A rectangular nylon [E =8 GPa; v=0.35; a= 23x10 6/°C] plate has a circular hole in its center. At an initial temperature of T₁ = 22°C, the plate widthis b=310 mm, the plate height is h = 220 mm, the diameter of the central holeis d = 60 mm, and the thickness of the plateist= 18 mm. At a final temperature of Tf=59°C, determine (a) the diameter d of the central hole. (b) the thickness t of the plate. Answers: (a) df = i (b) t= i b d mm mm
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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 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 hA 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?
- 5. A steel bolt through a 25-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 79 degrees Fahrenheit. The cross- sectional area of the bolt is 0.08 sq. inch and the cross-sectional area of the tube of 0.25 sq. inch. For steel: E = 30 x 106 psi, coefficient of thermal expansion = 6.5 x 10-6/°F For aluminum: E = 10 x 106 psi, coefficient of thermal expansion = 13.0 x 10-6/°F a. Find the thermal deformation (in inches) of the bolt. b. Find the thermal deformation (in inches) of the aluminum tube. c. Find the stress (in psi) induced in the bolt by the temperature change. d. Find the stress (in psi) induced in the aluminum tube by the temperature change.The block shown is made of a magnesium alloy for which E=X2GPaand ϑ=0.35. Knowing that σx= X1 MPa, determine (a) the magnitude of σyfor which the change in the height of the block will be zero, (b) the corresponding change in the area of the face ABCD, (c) the corresponding change in the volume of the block.a)Determine the change in temperature. Indicate increase or decrease in temperature.b)Determine the axial deformation of the steel rod at A (in inches).c)Determine the axial deformation of the steel rod at C (in inches)
- A circular nylon [E = 8 GPa; v=0.35; a=20x106/°C] disk with a circular hole in its center is shown. At an initial temperature of T;= 19°C, the outer diameter of the disk is D = 230 mm, the diameter of the central hole is d = 55 mm, and the thickness of the disk is t = 19 mm. At a final temperature of Tf= 52°C, determine: (a) the change in diameter Ad of the central hole (assume an increase Ad as positive, otherwise as negative). (b) the change in thickness At of the disk (assume an increase At as positive, otherwise as negative). (c) the normal strain in the circumferential direction around the outside of the disk. O Answers: (a) Ad= (b) At= (c) Ecirc 0.0363 0.01254 660 D mm mm με3. A steel bolt through a 25-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 79 degrees Fahrenheit. The cross-sectional area of the bolt is 0.08 sq. inch and the cross-sectional area of the tube of 0.25 sq. inch. For steel: E = 30 x 10^6 psi, coefficient of thermal expansion = 6.5 x 10^-6 per degree Fahrenheit. For aluminum: E = 10 x 10^6 psi, coefficient of thermal expansion = 13.0 x 10^-6 per degree Fahrenheit. Find the thermal deformation (in inches) of the steel bolt. (Write your answer to 6-decimal places. ) * Your answer This is a required question Find the thermal deformation (in inches) of the aluminum tube. (Write your answer to 6-decimal places.) * Your answer This is a required question Find the stress (in psi) induced in the steel bolt by the temperature change. * Your answerA polymer cylinder (2) is clamped between rigid heads by two steel bolts (1). The steel [E = 29,000 ksi; a = 6.5×10-6/°F] bolts have a diameter of 0.50 in. The polymer [E = 380 ksi; a = 39.7x 10-6/°F] cylinder has an outside diameter of 7.0 in. and a wall thickness of 0.40 in. Assume a = 22 in. and b = 30 in. If the %3D temperature of this assembly changes by AT = 125°F, determine: (a) the normal stress in the polymer cylinder. (b) the normal strain in the polymer cylinder. (c) the normal strain in the steel bolts. |(1) (2) C а (1) b. Answer:
- A polymer cylinder (2) is clamped between rigid heads by two steel bolts (1). The steel [E = 29,000 ksi; a = 6.5x10-6/°F] bolts have a diameter of 0.35 in. The polymer [E = 330 ksi; a = 38.3× 10-6/°F]cylinder has an outside diameter of 6.0 in. and a wall thickness of 0.75 in. Assume a = 23 in. and b = 27 in. If the temperature of this assembly changes by AT = 110°F, determine: (a) the normal stress in the polymer cylinder. (b) the normal strain in the polymer cylinder. (c) the normal strain in the steel bolts. (1) (2) (1) b Answer: (a) 02 = psi. (b) Ɛ2 = με (c) ɛ1 =If the gauge is made of a material having a yield stress equal 200 MPa, determine the minimumrequired diameter d. Using a factor of safety (F.S. = 2)Question 3: The block shown is made of a magnesium alloy for which E=760GPa and 9 =0.35. Knowing that o=157 MPa, determine (a) the magnitude of o, for which the change in the height of the block will be zero, (b) the corresponding change in the area of the face ABCD, (c) the corresponding change in the volume of the block.