Statically indeterminate simple linkage - how to calculate forces and reactions

[rohanskulkarni]

Hi members,

I'm Rohan here and I came across a simple linkage (fig. attached) where in I am unable to calculate the forces required to keep the system in equilibrium and the reactions developed due to the simple loading.

The link shown is pin mounted at the center hinge pin and rests against a roller support at the right end. The link has a weight attached at the right end through a hole made on it just below the roller support pin hole. It is held in static equilibrium by a holding cable at the left end as shown.

Now there would be a force along the cable and the horizontal reaction at roller support that would together maintain the link in equilibrium.

Despite trying to work it out, I am unable to find the value for the reactions - the no. of equations do not suffice to yield the values of all the reactions generated (1. the cable force, 2. the reactions at the center hinge , 3. the horizontal reaction at roller support) and it results in going round and round with the unknowns.

Kindly help me understand how the turning of the link around the center pin would induce/generate the required forces and reactions for equilibrium (how this seemingly statically indeterminate problem is resolved).

Can anyone suggest a good reference book or text book or any paper/notes that sheds light on how to systematically approach and solve such cases (so the concept is cleared).
Anybody with a F.B.D. or steps hinting a solution would help a great deal to understand the concept.
I want to understand this conceptually and not a mere numerical solution. (I think its better to learn fishing than the need to be served fish everytime).

Any explanation and method towards the solution will be greatly appreciated.

Thanks,

Rohan