Consider a cantilever beam as shown in the figure with length and the left end fixed to a wall. Derive the deflection of the beam along under a single downward force on the right, and assume that the moment of inertia is constant along. (Show complete derivation instead of the final function ) Now consider that the beam has two connected parts, with the part on the left (of length ) having a moment of inertia , and the part on the right . Derive the deflection again. Ignore stress concentration. Further, consider that the cross-sections for the two parts are both circular, and the total volume of the beam is constant. What should and be for the beam to have minimal maximum deflection?
Consider a cantilever beam as shown in the figure with length and the left end fixed to a wall.
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Derive the deflection of the beam along under a single downward force on the right, and assume that the moment of inertia is constant along. (Show complete derivation instead of the final function )
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Now consider that the beam has two connected parts, with the part on the left (of length ) having a moment of inertia , and the part on the right . Derive the deflection again. Ignore stress concentration.
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Further, consider that the cross-sections for the two parts are both circular, and the total volume of the beam is constant. What should and be for the beam to have minimal maximum deflection?
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