equilibrio de cuerpos rigidos

Equilibrium of rigid bodies

Estática

Universidad Cooperativa de Colombia

2

Equilibrium of rigid bodies The necessary and sufficient for a body is in static

equilibrium condition it is that the resulting force and moment of all external forces form a system equivalent to zero.

Decomposing each of the forces and moments six scalar equations is obtained.

00 FrMF O

000000

zyx

zyxMMMFFF


3

Free- Body diagram1. The first step in the analysis of static

equilibrium of a body is to identify all the forces acting on the body.

2. Select the solid base away from its support for and disclaims any other body. Then the contour is plotted .

3. Indicate the point of application, magnitude and direction of external forces , including weight

4. Unknown external forces normally consist reactions . Those exercised in the points at which the solid is supported or attached to other bodies.

5. The DCL must also include dimensions, which calculate moments of forces.


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Reactions in brackets and connections


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Reactions in brackets and connections


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Exercise

Exercise A fixed crane mass of 100 kg and whose center of gravity is located at G. SE US to lift a box having a total mass of 2400kg author is calculated The magnitude of reactive forces at A and B

DCL


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Solution A reaction is determined

using the sum of horizontal and vertical components .

0m6kN5.23

m2kN81.9m5.1:0

BM A

kN1.107B0:0 BAF xx

kN1.107xA

0kN5.23kN81.9:0 yy AF

kN 3.33yA


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Example of free-body diagrams


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Example of free-body diagrams


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Balancing two-dimensional rigid body For all forces and torques acting on a

two-dimensional structure .

The six equilibrium equations are reduced to :

wherein A is a point in the plane of the structure .

These three equations are solved to determine the unknown quantities

Ozyxz MMMMF 00

000 Ayx MFF


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Balancing a cuepor subjected to two forces

If two forces act on a body, for the balance they must be collinear

Consider a plate subjected to two forces.

So that the plate is in static equilibrium , the sum of moments about A must be zero.

The timing of F2 will be zero if its line of action passes through A. Similarly, the line of action of F1 must pass through B so that the sum of moments about B is zero.

Therefore a body subjected to two forces are in equilibrium , the forces must be equal magnitude and opposite in direction .


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Balancing a body subjected to three forces Consider a body subjected to

three forces acting on A, B and C.

Assuming that their lines of action when F1 and F2 intersect respect to point D is zero.

Since the rigid body is in equilibrium the sum of the moments of F1 , F2 and F3 around any axis may be zero . Is the line of action of F3 must also go through D.

Therefore the lines of action of the three forces must be concurrent


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Equilibrium of a rigid body in three dimensions

000000

zyx

zyx

MMMFFF

00 FrMF O


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Support Reactions


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Support Reactions


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Example

The sign of uniform density of 5 foot by 8 foot weighs 270 lbs and is supported by a ball joint at A and by two cables. Determine the tension in the cables and reaction A


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0lb1080571.2667.2:

0714.1333.5:

0lb 270ft 4

0:

0lb 270:

0:

0lb 270

72

32

73

31

76

32

ECBD

ECBD

ECEBDBA

ECBDz

ECBDy

ECBDx

ECBD

TTk

TTj

jiTrTrM

TTAk

TTAj

TTAi

jTTAF

kjiA

TT ECBD

lb 22.5lb 101.2lb 338

lb 315lb 3.101

Example

equilibrio de cuerpos rigidos

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