4-47 The stresses shown in Fig. P4-47a act at a point on the free surface of a steel (E = 30,000 ksi and v=0.30) machine com- ponent. Determine the normal strains Ea, Eb, and Ec that would be indicated by the strain rosette shown in Fig. P4-47b. 4 ksi T (a) Figure P4-47 6 ksi 12 ksi Gage c Gage b 120° (b) Gage a

4-47 The stresses shown in Fig. P4-47a act at a point on the free surface of a steel (E = 30,000 ksi and v=0.30) machine com- ponent. Determine the normal strains Ea, Eb, and Ec that would be indicated by the strain rosette shown in Fig. P4-47b. 4 ksi T (a) Figure P4-47 6 ksi 12 ksi Gage c Gage b 120° (b) Gage a

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 7.4.21P: -18 through 7.4-25 An clement in plane stress is subjected to stresses a,, ay., and axy. (see...

See similar textbooks

Similar questions

An clement of material in plane strain (see figure) is subjected to strains ex= 480 × 10-6, Ey= 70 × l0-6, and yxy= 420 × l0-6. Determine the following quantities: (a) the strains for an element oriented at an angle 0 = 75°, (b) the principal strains, and (c) the maximum shear strains. Show the results on sketches of properly oriented elements.
A solid aluminum bar (G = 27 GPa ) of diameter d = 40 mm is subjected to torques T = 300 N - m acting in the directions shown in the figure, Determine the maximum shear, tensile, and compressive stresses in the bar and show these stresses on sketches of properly oriented stress elements. Determine the corresponding maximum strains (shear, tensile, and compressive) in the bar and show these strains on sketches of the deformed elements.
The strains for an element of material in plane strain (see figure) are as follows: x = 480 ×10-6. y = 140 × l0-6, and xy = —350 x 10”. Determine the principals strains and maximum shear strains, and show these strains on sketches of properly oriented elements.
An element in plane stress is subjected to stresses ?? = -8400 psi, ??y = 1100 psi, and (see figure). The material is aluminum with modulus of elasticity E = 10,000 ksi and Poisson’s ratio v = 0.33. Determine the following quantities: (a) the strains for an element oriented at an angle 0 = 30°, (b) the principal strains, and (C) the maximum shear strains. Show the results on sketches of properly oriented elements.
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?
Solve the preceding problem if the cross- sectional dimensions are b = 1.5 in. and h = 5.0 in., the gage angle is ß = 750, the measured strains are = 209 × 10-6 and B = -110 × 10, and the material is a magnesium alloy with modulus E = 6.0 X 106 psi and Poisson’s ratio v = 0.35.
During a test of an airplane wing, the strain gage readings from a 45° rosette (see figure) are as follows: gage A, 520 × l0-6; gage B. 360 × l0-6; and gage C,-80 × 10-6. Determine the principal strains and maximum shear strains, and show them on sketches of properly oriented elements.
-11 A solid steel bar (G = 11.8 X 106 psi ) of diameter d = 2,0 in. is subjected to torques T = 8.0 kip-in. acting in the directions shown in the figure. Determine the maximum shear, tensile, and compressive stresses in the bar and show these stresses on sketches of properly oriented stress elements. Determine the corresponding maximum strains (shear, tensile, and compressive) in the bar and show these strains on sketches of the deformed elements.
An element in pure shear is subjected to stresses ??xy= 3750 psi, as shown in the figure. Using Mohr’s circle, determine the following: (a) The stresses acting on an clement oriented at a slope of 3 on 4 (sec figure). (b) The principal stresses. Show all results on sketches of properly oriented elements.
.4-2 An element in uniaxial stress is subjected to tensile stresses sx= 57 MPa. as shown in the figure. Using Mohr’s circle, determine the following. (a) The stresses acting on an clement oriented at an angle 0 = 33° from the x axis (minus means clockwise). (b) The maximum shear stresses and associated normal stresses. Show all results on sketches of properly oriented elements.
The normal strain in the 45n direction on the surface of a circular tube (sec figure) is 880 × 10 when the torque T = 750 lb-in. The tube is made of copper alloy with G = 6.2 × 106 psi and y = 0.35. If the outside diameter d2of the tube is 0.8 in., what is the inside diameter dt? If the allowable normal stress in the tube is 14 ksi, what is the maximum permissible inside diameter d?
An element of material in plain strain is subjected to strains x = 0.0015, , y . = -0.0002, and xy = 0.0003. (a) Determine the strains for an element oriented at an angle = 20°. (b) Determine the principal strains of the element. Confirm the solution using Mohr’s circle for plane strain.