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 ETi and ECu, respectively). 1.2 If d2=40 ??, d1=36 ??, ETi=120 ???, ECu=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).
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 ETi and ECu, respectively). 1.2 If d2=40 ??, d1=36 ??, ETi=120 ???, ECu=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).
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 ETi and ECu, respectively).
1.2 If d2=40 ??, d1=36 ??, ETi=120 ???, ECu=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).
Transcribed Image Text:Copper
d₁
d₂
Titanium
Figure Q1: Titanium-Copper Composite Beam.
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