The stresses which are not caused by external applied force.

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Chapter 12, Problem 20CQ

To determine

The stresses which are not caused by external applied force.

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The composite bar shown is rigidly attached to the two supports. The left portion of the bar is copper, of uniform cross-sectional area 80 c?^2 and length 30 cm. The right portion is aluminum, of uniform cross-sectional area 20 c?2 and length 20 cm. At a temperature of 26℃ the entire assembly is stress free. The temperature of the structure drops and during this process the right support yields 0.025 mm in the direction of the contracting metal. Determine the minimum temperature to which the assembly may be subjected in order that the stress in the aluminum does not exceed 160 MPa. For copper E = 200 GPa, ? = 17x10^-6/℃, and for Aluminum E = 80 GPa, ? = 23x10^-6/℃.

A flat bar of aluminum alloy 25 mm wide and 5 mm thick is placed between two steel bars each 25 mm wide and 10 mm thick to form a composite bar 25 mm x 25 mm as shown. The three bars are fastened together at their ends when the temperature is 15℃. Find the stress in each of the materials when the temperature of the whole assembly is raised to 55 ℃.Steel: Es = 200 GPa; Coefficient of expansion = 1.2x10^-5/℃.Aluminum: Eal = 200/3 GPa; Coefficient of expansion = 2.3x10-5/℃.

Problem 2: A bronze bar is fastened between a steel bar and an aluminum bar as shown. Axial loads are applied at the positions indicated. Find the largest value of P that will not exceed an overall deformation of 3.0 mm, or the following stresses: 140 MPa in the steel, 120 MPa in the bronze, and 80 MPa in the aluminum. Assume that the assembly is suitably braced to prevent buckling. Use Est = 200 GPa, Eal = 70 GPa, and Ebr = 83 GPa. Steel Bronze 480 mm² 650 mm² 3P 1.0 m 4P 2.0 m Aluminum 320 mm² 1.5 m 2P