Lami's theorem
This document discusses Lami's theorem and provides an example. It begins by introducing the topic of mechanics of solids and listing the group members and their enrollment numbers. It then defines different types of force systems including coplanar, non-coplanar, concurrent, parallel, and general systems of forces. The document explains the triangle and polygonal laws for graphical conditions of equilibrium. It states the conditions of equilibrium for concurrent forces as the sum of forces in the x and y directions equaling zero, or the sum of moments equaling zero. Lami's theorem is then introduced as stating that if a particle is in equilibrium under three forces, each force bears the same proportionality to the sine of the angle between the
Lami's theorem
- 1. 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) F1 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). Fig 1.(b) F2 F3 F1 F1 F5 F4 F3 F2 F1 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 Sin F Sin F Sin F 321 α Fig (2) F1 F3 F2
- 9. Example
- 10. Thank You