A steel rod, which is free to move, has a length of 200 mm and a diameter of 20 mm at a temperature of 15oC. If the rod is heated uniformly to 115oC, determine the length and diameter of this rod to the nearest micron at the new temperature if the linear coefficient of thermal expansion of steel is 12.5 x 10-6 m/m/C. Is there a stress on the rod at 115oC?

A steel rod, which is free to move, has a length of 200 mm and a diameter of 20 mm at a temperature of 15oC. If the rod is heated uniformly to 115oC, determine the length and diameter of this rod to the nearest micron at the new temperature if the linear coefficient of thermal expansion of steel is 12.5 x 10-6 m/m/C. Is there a stress on the rod at 115oC?

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter7: Analysis Of Stress And Strain

Section: Chapter Questions

Problem 7.7.7P: A thin square plate in biaxial stress is subjected to stresses ?? and ??., as shown in part a of the...

See similar textbooks

Similar questions

A steel rod, which is free to move, has a length of 200 mm and diameter of 20 mm at a temperature of 15°C. If the rod is heated uniformly to 115°C, determine the length and the diameter of this rod to the nearest micron at the new temperature if the linear coefficient of thermal expansion of steel is 12.5 x 10 m/m/°C. Wrong solution will be reported instantly
A solid prismatic rod is L₁ = 390 mm long and has a circular cross section with a diameter of d = 36 mm. After the temperature of the unconstrained rod is increased, its final length is measured as L₁= 390.240 mm. Determine the change in the rod's diameter after the temperature increase. Answer: Ad = i mm
A solid prismatic rod is L; = 390 mm long and has a circular cross section with a diameter of d = 40 mm. After the temperature of the unconstrained rod is increased, its final length is measured as L₁ = 390.270 mm. Determine the change in the rod's diameter after the temperature increase. Answer: Ad = i mm
A steel rod is heated from 25 to 250. Its coefficient of thermal expansion is 10-5/°C and E = 100 GN/m2. If the rod is free to expand, the thermal stress developed in it is..
The 40mm diameter steel rod AB shown in Figure 2 is resting on frictionless rollers between two steel plates. End A is just touching the left hand steel plate. 2. Steel plate Steel plate A В 1500mm 1mm Figure 2 There is a gap of 1mm between the end B and the right hand side steel plate. The temperature of the rod increases by an amount AT and this increase in temperature causes the two ends of the rod to press against the steel plates. This action causes the right hand steel plate to move to the right by 0.5mm while the left hand plate does not move. The Young's modulus value for steel is 210,000N/mm?. Taking any assumptions that you deem necessary calculate the increase in temperature AT required to cause the rod to buckle.
The aluminum cube (600x600x600 mm) is put inside a hole of a rigid boundary as shown below. Initially, there is a gap of 0.2 mm between the cube and the rigid boundary. Determine the new dimensions of the cube if a stress of 100 MPa is applied on the top face of the cube and the temperature of the cube increased by 35°C. For aluminum: Ea=73 GPa, va-0.35, aai = 23*10C y. o=100 MPa Rigid boundary Rigid boundary Aluminum cube 600 mm- 0.2 mm
(b) If a steel shaft of diameter 50 mm is subjected to cooling within the steel of 80 °C, determine the diameter of hole that the shaft can be inserted into. Take the coefficient of linear expansion of steel to be 15 x 10-6 K-1.
At a temperature of 21.4°C the hole in a steel plate has an area of 8.80 x 10- m2. You heat the plate until the area of the hole increases to 8.97 x 10- m2, which allows a steel rod to just slip through this hole. What is the final temperature of the plate? The coefficient of linear expansion of steel is 12 × 10-0/°C.
A copper rod with 0.15 cm diameter is enclosed by a steel tube that has an outside diameter of 0.3 cm and an internal diameter of 0.2 cm. The assembly is fixed at each end. Determine the stresses in the rod and tube if the temperature is at 220oC; at 10oC, there is no longitudinal stress. Based on laboratory results for steel, E = 2.1 x 105 N/mm2, a = 11x10-6/oC, and for copper, E = 1 x 105 N/mm2, a = 18x10-6/oC
2. The bar has a cross-sectional area A, length L, modulus of elasticity E, and coefficient of thermal expansion a. The temperature of the bar changes uniformly along its length from TA at A to TB at B so that at any point x along the bar T = TA + x(TB – TA)/L. Determine the force the bar exerts on the rigid walls. Initially no axial force is in the bar and the bar has a temperature of TA. A B TA TB
2. At a temperature of 80°C, a steel tire 12 mm thick and 90 mm wide that is to be shrunk onto a locomotive driving wheel 2 m in diameter just fits over the wheel, which is at a temperature of 25°C. Determine the contact pressure between the tire and wheel after the assembly cools to 25°C. Neglect the deformation of the wheel caused by the pressure of the tire. Assume a = 11.7 µm/(m°C) and E = 200 GPa. anin
Circumferential and longitudinal strains in the cylindrical boiler under internal steam pressure are ɛ, and ɛ, respectively. Change in the volume of the boiler cylinder per unit volume will be