Equilibrium
December 8, 2016
Categorised in: 1st Year Mechanics
Conditions of Equilibrium
(a) For co-planar concurrent forces
∑$F_x$ = 0 and ∑$F_y$ = 0
Thereforce, R = 0
(b) For co-planar non-concurrent forces
∑$F_x$ = 0 and ∑$F_y$ = 0 and ∑M = 0
Types of supports and Corresponding Reactions:
$\table Support\/Connection,Specification,No. of unknowns;Rollers,\text"Known reaction which is perp. to plane of roller",One;\text"Smooth Surface",\text"Reaction is perp. to the surface",One;\text"Rough Surface",\text"Two reactions components with unknown directions",Two;\text"Smoth pin or Hinge",\text"Two reaction components with unknown directions",Two;\text"Flexible cord,rope or cable of negligible weight",\text"One axial force acting away from body",One;\text"Fixed support",\text"Two reaction components and one moment with all components unknown in directions",Three;\text"A smooth pin in a slot",\text"Reaction with known line of action which is always perp. to slot in which pin is sliding",One;\text"A sliding collar",\text"Reaction is perp. to the rod along which collar is sliding without friction",One;\text"Ball and socket joint",\text"Three reaction components in unknown directions",Three;\text"A short link",\text"Force with known line of action",One$
Special condition of equilibriun under three forces
Lami’s Theorem:
$P/{sinα} = Q/{sinβ} = R/{sinγ}$ where mentioned angles are opposite to force vector named in numerator.
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