This presentation discusses equilibrium and the equation of equilibrium in 3 dimensions. It defines static and dynamic equilibrium, with static equilibrium occurring when the net force on a body is zero and it is at rest, and dynamic equilibrium occurring when the net force is zero and a body is in uniform motion. It presents the two conditions for equilibrium: 1) the vector sum of all forces is equal to zero, and 2) the algebraic sum of all clockwise and counterclockwise torques is equal to zero. An example problem is shown to demonstrate solving the 3D equation of equilibrium to determine unknown support reactions on a structure. Applications to lifting structures like cranes are also briefly discussed.

1. presentation on
equilibrium and equation of
equilibrium (3D)
Presented by
Tasmia Tazin
10.01.03.016
4th Year 2nd Semester (sec: A)
Dept. of CE, AUST

2. Newton’s First Law of Physics
If the resultant force on a particle is zero, the particle will remain at
rest or will continue at constant speed in a straight line.
Equilibrium
A key concept in statics is that of equilibrium. If an object is at rest, we
will assume that it is in equilibrium and that the sum of the forces
acting on the object equal zero.
Resultant of all forces
acting on a particle is zero.
Equilibrium

3. Types of equilibrium
1.
Static equilibrium
2.
Dynamic equilibrium
Static equilibrium
If the combined effect of all the forces acting on a body is zero and the body
is in the state of rest then its equilibrium is termed as static equilibrium.
For example: A book lying on
the table

4. Dynamic equilibrium
When a body is in state of uniform motion and the resultant of all the
forces acting upon it is zero then it is said to be in dynamic equilibrium.
For example: Jump by using
parachute

5. Conditions of equilibrium
first condition:
To maintain the transitional equilibrium in a body the vector sum of all
the forces acting on the body is equal to zero.
i.e. ∑ F = 0
second condition:
A body will be in rotational equilibrium when the algebraic sum of clock
wise moment and anti clock wise moment is zero.
i.e. ∑ M = 0
In other words:
A body will be in rotational equilibrium if vector sum of all the torque
acting on the body is zero.

6. Equation of equilibrium (3D)

7. Example
Problem: Determine the support
reactions at the fixed support,
point A
Solution:
Step-1: Drawn free body diagram

8. Example (Cont.)
Step-2: Determined Forces
Step-3: Determined moments

9. More compatible supports
 Roller or wheel support with lateral constraint
 Ball-and-socket joint

10. Compatible supports (Cont.)
 Fixed connection (embedded or welded)
Thrust-bearing support

11. Applications of equilibrium (3D)
Straps
This shear leg derrick is
designed to lift a maximum of
200 kg of fish.
The crane is lifting a load.

12. Thank you! …