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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.
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Equilibrium & Equation of Equilibrium :3D
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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.
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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.
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Basic Idea of Equilibrium
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Terms Related To Equilibrium
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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.
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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.
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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.
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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.
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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
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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.
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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.
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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.
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Categories of equilibrium according to Force system
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Three-Dimensional Reaction at Supports & Connections
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Free Body Diagram(FBD)
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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).
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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.
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Steps of Drawing a FBD
FBDIdealized modelReal world example
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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.
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APPLICATION
Ball-and-socket jointCrane
Straps
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Application
Journal bearing Pinned connection
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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.
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Thank You