Additional interpretations of the solution of the straight beam differential equation
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The fundamental differential equation of the transversely loaded straight beam, the Bernoulli-Euler equation, has been subject to various interpretive solutions. Perhaps the two best known solutions of this kind are the moment-area and conjugate beam methods which solve the equation with the aid of certain properties of the curves for the beam in question. The present paper applies two separate mathematical methods to the solution of this equation. The first method makes use of the Green's function and obtains a solution for the beam built-in both ends. The second method utilizes the so-called "superposition theorem" which is frequently applied to problems involving transient phenonema such as those encountered in electrical network and vibration problems, and obtains a solution valid for any type of support.
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