lami's theorem
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Gandhinagar Institute of Technology
Mechanics of solidsLami’s Theorem
&Example
Branch : Mechanical Div: 3-C Engineering
Force SystemsSystem of forces tells us the arrangement of
forces and is classified as follows:system of forces
coplanar
noncoplanar
concurrent
parallel general
Graphical conditions for Equilibrium
Triangle Law: If three forces are in equilibrium, then, they form a closed triangle when represented in a Tip to Tail arrangement, as shown in Fig 1.(a).
Fig 1.(a)
F 3 F2
F1Polygonal Law: If more than three forces are in equilibrium, then, they form a closed polygon when represented in a Tip to Tail arrangement, as shown in Fig 1.(b).
F5
F4 F3
F2Fig 1.(b)
F2
F3
F1
F1
F5
F4
F3 F2
F1
5
Equilibrium of concurrent forcesConditions of equilibrium for concurrent
system of forces in a plane:∑Fx=0∑Fy=0 or∑Fx=0∑Ma=0 or∑Ma=0∑Mb=0
Lami’s theoremIf a particle acted upon by three forces remains in
equilibrium then, each force acting on the particle bears the same proportionality with the since of the angle between the other two forces”. Lami’s theorem is also known as law of sines.
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