21 The volume coefficient of thermal expans ion is equal to two times the value of area coefficient of expansion.( O True 22 False The deformation ¤LAT, is the deformation when material is exposed to temperature increase or decrease. ( True O False
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- 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 diameterthe cross-sectional area of the bar 1 of the two bars supported on the left and right sides is 1.2 cm^2, the coefficient of thermal expansion is 20.9 10^(-6)/K; The cross-sectional area of bar 2 is 3 cm^2 and its coefficient of thermal expansion is 25.4 10^(-6)/K. Since the modulus of elasticity of the material is 207 GPa, these two bars are heated to 99 °C.a) What will be the change in length (mm) of bar 1?b) What is the stress in bar 1 in MPa?c) What is the stress in bar 2 in MPa?this is about thermal stress
- The brass shell (αb511.6 3 10–6/°F) is fully bonded to the steel core (αs56.5 3 10–6/°F). Determine the largest allowable increase in tem-perature if the stress in the steel core is not to exceed 8 ksi.A solid cube of side 1 m is kept at a room temperature of 32°C. The coefficient of linear therma expansion of the cube material is 1 x 105/°C and the bulk modulus is 200 GPa. If the cube is constrained all around and heated uniformly to 42°C, then the magnitude of volumetric (mean) stress (in MPa) induced due to heating is و او راA brass wire of diameter d = 2.33 mm is stretched tightly between rigid supports so that the tensile force is T = 93 N (see figure). T The coefficient of thermal expansion for the wire is 19.5 x 106/°c, and the modulus of elasticity is E = 110 GPa. (a) What is the maximum permissible temperature drop (in °C) if the allowable shear stress in the wire is 60 MPa? (Enter the magnitude.) °C (b) At what temperature change (in °C) does the wire go slack? °C
- The aluminum shell is fully bonded to the brass core, and the assembly is unstressed at a temperature of 78°F. The temperature of the assembly reaches 210°F. Consider only axial deformations. 1 in. Brass core E = 15 x 10° psi a = 11.6 x 10-°F Aluminum shell E = 10.6 x 10° psi a = 12.9 x 10-%°F -2.5 in.- Determine the stress in the brass core. The stress in the brass core is |ksi.Calculate Young's modulus for an iron crystal when tension is applied along [2 -2 1] direction. S11=7.6 (TPa)-', S12 = - 2.8 (TPa)-', S44 = 8.6 (TPa) -!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 core
- The material returns to its original shape when the load is removed. (A Elastic Limit B Elastic Behavior Limit c) Maximum Limit D D Proportional LimitA 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)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.