pleas QUESTION 4.If lengths of rail track are laid down in cold weather, they may deform asthey expand when the weather becomes warmer. Therefore, when railsare laid in cold weather they are stretched and fixed into place while stillstretched. This is called pre-straining.The following data is typical for a length of steel rail:Young modulus of steel =2.0 x 101 PaCross sectional area of a length of rail =7.5 x 10-3 m2Amount of pre-strain =rise in temperature the rail is expected to experience.2.5 x 10-5 for each kelvinA steel rail is laid when the temperature is 8 °C and the engineerdecides to use a pre-strain of 3.0 x 104.(a) Calculate the tensile force required to produce the pre-strain inthe rail required by the engineer.(b) Calculate the elastic strain energy stored in a rail of unstressedlength 45 m when pre-strained as in part (a)(c)Calculate the temperature at which the steel rail becomesunstressed.(d) Explain why the engineer does not use the highest observedtemperature at the location of the railway track to determine theamount of pre-strain to use.

Answered: Image /qna-images/answer/4acbf4aa-cfeb-4039-9288-bc5afa0c0c42.jpg

If lengths of rail track are laid down in cold weather, they may deform as they expand when the weather becomes warmer. Therefore, when rails are laid in cold weather they are stretched and fixed into place while still stretched. This is called pre-straining. The following data is typical for a length of steel rail: Young modulus of steel = 2.0 x 1011 Pa Cross sectional area of a length of rail = 7.5 x 10-3 m2 2.5 x 10-5 for each kelvin Amount of pre-strain = rise in temperature the rail is expected to experience. A steel rail is laid when the temperature is 8 °C and the engineer decides to use a pre-strain of 3.0 x 10-4. (a) Calculate the tensile force required to produce the pre-strain in the rail required by the engineer. (b) Calculate the elastic strain energy stored in a rail of unstressed length 45 m when pre-strained as in part (a) (c) Calculate the temperature at which the steel rail becomes unstressed.

If lengths of rail track are laid down in cold weather, they may deform as they expand when the weather becomes warmer. Therefore, when rails are laid in cold weather they are stretched and fixed into place while still stretched. This is called pre-straining. The following data is typical for a length of steel rail: Young modulus of steel = 2.0 x 1011 Pa Cross sectional area of a length of rail = 7.5 x 10-3 m2 2.5 x 10-5 for each kelvin Amount of pre-strain = rise in temperature the rail is expected to experience. A steel rail is laid when the temperature is 8 °C and the engineer decides to use a pre-strain of 3.0 x 10-4. (a) Calculate the tensile force required to produce the pre-strain in the rail required by the engineer. (b) Calculate the elastic strain energy stored in a rail of unstressed length 45 m when pre-strained as in part (a) (c) Calculate the temperature at which the steel rail becomes unstressed.

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter1: Tension, Compression, And Shear

Section: Chapter Questions

Problem 1.6.7P: A wine of length L = 4 ft and diameter d = 0.125 in. is stretched by tensile forces P = 600 lb. The...

See similar textbooks

Similar questions

A wine of length L = 4 ft and diameter d = 0.125 in. is stretched by tensile forces P = 600 lb. The wire is made of a copper alloy having a stress-strain relationship that may be described mathematically by =18,0001+30000.03(=ksi) in which is nondimensional and has units of kips per square inch (ksi). (a) Construct a stress-strain diagram for the material. (bj Determine the elongation, of the wire due to the Forces P. (c) IF the forces are removed, what is the permanent set of the bar? (d) If the forces are applied again, what is the proportional limit?
Two steel wines support a moveable overhead camera weighing W = 28 lb (see figure part a) used For close-up to viewing of field action at sporting, events. At some instant, wire I is at an angle a = 22° to the horizontal and wire 2 is at angle fi = 40°. Wires I and 2 have diameters of 30and 35 mils, respectively. (Wire diameters are often expressed in mils; one mil equals 0.001 in.) (a) Determine the tensile stresses s and s2 in the two wires. (b) If the stresses in wires 1 and 2 must be the same, what is the required diameter of wire 1 ? (c) To stabilize the camera for windy outdoor conditions, a third wire is added (see figure part b). Assume the three wires meet at a common point coordinates (0, 0. 0) above the camera at the instant shown in figure part b. Wire I is attached to a support at coordinates (75 ft, 48 ft, 70 Ft). Wire 2 is supported at (-70 ft. 55 ft, 80 Ft). Wire 3 is supported at (-10 ft. -85 Ft, 75 ft). Assume that all three wires have a diameter of 30 mils. Find the tensile stresses in all three wires
A high-strength steel bar used in a large crane has a diameter d = 2.00 in. (sec figure). The steel has a modulus of elasticity E = 29 × 10 psi and Poisson’s ratio is v = 0.29. Because of clearance requirements, the diameter of the bar is limited to 2.001 in. when it is compressed by axial forces. What is the largest compressive load Pmaxthat is permitted?
Determine the strain energy per unit volume (units of psi) and the strain energy per unit weight (units of in ) that can be stored in each or the materials listed in the accompanying table, assuming that the material is stressed to the proportional limit. DATA FOR PROBLEM 2.7-5 Material Weight Density (lb/in3) Modulus of Elasticity (ksi) Proportional Limit (psi) Mild sleel 0.284 30,000 36,000 Tool steel 0.284 30,000 75,000 Aluminum 0.0984 10,500 60,000 Rubber (soft) 0.0405 0.300 300
An aluminum bar has length L = 6 ft and diameter d = 1.375 in. The stress-strain curse for the aluminum is shown in Fig. 1.34. The initial straight, line part of the curve has a slope (modulus of elasticity) of 10.6 × 106 psi. The bar is loaded by tensile forces P = 44.6 k and then unloaded. (a) That is the permanent set of the bar? (b) If the bar is reloaded. what is the proportional limit? hint: Use the concepts illustrated in Figs. l.39b and 1.40.
(a) Solve part (a) of the preceding problem if the pressure is 8.5 psi, the diameter is 10 in., the wall thickness is 0,05 in., the modulus of elasticity is 200 psi, and Poisson's ratio is 0.48. (b) If the strain must be limited to 1.01, find the maximum acceptable inflation pressure
Rigid bar ACB is supported by an elastic circular strut DC having an outer diameter of 15 in. and inner diameter of 14.4 in. The strut is made of steel with a modulus elasticity of E = 29,000 ksi. Point load P = 5 kips is applied at B. Calculate the change in length of the circular strut DC. What is the vertical displacement of the rigid bar at point B?
A joint between two glass plates A and B is filled with a flexible epoxy that bonds securely to the glass. The height of the joint is/p = 0.5 in, its length is L = 30 in, and its thickness is/ = 0.5 in. Shear force of I' = 25 kips is applied to the joint. Calculate the displacement of the joint if the shear modulus of elasticity G of the epoxy is 100 ksi. Calculate the average shear strain in the epoxy.
A spherical steel pressure vessel (diameter 500 mm, thickness 10 mm) is coated with brittle lacquer that cracks when the strain reaches 150 X 10~ (see figure). (a) What internal pressure p will cause the lacquer to develop cracks? (Assume E = 205 GPa and v = 0.30.) (b) If the strain is measured at 125 x 10-6, what is the internal pressure at that point?
You are given a square rod of 6061-T6 aluminum (cross-section = 4mm X 4mm, length = 2.3m). The material has a Young’s modulus of 72 GPa. If a tensile load of 3 kN is applied parallel to the 2.3m dimension, what is the change in length of the rod?
Experiments were conducted in a tension testing machine to evaluate the material properties of two metallic rods both having diameter equal to 10 mm. First rod having modulus of rigidity of the material equal to 400 tonnes/cm2 when subjected to an axial tensile force of 6 kN, the change in its diameter was observed to be 0.0018 cm. The value for the bulk modulus of the second metallic rod is same as that of the first one but modulus of elasticity 18% more. Based on the material properties calculate and compare the values of different moduli as well as Poisson’s ratio for both metallic rods. Justify your answer with reasons.
A tensile force of 100 kN is applied on a 0.02-m diameter and 2-m long rod. After applying the load, the diameter of the rod decreases to 0.01998 m and the length increases to2.01 m. The true axialstrain is?