chapter 4 part 1 notes

7/24/2019 Chapter 4 Part 1 Notes

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BIOE 3110

Introduction to Biomechanics

Eda Yildirim-Ayan

Bioengineering Department

Chapter 4Analyses of System in Equilibrium

Principles of statics and their applications


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Chapter 4- Analyses of System in Equilibrium

Newtons Laws

Conditions of EquilibriumFree-Body Diagram

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Equilibrium in Mechanics

and Rigid Body

In mechanics, the term equilibrium implies that

The body of concern is either at rest or moving

with constant velocity.

Rigid Body: Undergo no deformation under the

effect of externally applied forces


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The entire structure of mechanics is based on Newtons Laws

Newtons First Law

Newtons Second Law

Newtons Third Law


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First

Law

An object at rest

tends to stay atrest and anobject in motiontends to stay inmotion unlessacted upon by anunbalanced

force.

Second

Law

Force equalsmass timesacceleration.

F = ma

Third

Law

Newtons Laws

For every action

there is anequal andoppositereaction.


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Newtons Second Law (F=ma)

If Fnet 0 and Mnet 0 then a 0

If Fnet =0 and Mnet=0 then a =0 (velocity is constant or 0)

When a=0 then the body is in equilibrium

When =0 then the body is in static equilibrium


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Conditions for Equilibrium in Mechanics

Two conditions need to be satisfied for equilibrium

1. It has to be in translational equilibrium (net force=0)

F =0

2. It has to be in rotational equilibrium (net moment=0)

M =0


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- Translational equilibrium-

Translational equilibrium (net force=0) F =0

F = F1+ F2+ F3=0

Fx=0, Fy=0, Fz=0

Net Force acting on x, y,

and z directions must

be equal to zero.


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- Rotational Equilibrium-

Rotational equilibrium (net moment=0) M =0

M = M1+ M2+ M3=0

Mx=0

My=0

Mz=0


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Procedure to Analyze Systems in

Equilibrium

1. Draw a simple diagram of the system

2. Draw free-body diagram of the parts in the system

Show all known and unknown forces and moments

Indicate correct directions of the known forces and moments

If directions are unknown, predict directions for them, at the

end of the analysis the correct directions will be identified.

For instance if the result is positive numerical value, it means

the right direction for that force or moment was picked.

3. Adopt a proper coordinate system


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Procedure to Analyze Systems in

Equilibrium

4. For each free-body diagram, apply the translational androtational equilibrium conditions.

F =0

M =0

For 3D system (x,y,z), 6 equations three translational and three rotational Fx=0 Mx=0

Fy=0 My=0

Fz=0 Mz=0

For 2D system (x,y), 3 equations are available Fx=0, Fy =0, Mz =0

5. Solve the equations simultaneously for the unknowns.


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Free-Body Diagrams

WHY? ----- To identify the forces and moments acting on

individual part of a system

HOW?---- Isolating the parts from their surroundings,and the effects of surroundings are replaced by

proper forces and moments.


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Free Body Diagram

Isolate the portion of the body that is included

in the analysis

Sketch all known applied loads

Sketch unknown forces couples (external and

internal), assign symbols

Jot down axes, label points of importance

No redundant information, keep it simple

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Support Reactions and Member

Connections

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Support Reactions and Member

Connections

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In Class Exercise

The vertical four-sided plate shown in the figure below is pinned at A andsupported by a smooth roller at B. The loading consists of two horizontal

forces, each of magnitude 60 N, together with a couple that gives a moment

as shown of 50 Nm. Determine the reaction force at B.

chapter 4 part 1 notes

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