equilibrium & equation of equilibrium in 3d

AHSANULLAH UNIVERSITY OF SCIENCE & TECHNOLOGY

• Name : MD. Moinul Islam.• Student ID : 10.01.03.076.• Course No : CE-416.• Course Title: Prestress Concrete Design

Sessional.

Equilibrium & Equation of Equilibrium :3D

The Word Equilibrium Derived From

• The word equilibrium is derived from the Latin word æquilībrium, from æquus (“equal”) + lībra (“balance”). which means equal balance.

• In physics it means a state of even balance in which opposing forces or tendencies neutralize each other.

Equilibrium

• Is the condition of force where it is acted but simply cancelled out. These forces may be even large enough to cause permanent deformation.

Basic Idea of Equilibrium

Terms Related To Equilibrium

CENTER OF GRAVITY

• The center of gravity of a body is the point where its entire weight maybe assumed concentrated.

Practical example of equilibrium and center of gravity: A tight rope walker in a circus carries a weighted pole or an umbrella.

Concurrent & Non-Concurrent

Force System

Concurrent system occur when the lines of actions of the forces acting on a body intersect at a common point.

Non-concurrent system occurs when the forces are acting at different points.

TypesThere are two basic conditions of equilibrium.

Translational equilibrium.Rotational equilibrium.

• The term "translational equilibrium" describes an object that experiences no linear acceleration. (First condition of equilibrium )

• An object experiencing no rotational acceleration (a component of torque) is said to be in rotational equilibrium. (Second condition of equilibrium )

• Typically, an object at rest in a stable situation experiences both linear and rotational equilibrium.

Types

There are two kinds of mechanical equilibrium:

static equilibrium anddynamic equilibrium.

• Any object which is in static equilibrium has zero net force acting on it and is at rest.

• Any object which is in dynamic equilibrium has zero net force acting on it and is moving at a constant velocity.

Newton’s First Law of Physics:

• A body at rest will stay at rest and a body in motion will stay in motion unless acted upon by an unbalanced force.

• Therefore, sum of all forces must be zero. F = 0

Resultant of all forces acting on a particle is zero.

Equilibrium

Equilibrium Equation from Newton’sLaw

• If an object is in equilibrium, then the resultant force acting on an object equals zero. This is expressed as follows:

equation)(vector 0R FF

Some problems can be analyzed using only 2D, while others require 3D.

Necessary Condition for Equilibrium

• The necessary conditions for equilibrium are:

(i) the vector sum of all external forces is zero. (ii) the sum of the moments of all external

forces about any line is zero.

EQUATIONS OF EQUILIBRIUM

• As stated earlier, when a body is in equilibrium, the net force and the net moment equal zero, i.e.

F = 0 and M = 0These two vector equations can be written as six scalar equations of equilibrium. These are

FX = 0 FY = 0 FZ = 0

åMX = 0 MY = 0 MZ = 0

6 equations for 3D equilibrium

Note: The moment equations can be determined about any point. Usually, choosing the point where the maximum number of unknown forces are present simplifies the solution.

Categories of equilibrium according to Force system

Three-Dimensional Reaction at Supports & Connections

Free Body Diagram(FBD)

THE WHAT, WHY AND HOW OF A FREE BODY DIAGRAM (FBD)

Free Body Diagrams are one of the most important things for you to know how to draw and use.

What ? - It is a drawing that shows all external forces acting on the particle.

Why ? - It is key to being able to write the equations of equilibrium— which are used to solve for the unknowns (usually forces or angles).

Steps of Drawing a FBD

1. Imagine the particle to be isolated or cut free from its surroundings.

2. Show all the forces that act on the particle.Active forces: They want to move the particle. Reactive forces: They tend to resist the motion.

3. Identify each force and show all known magnitudes and directions.

Steps of Drawing a FBD

FBDIdealized modelReal world example

THE PROCESS OF SOLVING RIGID BODY EQUILIBRIUM PROBLEMS

1) Draw a free-body diagram (FBD) showing all the external forces.

2) Apply the equations of equilibrium to solve for any unknowns.

Note: If there are more unknowns than the number of independent equations, then we have a statically indeterminate situation. We cannot solve these problems using just statics.

APPLICATION

Ball-and-socket jointCrane

Straps

Application

Journal bearing Pinned connection

The tie rod from point A is used to support the overhang at the entrance of a building. It is pin connected to the wall at A and to

the center of the overhang B.

If A is moved to a lower position D, will the force in the rod change or remain the same? By making such a change without understanding if there is a change in forces, failure might occur.

Thank You