4.90 A bending couple is applied to the bar indicated, causing plastic zones 3 in. thick to develop at the top and bottom of the bar. After the couple has been removed, determine (a) the resid- al stress at y = 4.5 in., (b) the points where the residual stress is Zero, (c) the radius of curvature corresponding to the permanent deformation of the bar.

An extruded polymer beam is subjected to a bending moment M. The length of the beam is L = 680 mm. The cross-sectional dimensions of the beam are b1 = 33 mm, d1 = 93 mm, b2 = 20 mm, d2 = 20 mm, and a = 6.5 mm. For this material, the allowable tensile bending stress is 16 MPa, and the allowable compressive bending stress is 9 MPa. Determine the %3D largest moment M that can be applied as shown to the beam. b2 M d2 d1 | A B L b1 Answer: M = i N•m

2.58 Knowing that a 0.02-in. gap exists when the temperature is 75°F, determine (a) the temperature at which the normal stress in the alu- minum bar will be equal to -11 ksi, (b) the corresponding exact length of the aluminum bar. 0.02 in. - 14 in. - Bronze A = 2.4 in² E = 15 x 106 psi a = 12 x 10-6/°F Fig. P2.58 and P2.59 18 in.. Aluminum A = 2.8 in² E = 10.6 x 106 psi a = 12.9 x 10-6/°F 300 mm 0.5 mm 250

The composite beam is made of steel (A) bonded to brass (B) and has the cross section shown. It is subjected to a moment of M = 6.3 kN?m .Ebr = 100 GPa, Est = 200 GPa A: Determine the maximum bending stress in the brass. B:Determine the maximum bending stress in the steel. C: Determine the stress in the brass at the seam where the brass and steel are bonded together. D:Determine the stress in the steel at the seam where the brass and steel are bonded together. B M 175 mm 150 mm 200 mm