equilibrium and equation of equilibrium (3D)

presentation on

Presented by

Tasmia Tazin10.01.03.016

4th Year 2nd Semester (sec: A)

Dept. of CE, AUST

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.

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.

Resultant of all forces acting on a particle is

zero.

Equilibrium

Newton’s First Law of Physics

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

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

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

= 0second 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

= 0In other words: A body will be in rotational equilibrium if vector sum of all the torque acting on the body is zero.

Equation of equilibrium (3D)

Example

Problem: Determine the support reactions at the fixed support, point A

Solution:Step-1: Drawn free body diagram

Example (Cont.)

Step-3: Determined moments

Step-2: Determined Forces

More compatible supports

Ball-and-socket joint

Roller or wheel support with lateral constraint

Compatible supports (Cont.)

Thrust-bearing support

Fixed connection (embedded or welded)

Applications of equilibrium (3D)

The crane is lifting a load.

This shear leg derrick is designed to lift a maximum of 200 kg of fish.

Straps

Thank you! …