What is Lami’s Theorem?

Lami’s Theorem, named after the 18^th-century Armenian-French mathematician Gabriel Lami; is a principle in static and structural engineering. Lami’s Theorem verifies the equilibrium of the system under concurrent forces.

Lami’s Theorem is particularly useful when analyzing the equilibrium of structures and trusses subjected to concurrent forces. Lami’s Theorem provides a mathematical relationship between the magnitudes and directions of these forces when the system is in static equilibrium.

Statement of Lami’s Theorem

When three coplanar forces act simultaneously at a point, achieving equilibrium among them, each force is proportional to the sine of the angle between the other two forces.

Lami’s Theorem Formula

The theorem states that for a body in static equilibrium if three coplanar forces act on a point and keep it in equilibrium, each force is proportional to the sine of the angle between the other two forces. Mathematically, it can be expressed as:

F₁/sin α= F₂/sin β = F₃/sin γ

Where,

• F₁, F₂, and F₃ are the magnitudes of the forces, and
• α, β, and γ are the angles between the forces.

Lami’s Theorem, also known as Lami’s Law, is a principle in statics and mechanics of materials that relates the forces acting on a body in static equilibrium. It is named after the Italian mathematician and physicist Bernard Lami. Lami’s Theorem is typically applied to a body or structure subjected to concurrent forces. Imagine three friends pulling a string simultaneously from different directions, considering the plane is coplanar. Through the help of Lami’s theorem, one can easily find the forces each friend is exerting.

Further in this article, we will learn about the statement, formula, step-by-step proof, essential assumptions, and practical applications of Lami’s Theorem. Additionally, there will be a few practice problems for better understanding and clarification.