Solution:

( details are explained below, in the Epilogue)

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The most dangerous load for a simple supported beam	The optimal distribution of the stiffness in a simple supported beam

Optimal design of a composite

made of two elastic materials

	The laminate composite offers the best resistance to a uniaxial stress and to any stress close to the uniaxial one.
	The set of admissible additional loadings. If the magnitude of additional loading is small enough, the laminate design remains optimal.