The figure shows a propped cantilever with uniform flexural rigidity EI (in N.m²) and subjected to a moment $M$ (in N.m). Consider forces and displacements in the upward direction as positive.

Find the upward reaction at the propped support B (in N) when this support settles by $(-\Delta)$, given in metres.

Two beams are connected by a linear spring as shown in the following figure. For a load $$P$$ as shown in the figure, the percentage of the applied load $$P$$ carried by the spring is ______________.

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 _______________