number unknowns and
• Fewer unknowns equations but improperly than equations, constrained partially constrained
Kaustubh Dasgupta

7

Rigid Body Equilibrium: Example
Solution:
• Create a free-body diagram of the joist.
- The joist is a 3 force body acted upon by the rope, its weight, and the reaction at A.

A man raises a 10 kg joist, of length 4 m, by pulling on a rope. Find the tension in the rope and the reaction at A.

• The three forces must be concurrent for static equilibrium.
- Reaction R must pass through the intersection of the lines of action of the weight and rope forces.
- Determine the direction of the reaction force R.
• Utilize a force triangle to determine the magnitude of the reaction force R.

ME101 - Division III

Kaustubh Dasgupta

8

Rigid Body Equilibrium: Example
• Create a free-body diagram of the joist
• Determine the