Concept explainers
A r o lukI f/frm f «m t ub e of ou t sid e d ia met er ^ and a copper core of diameter dxare bonded to form a composite beam, as shown in the figure,
(a) Derive formulas for the allowable bending moment M that can be carried by the beam based upon an allowable stress <7Ti in the titanium and an allowable stress
copper (Assume that the moduli of elasticity for the titanium and copper are Er- and £Cu, respectively.)
(b)
If d1= 40 mm, d{= 36 mm, ETl= 120 GPa, ECu= 110 GPa, o-Ti = 840 MPa, and
ctqj = 700 MPa, what is the maximum bending moment Ml (c)
What new value of copper diameter dtwill result
in a balanced design? (i.e., a balanced design is
that in which titanium and copper reach allow-
able stress values at the same time).
i.
The formula for the allowable bending moment M for titanium tube and copper core of the composite beam
Answer to Problem 6.2.6P
Explanation of Solution
Given:
Allowable stress for titanium is sti
Allowable stress for titanium is scu
Diameter of the copper rod = d1
Outer Diameter of the titanium rod = d2
Concept Used:
Calculation:
Conclusion:
ii.
The allowable bending moment for titanium and copper.
Answer to Problem 6.2.6P
Allowable bending moment for titanium, Mallowableti = 4989 N-m
Allowable bending moment for Copper, MallowableCu =5039.6 N-m
Explanation of Solution
Given:
Allowable stress for titanium, sti = 840 MPa
Allowable stress for titanium, scu= 700 MPa
Diameter of the copper rod, d1= 36 mm
Outer Diameter of the titanium rod, d2 = 40 mm
Eti= 110 GPa
Ecu= 120 GPa
Concept Used:
Calculation:
Allowable bending moment for titanium, Mallowableti = 4989 N-m
Allowable bending moment for Copper, MallowableCu =5039.6 N-m
iii.
The value of the diameter of the copper rod for a balanced design
Answer to Problem 6.2.6P
The diameter of the copper for a balanced design is 36.4 mm
Explanation of Solution
Given:
Allowable stress for titanium, sti = 840 MPa
Allowable stress for titanium, scu= 700 MPa
Outer Diameter of the titanium rod, d2 = 40 mm
Eti= 110 GPa
Ecu= 120 GPa
Concept Used:
Calculation:
Conclusion:
The diameter of the copper for a balanced design is 36.4 mm
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Chapter 6 Solutions
Mechanics of Materials (MindTap Course List)
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- Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning