Lami's theorem

By : Chandresh Suthar
Govind Tade
Manav Sonani

1. Gandhinagar Institute of Technology Mechanics of solids Lami’s Theorem & Example Branch : Mechanical Div: 3-C Engineering

2. Group Members Name- Enrollment no- Chandresh Suthar 140120119229

3. Branches of Engg. Mechanics

4. Force Systems System of forces tells us the arrangement of forces and is classified as follows: system of forces coplanar noncoplanar concurrent parallel general

5. 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 F 2 F 1 Polygonal 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). F 5 F 4 F 3 F 2 Fig 1.(b) F 2 F 3 F 1 F 1 F 5 F 4 F 3 F 2 F 1 5

6. Equilibrium of concurrent forces Conditions of equilibrium for concurrent system of forces in a plane: ∑Fx=0 ∑Fy=0 or ∑Fx=0 ∑Ma=0 or ∑Ma=0 ∑Mb=0

7. Lami’s theorem If 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.

8. Figure LAMI’S THEOREM α Fig (2) F 1 F 3 F 2

9. Example

10. Thank You