Lami's theorem?

Question

What's the application of lami's theorem in engineering?

Answer 1

It's a way of resolving three static forces so that they can be acting through one point and producing a resultant of zero.

If for example, we have two beams at an angle and we know the forces in the beams, we can work out the force in another beam at an angle to both ot them so that the junction will not move.

It can be used in stress analysis as well as designing balance loads.

Answer 2

Lami's theorem in statics states that if three coplanar forces are acting on a same point and keep it stationary, then it obeys the relation where A, B and C are the magnitude of forces acting at the point (say P), and the values of α, β and γ are the angles directly opposite to the forces C, B and A respectively. Lami's theorem is applied in static analysis of mechanical and structural systems. See also Mathematics of Vectors Vectors in Mechanics TextBook 'Engineering Mechanics' by Beer & Johnson TextBook 'Physics' by Hayt & Kemmerly

Answer 3

Lami's theorem in statics states that

if three coplanar forces are acting on a same point and keep it stationary, then it obeys the relation

where A, B and C are the magnitude of forces acting at the point (say P), and the values of
α, β and γ
are the angles directly opposite to the forces C, B and A respectively.


Lami's theorem is applied in static analysis of mechanical and structural systems.


See also
Mathematics of Vectors
Vectors in Mechanics
TextBook 'Engineering Mechanics' by Beer & Johnson
TextBook 'Physics' by Hayt & Kemmerly

Answer 4

Static (unmoving) analysis of the forces in structures.

Answer 5

to find the forces-tensile or compressive that a structure might be subjected to.Hence we can design safe buildings.

Answer 6

Understand the application of Lami's Theorem. Click on the link to Watch the VIDEO explanation:
http://bit.ly/1qyzrCl

Lets understand the application of Lami's theorem in solving problem
A weight is supported on a smooth plane of inclination alpha to the horizontal by a string inclined to the vertical at an angle gamma. if the slope of the plane be increased to beta and the slope of the string is unaltered, the tension of the string is doubled to support the weight. Prove that cot alpha minus cot gamma is equal to 2 cot beta.
Now let us see how to prove the given relation using Lami's theorem
Let R1 be the reaction on the weight W in case 1 and R2 be the reaction on the weight W in case 2
Click on the button Case 1
When the inclination is alpha. The forces R1, T and W acting at the weight are in the equilibrium
Appling Lami's theorem to the 3 forces, we have
R1 by sin of pie minus gamma is equal to T by sin of pie minus alpha is equal to W by sin of alpha plus gamma
This is equal to R1 by sin gamma is equal to T by sin alpha is equal to W by sin of alpha plus gamma. let this equation be equation 1
Click on the button Case 2
In this case the inclination of R2 with the weight W is beta. The forces R2, 2T and W acting at the weight are in the equilibrium
Therefore, Lami's theorem we have
R2 by sin of pie minus gamma is equal to 2T by sin of pie minus beta is equal to W by sin of beta plus gamma.
This implies R2 by sin gamma is equal to 2T by sin beta is equal to W by sin of beta plus gamma. Now let this equation be equation 2
From equation 1 we have T by W is equal to Sin alpha by sin of Alpha plus gamma and
From equation 2 we have T by W is equal to Sin beta by 2sin of beta plus gamma.
Now equating the two equations we have
Sin alpha by sin of Alpha plus gamma is equal to Sin beta by 2sin of beta plus gamma.
Simplifying the steps we have 2 cot beta is equal to cot alpha minus cot gamma Which is the required equation