A torque of magnitude T = 12 kNm is applied to the end of a tank containing compressed airunder a pressure of 8 MPa (Figure Q1). The tank has a 180 mm inner diameter and a 12 mmwall thickness. As a result of several tensile tests, it has been found that tensile yeild strengthis σy = 250 MPa for thr grade of steel used. Determine the factor of safety with respect to yeild,using:(a) The maximum shearing stress theory(b) The maximum distortion energy theoryTFigure Q1

Answered: A torque of magnitude T = 12 kNm is…

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter2: Axially Loaded Members

Section: Chapter Questions

Problem 2.3.19P: Repeat Problem 2.3-18, but assume that the bar is made of copper alloy. Calculate the displacements...

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Solve the preceding problem if the internal pressure is 3,85 MPa, the diameter is 20 m, the yield stress is 590 MPa, and the factor of safety is 3.0. (a) Determine the required thickness to the nearest millimeter. (b) If the tank wall thickness is 85 mm, what is the maximum permissible internal pressure?
Two sections of steel drill pipe, joined by bolted flange plates at Ä are being tested to assess the adequacy of both the pipes. In the test, the pipe structure is fixed at A, a concentrated torque of 500 kN - m is applied at x = 0.5 m, and uniformly distributed torque intensity t1= 250 kN m/m is applied on pipe BC. Both pipes have the same inner diameter = 200 mm. Pipe AB has thickness tAB=15 mm, while pipe BC has thickness TBC= 12 mm. Find the maximum shear stress and maximum twist of the pipe and their locations along the pipe. Assume G = 75 GPa.
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
Three round, copper alloy bars having the same length L but different shapes are shown, in the figure. The first bar has a diameter d over its entire length, the second has a diameter d over one-fifth of its length, and the third has a diameter d over one-fifteenth of its length. Elsewhere, the second and third bars have a diameter Id. All three bars are subjected to the same axial load P. Use the following numerical data: P = 1400 kN, L = 5m,d= 80 mm, E= 110 GPa. and v = 0.33. (a) Find the change in length of each bar. (b) Find the change in volume of each bar.
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?
A safety valve on the top of a tank containing steam under pressure p has a discharge hole of diameter d(see figure). The valve is designed to release the steam when the pressure reaches the value Pmax If the natural length of the spring, is L and its stiffness is k, what should be the dimension ft of the valve? (Express your result as a formula for h.)
The strength-to-weight ratio of a structural material is defined as its load-carrying capacity divided by its weight. For materials in tension, use a characteristic tensile stress obtained from a stress-strain curve as a measure of strength. For instance, either the yield stress or the ultimate stress could be used, depending upon the particular application. Thus, the strength-to-weight ratio RS/Wfor a material in tension is defined as Rs/w= in which a is the characteristic stress and 7 is the weight density. Note that the ratio has units of length. Using the ultimate stress Uas the strength parameter, calculate the strength-to-weight ratio (in units of meters) for each of the following materials: aluminum alloy 606I-T6, Douglas fir (in bending}, nylon. structural steel ASTM-A57.2, and a titanium alloy. Obtain the material properties from Tables [-1 and 1-3 of Appendix I. When a range of values is given in a table, use the average value.
Given: A part is made of ductile material and subjected to principal stresses o1, 02, 03. It is statically loaded. Find: Determine the factor of safety for the part. Use the following parameters in your analysis: ơ1 40 kpsi, Sut = 90 kpsi, Suc = 20 kpsi, 02 = 5 kpsi, oz = -10 kpsi, Sy = %3D = –130 kpsi
Example 31: A thin cylinder 75 mm internal diameter, 250 mm long with walls 2.5 mm thick is subjected to an internal pressure of 7 MN/m Determine the change in internal diameter and the change in length, If in addition to the infernal pressure, the cylinder is subjected to a torque of 200 N.m find the magnitude and nafure of the stresses set up in the cylinder.E=200 GN/m², v=0.3. d-7s mm T-200 N-m
(d) Define Modulus of Resilience 2. Draw the stress-strain diagram for a typical ductile material and locate the salient points onit 3. A bar of 25 mm diameter is tested in tension. It is observed that when a load of 60 kN is applied, the measured over a gauge length of 200 mm is 0.12 mm and contraction in diameter is 0.0045 mm. Find Poissa 4. A circular rod of diameter 16 mm and 500 mm long is subjected to a tensile force 40 kN. The modulus of e steel may be taken as 200 kN/mm?. Find the elongation and strainin the bar due to applied load. 5. Define (a) Resilience (b) Proof resilience PART -B structions: Part B consists of 3 Units. Answer any one full question from each unit. Each questioncarries 8 marks and may have su 1. A steel circular bar has three segments as shown in the fig. Determine the total elongation ofthe bar. Take E = 210 GPa. 300 kNI 330 kN 30 mm 50KN 15 mm 20 mm 80 kN A + 150 mm 200 mm 250 mm B. D (OR)
A closely coiled helical spring is to carry a load of 500N. Its mean coil diameter is to be 10 times that of the wire diameter. Calculate these diameters if the maximum shear stress in the material of the string is to be BOMN/m*2.

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