Lami's theorem

In statics, Lami's theorem is an equation relating the magnitudes of three coplanar, concurrent and non-collinear forces, which keeps an object in static equilibrium, with the angles directly opposite to the corresponding forces. According to the theorem,

$\frac{A}{\sin \alpha}=\frac{B}{\sin \beta}=\frac{C}{\sin \gamma}$

where A, B and C are the numerical values of three coplanar, concurrent and non-collinear forces, which keep the object in static equilibrium, and α, β and γ are the angles directly opposite to the forces A, B and C respectively.^[1]

Lami's theorem is applied in static analysis of mechanical and structural systems. The theorem is named after Bernard Lamy.^[2]

Proof

By making all the forces touch its tip and tail we can get a triangle with sides A,B,C and angles $\alpha ,\beta ,\gamma$ . By sine rule,^[1]

${\frac {F_{A}}{\sin(180^{o}-\alpha )}}={\frac {F_{B}}{\sin(180^{o}-\beta )}}={\frac {F_{C}}{(180^{o}\sin -\gamma )}}$

$\therefore {\frac {A}{\sin \alpha }}={\frac {B}{\sin \beta }}={\frac {C}{\sin \gamma }}$

References

1 2 Dubey, N. H. (2013). Engineering Mechanics: Statics and Dynamics. Tata McGraw-Hill Education. ISBN 9780071072595.
↑ "Lami's Theorem - Oxford Reference". doi:10.1093/oi/authority.20110803100049237. Retrieved 2018-10-03.

Lami's theorem

Proof

See also

References

Further reading