The horizontal beam is rigid while two vertical rods have ax

The horizontal beam is rigid, while two vertical rods have axial rigidity EA. At point A the rod is connected to the beam with a pin, but at point C there is a small gap 5. The rod is extended and connected to tire beam with a pin, and then the structure is released. Find the forces in the rods and the final angle of rotation of tire rigid beam.

Solution

Let the extension of upper rod after connection of the Point C = x

Strain in the upper beam = x / (h - s) ; Tensile Force F of the upper rod = EA*x/(h-s)

Compressive strain on the lower rod = (s - x) / h - since the beam AC is rigid.

Compressive force on the lower rod = EA * (s-x) / h

For equilibrium the compressive force x L = Tensile force x L

or EA * (s-x) / h = EA * x /(h-s)

solving for x, we get x = s(h-s) / (2h - s); Strain on the upper rod = s/(2h-s)

Force of tension on upper rod or compression on the lower rod = EA * s/(2h-s)

Angle of rotation of beam = s/2L (in rad.)