Question: The beam AB shown in the figure is simply supported at A and B and supported on a spring of stiffness k at its midpoint

The beam AB shown in the figure is simply supported at A and B and supported on a spring of stiffness k at its midpoint C. The beam has flexural rigidity EI and length 2L.
What should be the stiffness k of the spring in order that the maximum bending moment in the beam (due to the uniform load) will have the smallest possible value?

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