spansion coefficient a = 2.6 × 10-6/°C. It is 1 mm thick with fixec of 60°C and 10°C, respectively, at the leftmost ends of its hot arn s shown below. Suppose the bimorph has a uniform internal he 100 W/m³, and ignore the effects of convective heat transfer. (1) eady-state temperature distribution in the thermal bimorph. (2) ermally induced deformation and stresses in the bimorph if the ed on their left ends.
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- The assembly consists of a brass shell (1) fully bonded to a solid ceramic core (2). The brass shell [E = 115 GPa, a = 18.7 × 10-6/°C] has dout 50mm. and din = 35mm. The ceramic core [E = 290 GPa, α = 3.1 x 10-6/°C] has a diameter dout = 35mm. At a temperature of 15°C, the assembly is unstressed. AT = 60°C. Find the internal stress in the brass. = 200 mm Brass shell (1) (2) Ceramic coreAt a temperature of 60°F, a 0.04-in. gap exists between the ends of the two bars shown. Bar (1) is an aluminum alloy [E = 10,000 ksi; v = 0.32; a = 12.5 x 10-6/°F] bar with a width of 3.0 in. and a thickness of 0.75 in. Bar (2) is a stainless steel [E = 28,000 ksi; v = 0.12; a = 9.6 x 10-6/°F] bar with a width of 2.0 in. and a thickness of 0.75 in. The supports at A and C are rigid. Determine (a) the lowest temperature at which the two bars contact each other. (b) the normal stress in the two bars at a temperature of 250°F. (c) the normal strain in the two bars at 250°F. (d) the change in width of the aluminum bar at a temperature of 250°F. (1) 3.0 in. 32 in. 2.0 in. B ↓ (2) 44 in. 0.04-in. gap Determine the lowest temperature, Tcontact, at which the two bars contact each other.6 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°C. For steel, Young's modulus is 200 GN/m², and the coefficient of linear thermal expansion is 11.7x10-6 1/°C. For brass, Young's modulus is 93.33 GN/m², and the coefficient of linear thermal expansion is 1.872 x 10-5 1/°C. What is the stress in the steel tube when the temperature is raised to 121°C? brass rod (solid) 37.5 mm diameter steel tube 50 mm outside diameter 43.75 mm inside diameter
- At a temperature of 60°F, a 0.04-in. gap exists between the ends of the two bars shown. Bar (1) is an aluminum alloy [E = 10,000 ksi; v = 0.32; a = 12.7 x 10-6/°F] bar with a width of 3 in. and a thickness of 0.75 in. Bar (2) is a stainless steel [E = 28,000 ksi; v = 0.12; a = 8.6 x 10-6/°F] bar with a width of 2 in. and a thickness of 0.75 in. The supports at A and C are rigid. Determine the lowest temperature at which the two bars contact each other. (1) 3 in. 32 in. 90.2°F O 69.9°F 139.2°F 103.5°F O 111.0°F B ↑ 2 in. ↓ 44 in. -0.04-in. gapThe constant a for a steel material having an ultimate strength of 106.5 ksi isAt a temperature of 60°F, a 0.04-in. gap exists between the ends of the two bars shown. Bar (1) is an aluminum alloy [E = 10,000 ksi; v = 0.32; a = 13.4 x 10-6/°F] bar with a width of 3 in. and a thickness of 0.75 in. Bar (2) is a stainless steel [E = 28,000 ksi; v = 0.12; a = 10.1 x 10-6/°F] bar with a width of 2 in. and a thickness of 0.75 in. The supports at A and Care rigid. Determine the lowest temperature at which the two bars contact each other. (1) ↑ 3 in. 32 in. O 75.9°F O 146.5°F O 105.8°F O 122.3°F O 111.3°F 2 in. (2) 44 in. -0.04-in. gap
- At a temperature of 60°F, a 0.04-in. gap exists between the ends of the two bars shown. Bar (1) is an aluminum alloy [E = 10,000 ksi; v = 0.32; a = 14.4 x 10-6/°F] bar with a width of 3 in. and a thickness of 0.75 in. Bar (2) is a stainless steel [E = 28,000 ksi; v = 0.12; a = 9.6 × 10-6/°F] bar with a width of 2 in. and a thickness of 0.75 in. The supports at A and Care rigid. Determine the lowest temperature at which the two bars contact each other. (1) 3 in. 32 in. 105.3°F 75.3°F O 147.3°F 86.6°F 113.4°F B ↑ 2 in. ↓ (2) 44 in. 0.04-in. gap3. A steel bolt through a 31-in long aluminum tube has the nut turned on until it just touches the end of the tube. No stress is introduced on the bolt or the tube. The temperature of the assembly is raised from 70 to 81 degrees Fahrenheit. The cross-sectional area of the bolt is 0.09 sq. inch and the cross-sectional area of the tube of 0.30 sq. inch. a. Find the thermal deformation (in inches) of the steel bolt. (Write your answer to 6-decimal places.) b. Find the thermal deformation (in inches) of the aluminum tube. (Write your answer to 6-decimal places.) c. Find the stress (in psi) induced in the steel bolt by the temperature change. d. Find the stress (in psi) induced in the aluminum tube by the temperature change.At a temperature of 60°F, a 0.04-in. gap exists between the ends of the two bars shown. Bar (1) is an aluminum alloy [E = 10,000 ksi; v = 0.32; α=α=12.5 x 10-6/°F] bar with a width of 2.5 in. and a thickness of 0.75 in. Bar (2) is a stainless steel [E = 28,000 ksi; v = 0.12; α=α=9.6 x 10-6/°F] bar with a width of 1.7 in. and a thickness of 0.75 in. The supports at A and C are rigid. Assume h1=2.5 in., h2=1.7 in., L1=31 in., L2=46 in., and Δ=Δ= 0.04 in. (A) Determine the lowest temperature, Tcontact, at which the two bars contact each other. (B) Find a geometry-of-deformation relationship for the case in which the gap is closed. Express this relationship by entering the sum δ1+δ2, where δ1 is the axial deflection of Bar (1), and δ2 is the axial deflection of Bar (2). δ1+δ2= _____in. (C) Find the force in the Bar (1), F1, and the force in Bar (2), F2, at a temperature of 225oF. By convention, a tension force is positive and a compression force is negative. IN KIPS (D) Find σ1 and σ2,…
- At a temperature of 60°F, a 0.02-in. gap exists between the ends of the two bars shown. Bar (1) is an aluminum alloy [E = 10,000 ksi; v = 0.32; α=α=12.5 x 10-6/°F] bar with a width of 2.8 in. and a thickness of 0.85 in. Bar (2) is a stainless steel [E = 28,000 ksi; v = 0.12; α=α=9.6 x 10-6/°F] bar with a width of 1.6 in. and a thickness of 0.85 in. The supports at A and C are rigid. Assume h1=2.8 in., h2=1.6 in., L1=26 in., L2=40 in., and Δ=Δ= 0.02 in. Determine(a) the lowest temperature at which the two bars contact each other.(b) the normal stress in the two bars at a temperature of 225°F.(c) the normal strain in the two bars at 225°F.(d) the change in width of the aluminum bar at a temperature of 225°F.A laminated [0/90/0/90]s graphite/epoxy beam is 1 mm thick, is 20 mm wide, and has 0.125 mm thick plies. The lamina properties are E1 = 180 GPa, E2 = 10 GPa, ν12 = 0.28, G12 = 7 GPa Xt = 1700 MPa, Xc = 1400 MPa, Yt = 40 MPa, Yc = 230 MPa (a) Determine the flexural modulus of the beam (b) How could the flexural modulus be improved without changing the ply materials, the number of plies, or the ply orientations? (c) Using the Maximum Stress Criterion for each ply, determine the magnitude of the maximum allowable bending moment that the beam can withstand. Which ply fails first?When a bar is cooled to -5°C, it will develop O(A) No stress OCB) Shear stress OC) Tensile stress O(D) Compressive stress