Textbook Problem

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 d_xare 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 <7_Ti in the titanium and an allowable stress ( _u in the

copper (Assume that the moduli of elasticity for the titanium and copper are E_r- and £_Cu, respectively.)

(b)

If d₁= 40 mm, d_{= 36 mm, E_Tl= 120 GPa, E_Cu= 110 GPa, o-_Ti = 840 MPa, and

ctqj = 700 MPa, what is the maximum bending moment Ml (c)

What new value of copper diameter d_twill 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).