The 45° strain rosette shown in figure below is mounted on the surface of a thin shell. Thefollowing readings are obtained for each gage: ea, eb, and ec.Note that Be is negative.Determine:• Shear strain yxy• Principal strains e1 and e2· The rotation angle (magnitude and direction) from x-axis to reach the principalorientation.Indicate direction as clockwise or counter-clockwise.epsilon a = 4.50E-04epsilon k= 2.00E-04epsilons = -1.00E-04%3Dyаb45°45°

The 45° strain rosette shown in figure below is mounted on the surface of a thin shell. The following readings are obtained for each gage: ea, eb, and eC .Note that Be is negative. Determine: • Shear strain yxy · Principal strains el and e2 · The rotation angle (magnitude and direction) from x-axis to reach the principal orientation. Indicate direction as clockwise or counter-clockwise. epsilon a = 4.50E-04 epsilon b = 2.00E-04 epsilon c = -1.00E-04

The 45° strain rosette shown in figure below is mounted on the surface of a thin shell. The following readings are obtained for each gage: ea, eb, and eC .Note that Be is negative. Determine: • Shear strain yxy · Principal strains el and e2 · The rotation angle (magnitude and direction) from x-axis to reach the principal orientation. Indicate direction as clockwise or counter-clockwise. epsilon a = 4.50E-04 epsilon b = 2.00E-04 epsilon c = -1.00E-04

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 7.7.20P: A strain rosette (see figure) mounted on the surface of an automobile frame gives the following...

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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.
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.
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.
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A solid spherical ball of magnesium alloy (E = 6.5 × l0-6 psi, v = 0.35) is lowered into the ocean to a depth of 8000 ft. The diameter of the ball is 9.0 in. (a) Determine the decrease ?d in diameter, the decrease, ?V in volume, and the strain energy U of the ball. (b) At what depth will the volume change be equal to 0.0324% of the original volume?
1 A rectangular steel plate with thickness t = 5/8 in. is subjected to uniform normal stresses a and ., as shown in the figure. Strain gages A and B. oriented in the x and v directions. respectively, arc attached to the plate. The gage readings give normal strains = 0.00065 (elongation) and £. = 0.00040 (elongation). Knowing that E = 30 X 106 psi and v = 0.3, determine the stresses c7 and a, and the change .11 in the thickness of the plate.
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On the surface of a structural component in a space vehicle, the strains arc monitored by means of three strain gages arranged as shown in the figure. During a certain maneuver, the following strains were recorded: e, = 1100 X l0_6, 6h = 200 X lO_6, and e = 200 X 10-6. Determine the principal strains and principal stresses in the material. which is a magnesium alloy for which E = 6000 ksi and v = 0.35. Show the princ ipal strains and principal stresses on sketches of properly oriented elements.
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