In a system, two connected rigid bars $$AC$$ and $$BC$$ are of identical length $$L$$ with pin supports at $$A$$ and $$B.$$ The bars are interconnected at $$C$$ by a frictionless hinge. The rotation of the hinge is restrained by a rotational spring of stiffness, $$k.$$ The system initially assumes a straight line configuration, $$ACB.$$ Assuming both the bars as weightless, the rotation at supports, $$A$$ and $$B,$$ due to a transverse load, $$P$$ applied at $$C$$ is:

A steel strip of length, $$L = 200$$ $$mm$$ is fixed at end $$A$$ and rests at $$B$$ on a vertical spring of stiffness, $$k = 2$$ $$N/mm.$$ The steel strip is $$5$$ $$mm$$ wide and $$10$$ $$mm$$ thick. $$A$$ vertical load, $$P = 50$$ $$N$$ is applied at $$B,$$ as shown in the figure. Considering $$E = 200$$ $$GPa,$$ the force (in $$N$$) developed in the spring is _______________

The axial load (in $$kN$$) in the member $$PQ$$ for the arrangement/assembly shown in the figure given below is ___________

Consider a propped cantilever $$ABC$$ under two loads of magnitude $$P$$ each as shown in figure below. Flexural rigidity of the beam is $$EI$$.

The rotation at $$B$$ is