THERMAL STRESS3. A rigid bar is supported by two copper rodsand the gap between the aluminum rod andthe bar is 1.50 mm. If the temperature for allmaterials is increased by 40 degrees Celsius,will the aluminum rod touch the rigid bar ornot? Prove your answer.For each copper bar,A = 500 mm^2, E = 120 GPa and a = 16.8um/(m C).For the aluminum bar,A = 400 mm^2, E = 70 GPa , and a = 23.1um/(m C).

Stress that is produced in the rigid body due to a change in the temperature is called thermal…

Answered: THERMAL STRESS 3. A rigid bar is…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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A 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
In 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 GPa
The assembly shown in the figure consists of an aluminum tube AB and a steel rod BC. The rod is attached to the tube through the rigid collar at B and passes through the tube. The cross-sectional area of the rod is 75 mm2 and the cross-sectional area of the tube is 400 + UV in mm2, where UV is 99. A tensile load of 80 kN is applied to the rod. Take Est = 200 GPa for the steel rod, Eal = 70 GPa for the aluminum tube. Determine: (a) the displacement of end C with respect to end B (i.e., the elongation of the steel rod), (b) the displacement of end B with respect to the fixed end A (i.e., the shrink of the aluminum tube), (c) the displacement of the end C of the rod (i.e., (a) + (b)).
Three aluminum rods support the rigid L-shaped bracket BCF as shown in the figure. Determine the stress in rod DE (express answer in MPa) if rod FG is cooled by 50°C. All three rods have the same cross-sectional area of 1000 mm^2. Use 73.1 GPa and 23 x 10^-6 /°C for the modulus of elasticity and the coefficient of thermal expansion of aluminum, respectively.
Three aluminum rods support the rigid L-shaped bracket BCF as shown in the figure. Determine the stress in rod DE (express answer in MPa) if rod FG is cooled by 50°C. All three rods have the same cross-sectional area of 1000 mm^2. Use 73.1 GPa and 23 x 10^-6/°C for the modulus of elasticity and the coefficient of thermal expansion of aluminum, respectively.
Two uniform spheres are positioned as shown. Determine the gravitational force F which the titanium sphere exerts on the copper sphere. The value of R is 30 mm. Assume a = 4.9, b = 2.3, 0=29° y R 1 aR Titanium Copper bR - X
PROBLEM 4: As shown in the diagram shown, there is a gap of 0.5 mm between the rods at 10°C. Determine the stress in each rod if the temperature is raised to 150°C. The properties of each material are shown in the diagram. 0.5 mm FINAL ANSWERS 300 mm -250 mm MPa O alum O steel MPа Aluminum Stainless steel A = 2000 mm2 E = 75 GPa a = 23 × 10-6°C A = 800 mm? E = 190 GPa 17.3 x 10-6/°C
3. 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 answer
3. An aluminum rod is rigidly attached between a steel rod and a bronze rod as shown in the figure. Axial loads are applied at the positions indicated. Find the maximum value of P that will not exceed a stress in steel of 140 MPa, in aluminum of 13.05 ksi, or in bronze of 100 MPа. Aluminum A = 400 mm? Bronze A = 200 mm Steel A = 500 mm? 2P 4D 2.5 m 2.0 m 1.5 m
The rigid horizontal bar ABC of negligible mass is connected to two rods as shown in the figure. If the system is initially stress-free, calculate the temperature change that will cause a tensile stress of 90 MPa in the brass rod. Assume that both rods are subjected to the same change in temperature. Brass L=2 m A= 1200 mm E= 100 GPa a = 18,7 x 10-y°C B -2 m Соpper L=3 m A = 1500 mm E= 120 GPa a = 16.8 x 10-bj°C FIG. P2.108
30. An aluminum alloy rod has a circular cross section with a diameter of 8mm. The rod is subjected to a tensile load of 5kN. Assume that the material is in the elastic region and E = 69 GPa. If Poisson's Ratio is 0.33, what will be the lateral strain? E= 6/8 v = -E(lateral)/(axial)
2. A rod is composed of an aluminum section rigidly attached between steel and bronze sections as shown in the figure. Axial loads are applied at the positions indicated. The cross-sectional area of the rod is 300sq.mm. Express your answer in MPa. Determine the stress in the steel. b. a. Determine the stress in the aluminum. Determine the stress in the bronze. C. STEEL ALUMINUM BRONZE 56kN 14kN -0.6m- -0.9m- -0.76m-

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