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Applied Mechanics CCECE2110N

Diploma 2nd Year –Architectural Engineering

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Chapter 2

Non – Concurrent Forces

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Non Concurrent Forces

• Forces action on the body are not

usually Concurrent.• For Equilibrium of a body the

condition R ! "#he resultant Force

$ero% is not a su&cient condition.•  #endency of the force to produce

rotation of the body "'oment%.

Rigid (ody

F)F*

F2

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+on Concurrent Forces Equilibrium

Conditions

"i% R ! "Resultant Force ,ero% and

(ιι)Σ' ! "-um of 'oment about the Forces%

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Moment• 'oment of a force means turning or

rotating eect of the force on the body.

• 'agnitude of the moment is obtained by

multiplying /erpendicular Distance

"from the particular point on the line of

action of the force% and Force.• Moment about a point ‘O’, Mo F ! d

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Moment

Anti0Cloc1ise 'oment 3 'o F4d

"+egati5e 'oment%

Cloc1ise 'oment 3 'o F4d

"/ositi5e 'oment%

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"a# o$ Moments %&eri'non’s (heorem)

'oment of the resultant of force system is

equal to the algebraic sum of moments of allcomponents or forces in the system aboutthe same point.

'athematically

d!* d1!F1+d2!F2+

6here7 d is the perpendicular distance fromgi5en point on the line of action of R. and

d)7 d278 are perpendicular distance from thesame point on the line of action of F)7 F278

respecti5ely.

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"a# o$ Moments %&eri'non’s(heorem)

F) F2

d) d

2

9 9

R

d

d!* d1!F1+d2!F2

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Couple

 #o Equal 9pposite parallel forces form acouple.

F

F

Arm of the Couple ":d;%

Anti-Cloc.#iseCouple

F

F

Cloc.#ise Couple

Arm of the Couple ":d;%

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<nit of 'oment and Couple

<nit in -= -ystem 3 +0m or 1+0m

"e>pressed in Cloc1ise or Anti0cloc1ise%

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/roblems in5ol5ed in 'oments andapplication of ?erignon;s #heorem

Finding moment about a point

Finding resultant force of a system

and locating the resultant force

using ?erignon;s theorem

Finding equi5alent Force Couple

system at a particular point.

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Finding the moment about a point

Eg. @! + @ +

  B! +

'oment about A 'A "@! 4 2%"0

B!4@%"@4%

*@ +0m Cloc1ise moment " %

(eam

A ( C D

2m

*m

Gm

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n ng resu an orce o a sys em anlocating the resultant force using

?erignon;s theorem

  B! + ! +

  2m *m *m

G! + G! +/olution

)% Find the Resultant Force

2% Find the location of the resultantforce using ?erignonHs #heorem"cloc1 ise momentum 5e and

anticloc1ise momentun –5e%

A (

d!* d1!F1 d2!F2 d!F