Chapter 05 ( Part 1 -- 5.1-5.4 ) for Student (4)

8/9/2019 Chapter 05 ( Part 1 -- 5.1-5.4 ) for Student (4)

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Equilibrium of a Rigid Body55

Engineering Mechanics:

Statics in SI Units, 12e

Copyright 2010 Pearson Education South Asia Pte Ltd


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ha!ter "utline

Conditions for Rigid Equilibriu

Equilibriu in t!o diensions

1" #ree$%ody &iagras

2" Equations of Equilibriu'" (!o and (hree$#orce )ebers

Equilibriu in three diensions

1" #ree %ody &iagras

2" Equations of Equilibriu

'" Constraints and Statical &eterinacy


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#$1 onditions for Rigid%Body Equilibrium

* (he equilibriu of a body is e+pressed as

* Consider suing oents about soe other point,

such as point A, !e require

( )

==

==

0

0

OOR

R

MM

FF

( ) =+= 0ORRA MFrM


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E&UI'IBRIUM I( )*"+IME(SI"(S



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#$2 ree Body +iagrams

Procedure for &ra!ing a #%&

1" &ra! -utlined Shape

2" Sho! All #orces and Couple )oents

'" .dentify Each Loading and /ie &iensions


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E-am!le #$1

&ra! the free$body diagra of the unifor bea" (he

bea has a ass of 100g"


7/21Copyright 2010 Pearson Education South Asia Pte Ltd


Support Reactions

* .f a support preentsthe translation of a body in a

gien direction, then a force is deeloped on the body

in that direction"* .f rotation is preented, a couple oent is e+erted on

the body"




#orces

* E+ternal and internal forces can act on a rigid body

* #or #%&, internal forces act bet!een particles !hich

are contained !ithin the boundary of the #%&, are notrepresented

* Particles outside this boundary e+ert e+ternal forces

on the syste




eight and Center of /raity

* Each particle has a specified !eight

* Syste can be represented by a single resultant

force, no!n as !eight *of the body* Location of the force application is no!n as the

center of graity


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E-am!le #$.

* &ra! the free$body diagra of the unloaded platfor

that is suspended off the edge of the oil rig" (he platfor

has a ass of 200 3g"



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#$/ Equations of Equilibrium

* #or equilibriu of a rigid body in 2&,

4#+5 06

4#y5 06

4)-5 0

* 4#+and 4#yrepresent sus of + and y coponents of

all the forces

* 4)-represents the su of the couple oents and

oents of the force coponents


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E-am!le #$#

&eterine the hori7ontal and ertical coponents of

reaction on the bea caused by the pin at % and the

rocer at A" 8eglect the !eight of the bea in the

calculations"


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E-am!le #$0

(he eber sho!n in the figure is pin$connected at A

and rests against a sooth support at %"


reaction at the pin A"


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E-am!le #$


reaction on the eber at the pin A, and the noral

reaction at the roller % in the figure"


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E-am!le #$12

&eterine the support reactions on the eber in the

figure"

(he collar at A is fi+ed to the eber and can slide

ertically along the ertical shaft"


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#$. )o% and )hree%orce Members

(!o$#orce )ebers

* hen forces are applied at only t!o points on a

eber, the eber is called a t!o$force eber

* -nly force agnitude ust be deterined


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#$. )o% and )hree%orce Members

(hree$#orce )ebers

* hen sub9ected to three forces, the forces are

concurrent or parallel


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E-am!le #$1/

(he leer A%C is pin$supported at A and connected to a

short lin %&" .f the !eight of the ebers are negligible,

deterine the force of the pin on the leer at A"

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Chapter 05 ( Part 1 -- 5.1-5.4 ) for Student (4)