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