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Ahsanullah University of Science & Technology
Presentation on :Equilibrium and equilibrium equation 2D
By : TOUFIQ RIFATH ID : 10.01.03.125
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.
In Equilibrium the forces are balanced . It is not necessary that the forces have to be equal in equilibrium state.
Types:
Example: A book laying on a table
1. Static Equilibrium If the object is at rest , it stays at rest.
2. Dynamic Equilibrium If the object is in motion , it
maintains a constant velocity .
Example:
Equations of Equilibrium for 2D
y
x Couple moment
1F
2F
3F
1M
2M
0M0F 0
0M
0F
0F
0
y
x
Here: Fx
Fy
0M
algebraic sum of x components of all force on the body.
algebraic sum of y components of all force on the body.
algebraic sum of couple moments and moments of allthe force components about an axis xy plane and⊥passing 0.
(1) Conditions of equilibrium
∑F=0 : The algebraic sum of all the horizontal or vertical forces acting on a body which is in equilibrium must equal zero.
0F
0F
y
x
∑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
0M0
How to apply :
First we have to draw a free body diagram.
FBD at A:
All the forces and couple moments and supports must be shown acting on the member.
Then Equation of Equilibrium is applied.
600N
200N
2m 3m 2m
100N
y
xBxA B
ByAy
3 unknown Ax, Bx, By
Equations of equilibrium
0.0245sin600545sin600721000
020010045sin6000
045cos6000
AyM
ByAyFy
BxFx
B
3 equations for 3 unknowns
Example:
Thank You