Presentation on Equilibrium and Equilibrium equation 2D

1. Ahsanullah University of Science &
Technology
Presentation on :
equilibrium and equilibrium equation 2d
By : TOUFIQ RIFATH
ID : 10.01.03.125

2. What is Equilibrium ?
 A state in which opposing forces or influences are
balanced.
 From Newton’s 1st law of motion:
An object at rest will remain at rest unless acted
on by an unbalanced force. An object in motion
continues in motion with same speed and in the
same direction unless acted by an resistance force.

3.  In Equilibrium the forces are balanced . It is
not necessary that the forces have to be
equal in equilibrium state.

4. Types:
1. Static Equilibrium
If the object is at rest , it stays at rest.
Example: A book
laying on a table

5. 2. Dynamic Equilibrium
If the object is in motion , it
maintains a constant velocity .
 Example:

6. Equations of Equilibrium for 2D
(1) Conditions of equilibrium

∑F = 0

∑ M0 = 0
∴ ∑ Fx = 0
∑F = 0
∑M = 0
y
0
Here:

F1
y

M2

F2

M1

F3
x
Couple moment
∑ Fx = algebraic sum of x components of all force on the body.
∑ Fy = algebraic sum of y components of all force on the body.
∑M
0
= algebraic sum of couple moments and moments of all
the force components about an axis ⊥ xy plane and
passing 0.

7. ∑F=0 : The algebraic sum of all the
horizontal or vertical forces acting on a
body which is in equilibrium must equal
zero.
∴ ∑ Fx = 0
∑F
y
=0

8. ∑M=0: The algebraic sum of the moments of all
the forces acting on a body which is in
equilibrium, about any point in the plane of
those forces, must equal zero
∑M
0
=0

9. How to apply :
 First we have to draw a free body diagram.
FBD at A:

10.  All the forces and couple moments
and supports must be shown acting
on the member.
 Then Equation of Equilibrium is
applied.

11. Example:
y
600N
200N
A
x
B Bx
2m
Ay
3m
2m
By
100N
3 unknown Ax, Bx, By
Equations of equilibrium
+ ∑ Fx = 0 600 cos 45° + Bx = 0
↑ + ∑ Fy = 0
Ay − 600 sin 45° − 100 − 200 + By = 0
+ ∑ M B = 0 100 × 2 − Ay × 7 + 600 sin 45° × 5 − 600 sin 45° × 02. = 0
3 equations for 3 unknowns

12. Thank You