Answered: A round titanium tube of outside…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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A round titanium tube of outside diameter d₂ and a copper core of diameter d₁ are bounded to form a composite beam, as depicted in Figure Q1.

1.1 Derive formulas for the allowable bending moment ? that can be carried by the beam based upon an allowable stress σTi in the titanium and an allowable stress σCu in the copper (Assume that the moduli of elasticity for the titanium and copper are E_Ti and E_Cu, respectively).

1.2 If d₂=40 ??, d₁=36 ??, E_Ti=120 ???, E_Cu=110 ???, σTi =840 ???, and σCu =700 ???, what is the maximum bending moment?

1.3 What new value of copper diameter ?1 will result in a balanced design? (i.e., a balanced design is that in which titanium and copper reach allowable stress values at the same time).

Copper
d₁
d₂
Titanium
Figure Q1: Titanium-Copper Composite Beam.

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