A member of uniform rectangular cross section is subjected to a bending moment M = 36.8 kN-m. The member is made of an elastoplastic material with a yield strength of 240 MPa and a modulus of elasticity of 200 GPa. Determine (a) the thickness of the elastic core, (b) the radius of curvature of the neutral surface. c = 60 mm c = 60 mm b = 50 mm ↑ YY
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- An aluminum alloy cylinder with a diameter of 76 mm and a height of 150 mm. is subjected to a compressive load of 220 kN. Assume that the mate-rial is within the elastic region and a modulus of elasticity of 75 GPa. a. What will be the lateral strain if Poisson’s ratio is 0.33?b. What will be the diameter after load application?c. What will be the height after load application?PROBLEM 1) An aluminum bar carries the axial loads at the positions shown. If E=70GPA, compute the total deformation of the bar. Assume that the bar is suitably braced to prevent buckling. 0.4m D 10KN 0.8m 0.4m B 5KN 0.6m AL 20KN What is the deformation &pE in mm? A=800 mm² A=1,200 mm²The solid shaft shown is made of a mild steel that is assumed to be elastoplastic with Ty= 145 MPa. Determine the radius of the elastic core caused by the application of a torque equal to 1.17y, where Ty is the magnitude of the torque at the onset of yield. Take d = 30.8 mm. 1.2 m The radius of the elastic core is mm.
- A beam of the cross section shown is made of a steel that is assumed to be elastoplastic with E=29×106psi and σY= 42 ksi. A bending couple is applied to the beam about the z axis, causing plasticzones 2 in. thick to develop at the top and bottom of the beam. After the couple has been removed, determine (a) the residual stress at y=2 in., (b) the points where the residual stress is zero, (c) the radius of curvature corresponding to the permanent deformation of the beam.Determine the plastic moment Mp of the cross section shown when the beam is bent about a horizontal axis. Assume the material to be elastoplastic with a yield strength of 169 MPa. 5 mm t=5 mm 120 mm 5 mm 80 mm The plastic moment is kN.m.PROBLEM 1) An aluminum bar carries the axial loads at the positions shown. If E=70GPA, compute the total deformation of the bar. Assume that the bar is suitably braced to prevent buckling. 0.4m D 10KN. 0.8m 0.4m B 5KN 0.6m Al 20KN Q2 5) What is the deformation 8, in mm? A=800 mm? A=1,200 mm?
- PROBLEM 4.75 A beam of the cross section shown is made of a steel that is assumed to be elastoplastic with E= 200 GPa and ay 350 MPa. For bending about the z axis, determine the bending moment and radius of curvature at which (a) yield first occurs, (b) the plastic zones at the top and bottom of the bar are 25 mm thick. 12.5 mm 60 mm 25 mm 60 mm 25 mm -12.5 mmA composite beam is made of two brass [E = 110 GPa] bars bonded to two aluminum [E = 71 GPa] bars, as shown. The beam is subjected to a bending moment of 260 N-m acting about the z axis. Using a = 10 mm, b = 85 mm, c = 20 mm, and d = 55 mm, calculate (a) the maximum bending stress in the aluminum bars. (b) the maximum bending stress in the brass bars. 2 Aluminum C Aluminum Answers: (a) Jal= Brass- (b) Obr= i i b Brass (2 (2 MPa O MPa EA composite beam is made of two brass [E = 110 GPa] bars bonded to two aluminum [E = 71 GPa] bars, as shown. The beam is subjected to a bending moment of 260 N-m acting about the z axis. Using a = 10 mm, b = 85 mm, c = 20 mm, and d = 55 mm, calculate (a) the maximum bending stress in the aluminum bars. (b) the maximum bending stress in the brass bars. Aluminum С Aluminum Answers: (a) Jal= Brass (b) Obr= i b Brass a MPa MPa
- A composite beam is made of two brass [E = 97 GPa] plates bonded to an aluminum [E = 72 GPa] bar, as shown. The beam is subjected to a bending moment of 2420 N-m acting about the z axis. Assume b=64 mm, d1=36 mm, d2=13 mm. Determine: (a) the maximum bending stresses opy,Gal in the brass plates and the aluminum bar. (b) the stress in the brass obrj at the joints where the two materials are bonded together. Brass (2) d2 Aluminum (1) Brass (2) dz b Answers: (a) obr = i MPa, oal = i MPа. (b) Obrj MPa.A composite beam is made of two brass [E = 120 GPa] bars bonded to two aluminum [E = 70 GPa] bars, as shown. The beam is subjected to a bending moment of 400 N-m acting about the z axis. Using a = 15 mm, b = 100 mm, c = 30 mm, and d = 65 mm, calculate (a) the maximum bending stress in the aluminum bars. (b) the maximum bending stress in the brass bars. Aluminum y Brass Aluminum b Brass C a dThe composite shaft shown in the figure consists of a bronzesleeve (1) securely bonded to an inner steel core (2). The bronze sleeve has an outside diameter of 25 mm, an inside diameter of 20 mm, and a shear modulus of G1 = 45 GPa. The solid steel core has a diameter of 20 mm and a shear modulus of G2 - 83 GPa. Assume L - 470 mm. The composite shaft is subjected to a torque of T-970 N-m. Determine a) the maximum shear stresses in the bronze sleeve and the steel core. b) the rotation angle of end B relative to end A. Answers: (a) TI = MPa T2 = MPa (b) PRIA = rad