The composite bar shown in the figure is rigidly attached to the two supports. The left portion of the bar is copper, of uniform cross-sectional area 80 cm2 and length 30 cm. The right portion is aluminum, of uniform cross-sectional area of 20 cm2 and length 20 cm. At a temperature of 26°C 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 = 100 GPa, a = 17

The composite bar shown in the figure is rigidly attached to the two supports. The left portion of the bar is copper, of uniform cross-sectional area 80 cm2 and length 30 cm. The right portion is aluminum, of uniform cross-sectional area of 20 cm2 and length 20 cm. At a temperature of 26°C 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 = 100 GPa, a = 17

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter2: Axially Loaded Members

Section: Chapter Questions

Problem 2.5.13P: Rectangular bars of copper and aluminum are held by pins at their ends, as shown in the figure. Thin...

See similar textbooks

Similar questions

The rails of a railroad track are welded together at their ends (to form continuous rails and thus eliminate the clacking sound of the wheels) when the temperature is 60°F. What compressive stress ?? =6.5×10-6 /? is produced in the rails when they are heated by the sun to 120"F if the coefficient of thermal expansion a = the modulus of elasticity E = 30 × 106 psi?
A two-story building has steel columns AB in the first floor and BC in the second floor, as shown in the figure. The roof load P:equals 400 KN, and the second-floor load P-, equals 720 kN. Each column has a length L = 3.75 m. The cross-sectional areas of the first- and second-floor columns are 11,000 mm" and 3900 mm", respectively. (a) Assuming that E = 206 GPa. determine the total shortenings aof the two columns due to the combined action of the loads Ptand P,. (b) How much additional load P0can be placed at t he top of t he column (point C) if t he total shortening: SACis not to exceed 4.0 mm?
The ends of the bars shown in the figure are 5 mm apart at 25 ° C. The left hand bar is brass and is 1.00 m long, and the right hand bar is steel and is 1.00 m long as well, assuming the outer ends of both bars are firmly supported against rigid supports. a) Determine at what temperature the ends of the facing bars just touch. b) If only 5 µm were separated, what would now be the necessary temperature to join them?
A copper rod with 0.15 cm diameter is enclosed by a steel tube that has an outside diameter of 0.3 cm and an internal diameter of 0.2 cm. The assembly is fixed at each end. Determine the stresses in the rod and tube if the temperature is at 220oC; at 10oC, there is no longitudinal stress. Based on laboratory results for steel, E = 2.1 x 105 N/mm2, a = 11x10-6/oC, and for copper, E = 1 x 105 N/mm2, a = 18x10-6/oC
Two circular plates with (2d) and (d) as outer and inner diameters respectively, are clamped together by means of a bolt as shown in figure. The bolt is made of plain carbon steel (Sy= 380 MPa and E = 207 GPa), while the plates are made of aluminium (E = 71 GPa) The initial pre-load in the bolt is 3 kN and the external force acting on the bolted joint is 7.5 kN. Determine the size of the bolt from the given table, if the factor of safety is 2.5 and assume coarse threads required.
The rigid bar ABC is supported by a hinge at B and two vertical steel rods at A and C as shown in Figure. Initially, the bar is horizontal, and the rods are stress-free. The coefficient of thermal contraction, α is 11.7x10-6 /oC and modulus of elasticity, E = 200 GPa for steel. If the temperature of the steel rod at A is decreased by 35oC while the temperature of steel rod at C remains constant, determine : The stress in the steel rod at A (in MPa). The stress in the steel rod at C (in MPa). The deformation of the steel rod at C. Include negative sign if contraction (in mm, in 3 decimal places). The deformation of the steel rod at A. Include a negative sign if contraction (in mm, in 3 decimal places)
A bar with a solid square cross-section is composed of three sections of equal length. The outer sections are made from material A and the middle section is made from material B, as shown in the figure. Assume the stress-strain curves for the particular materials used are as shown. a. What is the change in the length of the bar if a tensile load of 112 kN is applied? The square cross-section has 2 cm sides and the length of each part is 2 m The elastic modulus of material A is 150 GPa and the elastic modulus of material B is 100 GPa. b. When the bar in Part B is unloaded, it will have a permanent change in length. What is this permanent change in the length?
A cylindrical component 0.3 m long is solid for 1/3 of its length and hollow with inner diameter ½ the outer diameter for the rest of the length. At 300C a gap of 0.1 mm exists between the component and the rigid supports. The outer diameter is 60 mm and the stress is not to exceed 150 MN/m2. Determine the maximum temperature that will not cause failure of the component. Take α as 1.3x10-5/0c and E as 200 GN/m2
A steel rod with varying cross-sectional areas is fixed at both ends, as shown in the figure below. L1=100mm, L2=50mm, A1=300mm2, A2=100mm2. The elastic modulus is ?=2×105???, and the material has a thermal expansion coefficient of ?=12×10-6°C-1. Assuming that the rod is stress-free at 10°C . a. Calculate the normal stress in the rod assuming temperature increases to 30°C. b. Draw the normal force diagram at 30°C, with the origin and direction of x axis indicated by the red arrow.
The two ends of a cylindrical nickel rod 120 mm long and 12 mm in diameter are held rigid. If the bar is initially at 70°C, to what temperature must it be cooled for a reduction in diameter of 0.023 mm to occur? Consider the modulus of elasticity of nickel of 209 GPa, and the coefficient of expansion of 13 x 10-6 K-1.
A steel pipe with a 50 mm outside diameter and a 43.75 mm inside diameter surrounds a solid brass rod 37.5 mm in diameter as shown. Both materials are joined to a rigid cover plate at each end. The assembly is free to expand longitudinally. The assembly is stress free at a temperature of 27 degree C. For steel, Young's modulus is 200 GN/m^2, and the coefficient of linear thermal expansion is 11.7 x 10^-6 1/degree C. For brass, Young's modulus is 93.33 GN/m^2, and the coefficient of linear thermal expansion is 1.872 x 10^-5 1/degree C. What is the stress in the steel tube when the temperature is raised to 121 degree C?
The bronze bar 3.42 m long with a cross-sectional area of 627 mm2 is placed between two rigid walls. At a temperature of -14 °C, there is a gap Δ = 2.36 mm, as shown in the figure. Find the temperature at which the compressive stress in the bar will be 34.22 MPa. Use α = 18 × 10-6 /°C and E = 80.32 GPa. Round off your answer to two decimal places.