Chapter Name : Equilibrium
2.1 Equilibrium of Forces 2.7 Beam
Definition and explanation Definition
Conditions for equilibrium (ΣFx = 0, ΣFy = 0, ΣM = 0)
Practical examples Types and applications
Relevance in structures
2.2 Types of Equilibrium
Stable Equilibrium
2.8 Types of Beams
Unstable Equilibrium
Simply supported beam
Neutral Equilibrium
Cantilever beam
Diagrams and examples
Overhanging beam
2.3 General Procedure for the Solution of Problems in Equilibrium
Fixed and continuous beams
Step-by-step approach
Diagrams
Force identification
Diagram drawing
Equation formulation 2.9 Types of Loading
Point load
2.4 Equilibrant
Definition of equilibrant Uniformly distributed load (UDL)
Relation with resultant force Uniformly varying load (UVL)
How to find equilibrant vector Real-life examples
2.5 Free Body Diagram
2.10 Types of Supports
Definition and importance
Roller support
How to draw FBD
Hinged support
Common mistakes and tips
Fixed support
2.6 Lami’s Theorem
Support reactions and examples
Statement and formula
Application conditions (three concurrent, coplanar, non-parallel forces) Exercise
Solved examples Practice problems based on each section
,2.1 Equilibrium of Forces
Definition:
Equilibrium refers to the state of a body when all the forces acting on it are balanced and
there is no net force causing motion. In this condition, the body either remains at rest or
moves with constant velocity.
In simpler terms, a body is said to be in equilibrium when the resultant of all the forces acting
on it is zero.
---
Conditions for Equilibrium:
For a body to be in equilibrium, the following conditions must be satisfied:
1. Translational Equilibrium:
The sum of all horizontal forces must be zero:
ΣFx = 0
The sum of all vertical forces must be zero:
ΣFy = 0
This ensures the body does not move in a straight line in any direction.
2. Rotational Equilibrium:
The sum of all moments (torques) about any point must be zero:
ΣM = 0
This ensures the body does not rotate.
Types of Equilibrium:
Based on motion, equilibrium can be of two types:
Static Equilibrium: The body is at rest and remains at rest.
Dynamic Equilibrium: The body is in motion but moves with
constant velocity (no acceleration).
, Examples:
1. A book resting on a table is in static equilibrium.
Forces acting: Weight of the book (downward) and normal reaction
from the table (upward) are equal and opposite.
2. A car moving in a straight line with constant speed is in dynamic
equilibrium.
All the forces (engine force, friction, air drag) balance out.
---
Vector Representation:
If three or more forces act on a body in equilibrium, they must form a
closed polygon when drawn head to tail. This is called the Polygon Law of
Forces.
---
Important Points:
Equilibrium is a vector condition – both magnitude and direction of
forces matter.
If even one force is unbalanced, the body will no longer be in equilibrium.
Moments must be checked around at least one point to ensure full
equilibrium in 2D problems.
2.1 Equilibrium of Forces 2.7 Beam
Definition and explanation Definition
Conditions for equilibrium (ΣFx = 0, ΣFy = 0, ΣM = 0)
Practical examples Types and applications
Relevance in structures
2.2 Types of Equilibrium
Stable Equilibrium
2.8 Types of Beams
Unstable Equilibrium
Simply supported beam
Neutral Equilibrium
Cantilever beam
Diagrams and examples
Overhanging beam
2.3 General Procedure for the Solution of Problems in Equilibrium
Fixed and continuous beams
Step-by-step approach
Diagrams
Force identification
Diagram drawing
Equation formulation 2.9 Types of Loading
Point load
2.4 Equilibrant
Definition of equilibrant Uniformly distributed load (UDL)
Relation with resultant force Uniformly varying load (UVL)
How to find equilibrant vector Real-life examples
2.5 Free Body Diagram
2.10 Types of Supports
Definition and importance
Roller support
How to draw FBD
Hinged support
Common mistakes and tips
Fixed support
2.6 Lami’s Theorem
Support reactions and examples
Statement and formula
Application conditions (three concurrent, coplanar, non-parallel forces) Exercise
Solved examples Practice problems based on each section
,2.1 Equilibrium of Forces
Definition:
Equilibrium refers to the state of a body when all the forces acting on it are balanced and
there is no net force causing motion. In this condition, the body either remains at rest or
moves with constant velocity.
In simpler terms, a body is said to be in equilibrium when the resultant of all the forces acting
on it is zero.
---
Conditions for Equilibrium:
For a body to be in equilibrium, the following conditions must be satisfied:
1. Translational Equilibrium:
The sum of all horizontal forces must be zero:
ΣFx = 0
The sum of all vertical forces must be zero:
ΣFy = 0
This ensures the body does not move in a straight line in any direction.
2. Rotational Equilibrium:
The sum of all moments (torques) about any point must be zero:
ΣM = 0
This ensures the body does not rotate.
Types of Equilibrium:
Based on motion, equilibrium can be of two types:
Static Equilibrium: The body is at rest and remains at rest.
Dynamic Equilibrium: The body is in motion but moves with
constant velocity (no acceleration).
, Examples:
1. A book resting on a table is in static equilibrium.
Forces acting: Weight of the book (downward) and normal reaction
from the table (upward) are equal and opposite.
2. A car moving in a straight line with constant speed is in dynamic
equilibrium.
All the forces (engine force, friction, air drag) balance out.
---
Vector Representation:
If three or more forces act on a body in equilibrium, they must form a
closed polygon when drawn head to tail. This is called the Polygon Law of
Forces.
---
Important Points:
Equilibrium is a vector condition – both magnitude and direction of
forces matter.
If even one force is unbalanced, the body will no longer be in equilibrium.
Moments must be checked around at least one point to ensure full
equilibrium in 2D problems.
