An aluminum pipe has a length of 53 m at a temperature of 7°C. An adjacent steel pipe at the same temperature is 7 mm longer. At what temperature will the aluminum pipe be 21 mm longer than the steel pipe? Assume that the coefficient of thermal expansion for the aluminum is 22.5x10-6/°C and that the coefficient of thermal expansion for the steel is 12.5×106/°C. Answer: Tf = i °C
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- 3. 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.A 13 in length of aluminum tubing (with E = 11.4 x 106 psi and = 12 x 10-6 /deg F) having a cross-sectional area of 1.6 in2 is installed with “fixed” ends so that it is stress-free at 70 deg F. In operation, the tube is heated throughout to a uniform 500 deg F. Careful measurement at the higher temperature indicates that the fixed ends separate to 13.008 in. What loads are exerted on the ends of the tube, and what are the resultant stresses?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
- 6. The coefficient of linear expansion of steel is 1x10-5/°C. How much expansion should engineers anticipate in a 2,000 feet steel bridge if it undergoes a change in temperature from 0°C to 30°C? Complete FBD, FORMULA, AND SOLUTIONIn shown figure the aluminum is subjected to a thermal stress where T1 is 21.957 deg. C and T2 is 87.860 deg. C. Determine the required diameter (mm) of the steel rods to limit the expansion of the aluminum just 3.238 mm if the thermal coefficient of aluminum is 24.650 x10^-6 Where: H1 = 2000.392 mm H2 = 2047.231 mm H3 = 1999.692 mm Aal = 2288 mm^2 Eal = 70.018 GPa Est = 202.930 GPaA spherical stainless-steel tank having an inner diameter ‘D’, is used to store naturalgas at a pressure of ‘p’. The properties of the steel are as follows: yield stress in tensionis ‘T’; yield stress in shear is ‘S’ and modulus of elasticity is ‘E’. The desired factor ofsafety with respect to yielding is ‘F.S’.Determine the minimum permissible thickness t min of the tank. (D (mm)=620)( p (MPa)=25)( T (MPa)=1000)( S (MPa)=440)( E (GPa)=208)( F.S=3.4)
- A steel bar is heated from room temperature to 80oC while it is free to expand. The bar will therefore be subject to: A. compression B. tension C. no stress D. shear200 mm 3 kg/m Al. 3280mm 350 160 mm 80 mm Find maximum stresses in steel and aluminumA copper tube having a cross sectional area of 2000 mm2 and a length of 300 mm is rigidly fixed to two rigid caps on its longitudinal ends. Four steel bolts, each having a diameter of 22 mm, are symmetrically arranged parallel to the axis of the tube and are slightly fastened to the rigid caps, as well. The temperature of the assembly is then raised to 70oC. Take the elastic modulus for Copper and Steel as ECU=100 GLa and EST=200 GPa respectively; the coefficient of linear expansion for Copper and Steel as aCU=16x10-67°C and aST=12x10-6/°C respectively. Calculate the load carried by the copper tube and the load carried by each steel bolt
- A rectangular nylon [E = 8 GPa; ?= 0.35; ? = 24 ×10 6/°C] plate has a circular hole in its center. At an initial temperature of T¡ = 15°C, the plate width is b = 260 mm, the plate height is h = 160 mm, the diameter of the central hole is d = 45 mm, and the thickness of the plate is t = 17 mm. At a final temperature of Tf= 52°C, determine (a) the diameter d of the central hole. (b) the thickness t of the plate. b hPolicie Current Attempt in Progress A steel [E = 29900 ksi, a = 6.5x10-6/°F] bar is held between two rigid supports. The bar is stress free at a temperature of 72°F. The bar is then heated uniformly. If the yield strength of the steel is 45 ksi, determine the temperature at which yield first occurs. Answer: T= i °FThe aluminum and bronze cylinders are centered and secured between two rigid end-plates by tightening the two steel bolts. There is no axial load in the assembly at a temperature of 50°F. Find the stress in the steel bolts when the temperature is increased to 200°F. Use the following data: A (in.²) a (/°F) E (psi) Aluminum cylinder 2.00 12.8 × 10–6 10 × 106 Bronze cylinder 3.00 10.5 × 10–6 12 × 106 Each steel bolt 0.75 6.5 × 10–6 29 × 106 1.0 in. -3 in.→ →-4 in. F1.0 in. Aluminum Bronze